The Fahrenheit and Kelvin scales of temperature will give the same reading at
A liquid whose coefficient of volume expansion is γ r , completely fills a sealed metal tank, at negligible pressure. The coefficient of linear expansion of the metal is α and the compressibility of the liquid is k. If the temperature of the system is increased by t. The pressure of the liquid will be
The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are 2 δ a n d δ respectively. If coefficient of linear expansion of vessel A is α , the coefficient of linear expansion of vessel B is
In a vertical U tube containing a liquid, the two arms are maintained at different temperatures T 1 and T 2 . The liquid columns in the two arms have heights h 1 and h 2 respectively. The coefficient of volume expansion of the liquid is equal to
Two rods of lengths L 1 and L 2 are made of materials whose coefficient of linear expansion are α 1 and α 2 . If the difference between the two lengths is independent of temperature :
Oxygen boils at -183°C. This temperature is approximately:
For measurements of very high temperature say around 5000°C (of sun), one can use:
For a constant volume gas thermometer select the correct statement.
Assertion (A): At constant pressure when a gas is heated from 40 to 41°C, the increase in volumes is 1/273 of its initial volume at 273 K Reason (R): Volume coefficient of gas is 1/273 /°C
The coefficient of linear expansion of a metal is 1×10 -5 /°C. The percentage increase in area of a square plate of that metal when it is heated through 100°C is
What is the temperature on Fahrenheit scale corresponding to 30°C
The normal boiling point of liquid hydrogen is -253°C . What is the corresponding temperature on absolute scale
The diameter of iron wheel is 1cm. If its temperature is increased by 700°C What is the increase in circumference of the wheel? α = 12 × 10 − 6 / 0 C
What will be the ratio of increase in the volume of two uniform copper rods of length and radii in ratio 1: 2 and 2: 1 respectively which are heated to same temperature
The gas thermometers are more sensitive than liquid thermometers because
Which of the following is the smallest temperature?
When a strip made of iron ( α 1 ) and copper α 2 ( > α 1 ) is heated:
A long narrow uniform glass tube is closed at one end and contains a gas trapped by a mercury thread of length h. When this tube is held vertical with open end up, the length of the gas column is L. When the tube is turned upside down, the length of the gas column is doubled. If the pressure of atmosphere is 75 cm of Hg, the value of h in cm is
An iron tyre is to be fitted onto a wooden wheel 1.0 metre in diameter. The diameter of the time is 6 mm smaller than of the wheel. The tyre should be heated so that its temperature increases by a minimum of (coefficient of volume expansion of iron is 3 .6 x 10 -5 per degree C)
The density of water at 20 ° C is 998 kg / m 3 and 40 ° C 992 k g / m 3 . The coefficient of volume expansion of water is
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is ( α Cu = 1 . 7 × 10 – 5 K – 1 and α AI = 2 . 2 × 10 – 5 K – 1 )
Celsius is the unit of :
On the Celsius scale the absolute zero of temperature is at:
The scale of temperature on which the temperature are only positive is
Triple point temperature of water is :
Recently, the phenomenon of superconductivity has been observed at 95 K. This temperature is nearly equal to
An iron tyre is to be fitted onto a wooden wheel 1.0 m in diameter. The diameter of the tyre is 6 mm smaller than that of the wheel. The tyre should be heated so that its temperature increases by a minimum of ( coefficient of volume expansion of iron is 3.6 x 10 -5 /C 0 ).
A composite bar of length L = L 1 + L 2 , is made up from a rod of material I and of length L 1 attached to a rod of material 2 and of length L 2 as shown. If α 1 and α 2 are their respeclive coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is:
The coefficient of volume expansion of glycerine is 49 x 10 – 5 / 0 C . What is the fractional change in its density (approx.) for 30°C rise in temperature?
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C and α Cu = 1 . 7 × 10 – 5 / 0 C bulk modulus for copper B Cu = 140 x 10 9 N / m 2
A pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is 5 seconds fast each day at a temperature of l5°C and l0 seconds slow at a temperature of 30°C. The temperature at which it is designed to given correct time, is
A steel scale measures the length of a copper wire as 80.0 cm when both are at 20°C (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at 40°C? (Given α steel = 11 × 10 – 6 per ° C and α copper = 17 × 10 – 6 per 0 C )
Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be ( α 1 , α 2 = linear expansion coefficient A 1 , A 2 = Area of rods Y 1 , Y 2 = Young modulus)
Why is mercury used in thermometers?
Assertion (A): Gases are characterised with two coefficients of expansion Reason (R): When heated both volume and pressure increase with the rise in temperature.
A brass sheet is 25 cm long and 8 cm breadth at 0°C. Its area at 100°C is α = 18 × 10 − 6 / 0 C
A clock with an iron pendulum keeps correct time at 15°C. If the room temperature rises to 20°C, the error in seconds per day will be (coefficient of linear expansion for iron is 0.000012/°C)
When a thin rod of length ‘ l ’ is heated from t 1 0 C to t 0 2 C length increases by 1%. If plate of length 2l and breadth ‘l ’ made of same material is heated form t 1 0 C to t 0 2 C , percentage increase in area is
Two rods of different materials having coefficients of thermal expansion α 1 , α 2 and young’s modulus Y 1 , Y 2 respectively are fixed between two rigid walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α 1 : α 2 =2:3, thermal stress developed in the rods are equal provided Y 1 : Y 2 is equal to
There is some change in length when a 33000 N tensile force is applied on a steel rod of area of cross-section 10 -3 m 2 . The change of temperature required to produce the same elongation of the steel rod when heated is Y = 3 × 10 11 N / m 2 , α = 1.1 × 10 − 5 / 0 C
A thin copper wire of length L increases in length by one percent when heated from t 1 °C and t 2 °C. The percentage change in area when a thin copper plate having dimension 2L × L is heated from t 1 °C to t 2 °C is
Two marks on a glass rod 10cm apart are found to increase their distance by 0.06mm when the rod is heated from 0°C to 10°C. A flask made of the same glass as that rod measures a volume of 1000 c.c at 0°C. The volume it measures at 100°C in c.c. is
A pendulum clock runs fast by 5 seconds per day at 200c and goes slow by 10 seconds per day at 35°C. It shows correct time at a temperature of
A wire of length L 0 is supplied heat to raise its temperature by T. if g is the coefficient of volume expansion of the wire and Y is Young’s modulus of the wire then the energy density stored in the wire is
Calculate the compressional force required to prevent the metallic rod of length l cm and cross-sectional area A cm 2 when heated through t°C, from expanding along length wise. The Young’s modulus of elasticity of the metal is E and mean coefficient of linear expansion is a per degree Celsius
Distance between two places is 200 km. α of steel 12 × 10 − 6 / o C . Total space that must be left between steel rails to allow for a change of temperature from 90 ° C to is 100 ° C
The diameter of a metal ring is D and coefficient of linear expansion is α . If the temperature of the ring is increases by 1°C , the circumference of the ring will increases by
Two thin metal strips each of 2mm thick, one of brass and the other of iron are fastened together parallel to each other, to form a bimetallic strip. If the strips are of equal length at 0°c . The radius of the arc formed by the bimetallic strip when heated to C is (Coefficient of linear expansion of brass = 19 × 10 − 6 / ∘ C and of iron = 12 × 10 − 6 / ∘ C )
Two temperature scales A and B are related by A − 42 100 = B − 72 220 .At which temperature two scales have the same reading?
Two rods of lengths l 1 a n d l 2 are made of materials whose coefficients of linear expansion are α 1 a n d α 2 respectively. If the difference between the two lengths is independent of temperature, then
If a graph is plotted taking the temperature in Fahrenheit along the Y-axis and the corresponding temperature in Celsius along the x-axis, it will be a straight line
The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = a T , where a is a positive constant and T in 0 C . If the length of the rod is l at temperature 0 0 C , then the temperature at which the length will be 2 l is
A centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers 140 0 F . What is the temperature as registered by the centigrade thermometer?
A metallic solid sphere is rotating about its diameter. If the temperature is increased by 20 0 C , the percentage increase in its moment of inertia is(coefficient of linear expansion of metal = 10 − 5 per 0 C )
If the length of a cylinder on heating increases by 2%, the area of its base will increase by :
A uniform solid sphere of copper is rotating about a diameter with an angular speed ω . Its temperature is increased by 80°C. α Cu being the coefficient of linear expansion of Cu,new angular speed of the sphere will be :
A metal wire of length l and radius r is fixed between rigid supports. Initially it is just taut. Now, due to decrease in temperature, the tension developed in the wire
Three rods of equal length are joined to form an equilateral triangle ABC. D is midpoint of AB. Coefficient of linear expansion of AB is α 1 and α 2 for AC and BC. If distance DC remains constant for small changes is temperature, then
A vessel contains a liquid filled with 1/5 th of its volume. Another vessel contains same liquid up to 1/4 th of its volume. In both cases, the volume of empty space remains constant at all temperatures. Then ratio of coefficient of linear expansions of two vessels is
Density of a liquid at 0 ∘ C is 10.01 g/cc and at 100 ∘ C is 10g/cc. Coefficient of real expansion of that liquid is
Volume of mercury in the bulb of a thermometer is 10 − 6 m 3 . Area Of cross section of capillary tube is 2 × 10 − 7 m 2 ⋅ γ Hg = 18 × 10 − 5 / ∘ C , If temperature is raised by 100 ∘ C , length of mercury column raised in to the tube is (neglect expansion of glass)
Two beakers A and B of negligible coefficient of expansion are filled with water at 4 ∘ C . Beaker ‘A’ is heated and beaker ‘B’ is cooled. Then
A clock has a long pendulum made of brass. Due to a temperature change of 20 ° C the time period of oscillation of the pendulum is found to change by 0.02 %. The coefficient of linear expansion of brass is
Between 273 K and 277 K the coefficient of cubical expansion of water is
The numerical value of coefficient of linear expansion is independent of units of a) length b) temperature c) area d) mass
The gas constant for a molecule is (terms have usual meaning) a) K b) R/N c) R/NT d) R/m
Two metal rods A and B have lengths L 1 and L 2 and same radius. The coefficients of linear expansions of the materials of A and B are α 1 and α 2 respectively. If the two rods are joined to form a longer rod of length L 1 + L 2 , the equivalent coefficient of linear expansion of the composite rod will be
Two identical vessels each of volume V contain identical samples of ideal gas. The pressure and temperature in each are P and 2T respectively. Now they are joined by a very narrow pipe and one of them is cooled to a temperature T and the other one is heated to a temperature 3T. The common pressure of the system now is
An ideal gas has pressure P at absolute temperature T. Its pressure is increased by ΔP due to an increase in temperature ΔT . If the volume of the gas remains constant, the fractional change in pressure per unit rise in temperature ( ΔP / P ) / ΔT is proportional to
As the temperature is increased, the period of a pendulum [NCERT Exemplar]
The coefficient of cubical expansion of mercury is 0.00018/°C and that of brass 0.00006 /°C. If a barometer having a brass scale were to read 74.5 cm at 30°C, find the true barometric height at 0°C. The scale is supposed to be correct at 15°C.
Three rods of equal length l are joined to form an equilateral triangle PQR. O is the mid-point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same, i.e. α 2 but that for PQ is α 1 . Then,
Half a mole of helium at 27 0 C and at a pressure of 2 atmosphere is mixed with 1.5 mole of N 2 at 77 0 C and at a pressure of 5 atmosphere so that the volume of the mixture is equal to the sum of their initial volumes. If the temperature of the mixture is 69 0 C, its pressure in atmosphere is
In a faulty thermometer freezing point is marked as – 20 o and boiling point is 130 o . A temperature of human body 34 o C on this thermometer will be read as
Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point ‘A’ is d 0 . Density at point ‘B’ will be
A 2 litre glass flask contains some mercury. It is found that at all temperatures, the volume of air inside the flask, remains the same. The volume of mercury inside the flask is α for glass = 9 × 10 − 6 / 0 C , and for mercury = 1 .8 × 10 − 4 / 0 C )
Substance having very small co-efficient of linear expansion, among the following is
Two Brass rods of same length but with different diameters are heated by equal amounts of heat. The expansion is
Substance which contracts on heating, among the following is a) Invar b) Brass c) Silver Iodide d) Type metal
Two metal strips that constitute a thermostat must necessarly differ in their
Thermostat works on the principle of
By what temperature a rod should be heated so that its length becomes 2l o if its initial length is l 0 . Coefficient of linear expansion is α in that temperature range
A solid body is in the form of a cube of side A cm at —10°C. When it is heated through a small temperature difference of t°C, its volume increases by B cc. When it is completely converted into liquid at 0°C, its coefficient of volume expansion becomes ‘n’ times that of the substance in solid form. The fractional change in density of the liquid when heated through a temperature difference of t°C from 0°C is
The moment of inertia of a disc pivoted at its centre about the axis AB as shown is I. If the temperature of the disc increases by ΔT, then moment of inertia about AB increases by (I C = Moment of inertia about a diameter )
A body suspended from a spring balance is immersed in water. If the coefficient of cubical expanison of water is twice that of the suspended body, then on heating the liquid, which one of the following would occur ?
A block is hanged by means of two identical wires having cross section area 1mm 2 as shown. If the temperature is lowered by ΔT = 10°C, find the mass to be added to hanging mass such that the junction remains at its initial position (α = 2×10 -5 /°C, Y = 5 × 10 11 Pa, g = 10m/s²)
A steel rod of cross sectional area 4 c m 2 and length 1 m is heated so that its temperature is increased by 10 o C . What longitudinal compressive force is to be applied on both ends of the steel rod so that it regains its original length? Given that α s = 11 × 10 − 6 / o C a n d Y S = 20 × 10 10 N / m 2
When a copper ball is heated, the largest percentage increase will occur in its
The density of a substance at 0 0 C is 10g/cc and at 100 0 c in its density is 9.7 g/cc. The coefficient of linear expansion of the substance is
What should be the lengths of a copper rod and a brass rod be at 0 ο C , so that the difference in the lengths of the copper and brass rods remains 10 cm at all temperatures? Given α b = 1.8 × 10 − 5 / K and α c = 1.6 × 10 − 5 / K .
Two rods, one of aluminium and the other made of steel, having initial lengths l 1 and l 2 are connected together to form a single rod of length l 1 + l 2 .The coefficient of linear expansion for aluminium and steel are α a and α s respectively. If the length of each rod increases by the same amount when their temperature are raised by t° C, then find the ratio l 1 l 1 + l 2
No other thermometer is as suitable as platinum resistance thermometer to measure temperature in the entire range of:
Gas thermometers are more sensitive than liquid thermometers because
Pyrometer is an instrument used to measure:
The freezing point on a thermometer is marked as 20° and the boiling point as 150° . A temperature of 60°C on this thermometer will be read as :
When water is heated from 0°C to 10°C, its volume :
A metal wire of length l and radius r is fixed between rigid supports. Initially it is just taut. Now, due to decrease in temperature, the tension developed in the wire
A glass bottle of volume 100 cc at 0°C is filled with paraffin at 20°C. If the density of paraffin at 0°C is 0.8 g/cc, γ paraffin = 10 x 10 -4 /°C and the coefficient of linear expansion of glass is 10 x 10 -6 /°C, the mass of paraffin is
A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are α C and α B . On heating, the temperature of the strip goes up by ∆ T and the strip bends to form an arc of radius of curvature R. Then R is : (i) proportional to ∆ T (ii) inversely proportional to ∆ T (iii) proportional to α B – α C (iv) inversely proportional to α B – α C
A steel tape I m long is correctly calibrated for a temperature of 27.0°C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45°C. Coefficient of linear expansion of steel = 1.20 x 10 – 5 /K. What is the actual length of the steel rod on that day?
A copper and a tungsten plate having a thickness d each are riveted together so that at 0 0 C they form a flat bimetallic plate. Find the average radius of the curvature of this plate at temperature T. The coefficient of linear expansion for Copper and tungsten are α Cu and α w .
The coefficient of linear expansion of crystal in one direction is α 1 and that in every direction perpendicular to it is α 2 . The coefficient of cubical expansion is
When a bimetallic strip is heated, it
In figure which strip brass or steel have higher coefficient of linear expansion.
On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39°W and 239°W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39°C on the Celsius scale?
The water surface in a lake is just going to freeze. What is the temperature of water at the bottom ?
A brass sphere is heated to give it a small increase of temperature. Percentage change will be maximum in its :
A copper disc with a central hole is heated. The diameter of the hole:
A uniform metal rod (fixed at both ends) of 2 mm 2 crosssection is cooled from 40° C to 20° C. The co-efficient of the linear expansion of the rod is 12 x 10 – 6 per degree and its young modulus of elasticity is 10 11 N / m 2 . The energy stored per unit volume of the rod is:
A uniform metal sheet has a hole in its centre. What happens to hole when the sheet is uniformly heated?
Consider two spheres A and B of the same size and material. The sphere A is hollow and the sphere B is solid. Which of the following statements hold good if both the spheres are heated to the same temperature?
Oxygen boils at -183°C. This temperature is approximately
The pressure of a gas filled in the bulb of a constant volume gas thermometer at 0°C and 100°C are 28.6 cm and 36.6 cm of mercury respectively. The temperature of bulb at which pressure will be 35.0 cm of mercury will be
What force should be applied to the ends of steel rod of a cross sectional area 10 c m 2 to prevent it from elongation when heated form 273 K to 303 k? (a of steel 10 -5 ° C – 1 , Y = 2 × 10 11 Nm -2 )
The temperature of a substance increases by 27°C. On the Kelvin scale this increase is equal to
A steel rod of length 0.5km is used in the construction of a bridge. It has to withstand a temperature change of 40°C. The gap that is allowed for its expansion is [α = 10 -6 /°C]
A wire of length 100cm increases in length by 10 -2 m when it is heated through 100°C. The coefficient of linear expansion of the material of the wire expressed in /K units is
An iron bar whose cross sectional area is 4cm 2 is heated from 0°C and 100°C. The force required to prevent the expansion of the rod is [Y of Iron = 2 × 10 12 dyne / cm 2 α of Iron = 2 × 10 -6 /°C]
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0°C . What is the change in the diameter of the hole when the sheet is heated to 227°C ? α for copper = 1.70 × 10 − 5 K − 1
Distance between two places is 200km. a of metal is 2.5 × 10 -5 /°C. Total space that must be left between steel rails to allow a change of temperature from 36°F to 117°F is
Brass scale of a Barometer gives correct reading at 00C. coefficient of linear expansion of brass is 18 × 10 -6 /°C. If the barometer reads 76cm at 20°C, the correct reading is γ Hg = 18 × 10 − 5 / 0 C
When the temperature of a body increases from t to t + ∆ t, its moment of inertia increases from I to I + ∆ l. The coefficient of linear expansion of the body is α. The ratio ∆ I/I is
A steel scale is correct at 0°C. The length of a brass tube measured by it at 40°C is 4.5m. The correct length of the tube at 0°C is (Coefficients of linear expansion of steel and brass are 11 × 10 -6 /°C and 19 × 10 -6 /°C respectively).
Two rods of lengths L 1 and L 2 are welded together to make a composite rod of length (L 1 +L 2 ). If the coefficient of linear expansion of the materials of the rods are α 1 and α 2 respectively, the effective coefficient of linear expansion of the composite rod is
A steel tape is calibrated at 20°C. when the temperature of the day is -10°C, the percentage error in the measurement with the tape is α = 12 × 10 − 6 / 0 C
A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water find the melting point of lead.
A second’s pendulum clock having steel wire is calibrated at 20°C . When temperature is increased to 30°C , then how much time does the clock loose or gain in one week ? α stoel = 1 .2 × 10 − 5 ∘ C − 1
A metre scale made of steel is calibrated at 20°C to give correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at 10°C. Coefficient of linear expansion of steel is 1.1 × 10 –5 /°C
Distance between two places is 200 km. α of steel is 12 × 10 –6 /°C. Total space that must be left between steel rails to allow for a change of temperature from 36°F to 117°F is (in km)
A brass wire 1.8 m long at 27°C is held taut with little tension between the two rigid supports. If the wire is cooled to a temperature of -39°C , the tension developed in the wire, if its diameter is 2.0 mm, Coefficient of linear expansion of brass = 2.0×10 -5 K -1 ; Young’s modulus of brass = 0.91×10 11 Pa
A steel wire AB of length 100 cm is fixed rigidly at points A and B in an aluminium frame as shown in the figure. If the temperature of the system increases through 100°C, then the excess stress produced in the steel wire relative to the aluminium? α Al = 22 × 10 − 6 / 0 C and α steel = 11 × 10 − 6 / ∘ C young’s Modulus of steel is 2 × 10 11 Nm –2 .
The coefficient of linear expansion for a certain metal varies with temperature as α(T ) . If L 0 is the initial length of the metal and the temperature of metal changed from T 0 to T(T 0 > T) then,
A steel rod of length 5 m is fixed rigidly between two supports. α of steel = 12 × 10 − 6 / o C , Y = 2 × 10 11 Nm − 2 With the increase in its temperature by 40 0 C . the stress developed in the rod is
A clock with an iron pendulum keeps correct time at 15°C . If the coefficient of linear expansion of iron is 0.000012/ 0 C and the room temperature is 20°C it loses in a day
An iron tyre is to be fitted onto a wooden wheel 1.0 m in diameter. The diameter of the tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of : (coefficient of volume expansion of iron is 3.6 10 -5 /°C )
If the length of a cylinder on heating increases by 2%, the area of its base will increase by
Two thermometers are constructed in the same way except that, one has a spherical bulb and the other a cylindrical bulb. Which one will respond quicker to temperature change ?
A thin copper wire of length L increases in length by 1% when heated from 0°C to 100°C . If a thin copper plate of area 2L 2 is heated from 0oC to 50°C , the percentage increase in its area will be
A brass scale is accurate at 15°C . It is used to measure length of a cloth at 25°C . Measured length is
On which of the following scales of temperature, the temperature is never negative ?
A pendulum clock keeps correct time at 20°C. The correction to be made during summer per day, where the average temperature is 40°C, will be : α = 10 − 5 / o C
There is a rectangular metal plate in which two cavities in the shape of rectangle and circle are made, as shown with dimensions. P and Q are the centres of these cavities. On heating the plate, which of the following quantities increase?
A steel rod of length 1m is heated from 25 0 C t o 75 0 C keeping its length constant. The longitudinal strain developed in the rod is (Given : Coefficient of linear expansion of steel = 12 × 10 − 6 / 0 C )
A difference of temperature of 25 0 C is equivalent to a difference of
When a copper ball is heated, the largest percentage increase will occur in its
A flask of volume 10 3 cc is completely filled with mercury at 0 0 C . The coefficient of cubical expansion of mercury is 180 × 10 − 6 / 0 C and that of glass is 40 × 10 − 6 / 0 C . If the flask is now placed in boiling water at 100 0 C , how much mercury will overflow?
The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is
A rod of length l and radius r is bent into a ring of radius R with a cut which makes an angle of θ at the centre. If coefficient of thermal expansion is positive then on heating
When a copper ball is heated, the largest percentage increase will occur in its
A liquid whose coefficient of volume expansion is γ r , completely fills a sealed metal tank, at negligible pressure. The coefficient of linear expansion of the metal is α and the compressibility of the liquid is k. If the temperature of the system is increased by t. The pressure of the liquid will be
Two rods of length L 2 and coefficient of linear expansion α 2 are connected freely to a third rod of length L 1 of coefficient of linear expansion α 1 to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of L 1 which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if
A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are α C and α B . On heating, the temperature of the strip goes up by ∆ T and the strip bends to form an arc of radius of curvature R. Then R is : (i) proportional to ∆ T (ii) inversely proportional to ∆ T (iii) proportional to α B – α C (iv) inversely proportional to α B – α C
A glass bottle of volume 100 cc at 0°C is filled with paraffin at 20°C. If the density of paraffin at 0°C is 0.8 g/cc, γ paraffin = 10 x 10 -4 /°C and the coefficient of linear expansion of glass is 10 x 10 -6 /°C, the mass of paraffin is
A Vessel having coefficient of cubical expansion γ g contains liquid of coefficient of real expansion γ R up to certain level. When vessel Is heated, match column I and column II Column I Column II a) γ g < γ R p) liquid level rises continuously from beginning b) γ g = γ R q) liquid level falls continuously from beginning c) γ g > γ R r) liquid level remains same d) γ g = 0 s) liquid level first falls and then rises a b c d 1. s r q p 2. s r p q 3. q r s p 4. r q p s
Two beakers A and B of negligible coefficient of expansion are filled with water at 4 o C . Beaker ‘A’ is heated and beaker ‘B’ is cooled. Then
A liquid occupies 1/3 rd of a vessel at a particular temperature. The volume of unoccupied part remains constant at all temperatures. If α is coefficient of linear expansion of vessel and ‘ γ ’ is coefficient of real expansion of liquid , Then
If coefficient of real expansion γ R is 3% more than coefficient of apparent expansion , coefficient of linear expansion of material is
Volume of mercury in the bulb of a thermometer is 10 -6 m 3 . Area of cross section of capillary tube is 2 x 10 -7 m 2 . ? Hg = 18 × 10 – 5 / C 0 . If Temperature is raised by 100 o C, length of mercury column raised in to the tube is (neglect expansion of glass)
In an experiment to find coefficient of real expansion of a liquid , 70 cm column of liquid at 0 o C is found to balance 71.26 cm column of liquid at 100 o C, γ R of that liquid is
Brass plate at 30 ∘ C and steel plate at 20 ∘ C have equal area. α of brass = 18 × 10 − 6 / 0 C , α of steel = 12 × 10 − 6 / 0 C . The common temperature at which both will have equal area is
A metal tape is calibrated at 20 0 C . α of metal is 2 × 10 − 5 / 0 C . Distance between 2 points is measured as 1 m at 30 ∘ C . Correction to be made to get true distance is
Two rods of different materials having coefficients of linear expansions α 1 and α 2 and Young moduli Y 1 and Y 2 are fixed between two rigid walls and heated by same temperature difference thermal stress developed in both rods is same, If α 1 : α 2 = 2 : 3 , Y 1 : Y 2 is
In an experiment to find coefficient of real expansion of a liquid, 70 cm column of liquid at 0 ∘ C is found to balance 71.26 cm column of liquid at 100 ∘ C , γ R of that liquid is
A vessel of volume V is half filled with a liquid of density 2d and coefficient of apparent expansion 2x. The other half is filled another liquid of density ‘d’ and coefficient of apparent expansion ‘x’. When temperature is increased by 4 ∘ C , mass of liquid expelled is
A metal rod has length of 1m at 20 ∘ C . α of metal is 2 × 10 − 5 / 0 C . The temperature at which its length will be decreased by 1mm is
Two identical vessels each of volume V contain identical samples of ideal gas. The pressure and temperature in each are P and 2T respectively. Now they are joined by a very narrow pipe and one of them is cooled to a temperature T and the other one is heated to a temperature 3T. The common pressure of the system now is
It is said that the original Centigrade thermometer designed by Celsius had upper fixed point (steam point) as 0° and lower fixed point (ice point) as 100° . This temperature scale we label as Tuglak scale and temperatures in this scale represented by °T . A temperature of 50 ° T is equivalent to x ° C , then x is
List – I List – II A Isotropic solids I Expands on melting B Ice II Equal expansion in all directions C Anisotropic solids III contracts on melting D Copper IV unequal expansion in different directions A B C D 1 II IV III I 2 II III IV I 3 III IV I II 4 I II III IV
A rectangular metal plate has two circular holes drilled in it in a symmetric manner as shown in the figure. If the metal plate is uniformly heated, which of the shown distances “A”, “B” or “C” increases?
Water at 4°C is filled to the brim of two beakers of glass of negligible coefficient of expansion. A boy performed an experiment of heating beaker (A) and cooling the beaker (B). The observation he makes will be
Examine the two statements A and B, and choose the correct option from those given below. A: For a given gas at constant pressure, the density is directly proportional to its absolute temperature. B: For a given gas at constant temperature, the density is inversely proportional to its pressure.
A sample of an ideal gas is heated so that its volume as well as pressure are doubled. The percent increase in its absolute temperature must be
Water at 4°C is filled to the brim of two beakers of glass of negligible coefficient of expansion. A boy performed an experiment of heating beaker (A) and cooling the beaker (B). The observation he makes will be
Between 273 K and 277 K the coefficient of cubical expansion of water is
Coefficient of linear expansion of brass and steel rods are α 1 and α 2 . Lengths of brass and steel rods are l 1 and l 2 respectively. If l 2 − l 1 is maintained same at all tempera – tures, which one of the following relations holds good ?
A crystal has a coefficient of expansion 13 x 10 -7 in one direction and 237 x 10 -7 in every direction at right angles to it. Then the cubical coefficient of expansion is
Two straight metallic strips each of thickness t and length l are rivertted together. Their coefficients of linear expansions are α 1 and α 2 and ar. If they are heated through temperature ∆ T , the bimetallic strip will bend to form an arc of radius
A uniform brass disc of radius and mass m is set into spinning with angular speed ω 0 , about are axis passing through centre of disc and perpendicular to the plane of disc. If its temperature increases from θ 1 ∘ C to θ 2 ∘ C without disturbing the disc, what will be its new angular speed ? (the coefficient of linear expansion of brass is α )
A metal ball immersed in alcohol weights W 1 at 0°C and W 2 at 59°C. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that
Figure shows a rectangular plate of dimensions (l x b) from which the circular holes of radii r 1 and r 2 (r 1 > r 2 ) has been cut. The distance between the two holes is d (> r 2 ). If d’ be the respective distance at some higher temperature, then (d’/d) is
A thin brass sheet at 10°C and a thin steel sheet at 20°C have the same surface area. The common temperature at which both would have the same area is (coefficient of linear expansion for brass and steel are 19 x 10 -6 /°C and 11 x 10 -6 /°C respectively)
A metal ball immersed in alcohol weighs W 1 at 0°C and W 2 at 59°C. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that
A glass flask is filled up to a mark with 50 cc of mercury at 18°C. If the flask and contents are heated to 38°C, how much mercury will be above the mark ? ( α for glass is 9 x 10 -6 /°C and coefficient of real expansion of mercury is 18 x 10 -3 /°C)
An ideal gas has pressure P at absolute temperature T. Its pressure is increased by ΔP due to an increase in temperature ΔT . If the volume of the gas remains constant, the fractional change in pressure per unit rise in temperature ( ΔP / P ) / ΔT is proportional to
The resistance of a bulb filament is 100 Ω at a temperature of 100°C. If its temperature coefficient of resistance be 0 .005/°C, its resistance will become 200 Ω at a temperature of
Which one of the following statements is wrong
The e.m.f. developed in a thermo-couple is given by E = αT + 1 2 βT 2 where T is the temperature of hot junction, cold junction being at 0°C. The thermo electric power of the couple is
The temperature of the cold junction of a thermocouple is 0°C and the temperature of hot junction is T°C. The e.m.f. is e = 16 T − 0 .04 T 2 μV The inversion temperature T i is
A non-conducting body floats in a liquid at 20 o C with 2 3 of its volume immersed in the liquid. When liquid temperature is increased to 100 o C, 3 4 of body’s volume is immersed in the liquid. Then, the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)
A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are α c and α b . On heating, the temperature of the strip goes up by ∆ T and the strip bends to form an arc of radius of curvature R. Then, which of the following statement is correct about the radius of curvature?
When a liquid is heated in a glass vessel, its coefficient of apparent expansion is 1 . 03 × 10 – 3 / ∘ C . When the same liquid is heated in a copper vessel, its coefficient of apparent expansion is 1 . 006 × 10 – 3 / ∘ C . If the coefficient of linear expansion of copper is 17 × 10 – 6 / ∘ C , then the coefficient of linear expansion of glass is
Two rods of different materials having coefficients of thermal expansion α 1 , α 2 and Young’s modulli Y 1 , Y 2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If α 1 : α 2 = 2 : 3, the thermal stresses developed in the two rods are equal provided Y 1 : Y 2 is equal to :
Coefficient of linear expansion of brass and steel rods are α 1 and α 2 Lengths of brass and steel rods are l 1 and l 2 respectively. If ( l 2 – l 1 ) is maintained same at all temperatures, which one of the following relations holds good?
A vessel of linear coefficient of expansion ‘a’ is half filled with a liquid. On increasing the temperature, the volume of empty space remains the same at all temperature, then coefficient of real expansion of liquid is
A vessel of volume ‘V’ contains an ideal gas at a pressure ‘ P 0 ’. The gas being removed from the vessel by means of piston pump with single stroke by volume V 4 . The pressure of the gas inside the vessel after 3 rd stroke of the piston is
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is α Cu = 1 . 7 × 10 – 5 K – 1 and α Al = 2 . 2 × 10 – 5 K – 1
A pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is 5 seconds fast each day at a temperature of 15 o C and 10 seconds slow at a temperature of 30 o C . The temperature at which it is designed to give correct time, is
PV versus T graph of equal masses of H 2 , He and O 2 is shown in the figure.
The value of coefficient of volume expansion of glycerin is 5 × 10 – 4 K – 1 . The fractional change in the density of glycerin for a rise of 40°C in its temperature, is
A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?
Two glass bulbs A and B of volume V, 2V respectively are connected by a narrow capillary tube. The bulbs contain gas at temperature T and pressure P. Now the temperature of bulb A is doubled and that of B is tripled. The final number of moles of gas in bulb ‘A’ is
The radius of a ring is R and its coefficient of linear expansion is α . If the temperature of ring increases by θ , then its circumference will increase by :
A gas is confined inside a container having a movable piston. The gas is allowed to expand isobarically. If the initial volume of gas is V 0 and the speed of sound in the gas is C 0 , then the speed of sound when the volume of the gas increases to 4 V 0 is
The pressure P, volume V and temperature T of a gas in the jar A and the other gas in the jar B at pressure 2P, volume V/4 and temperature 2T, then the ratio of the number of molecules in the jar A and B will be
A solid floats submerged in a liquid. When the liquid is heated, which of the following is most likely to happen?
The coefficient of volume expansion for an ideal gas at constant pressure of 5 × 10 5 N / m 2 when the temperature of the gas is 27 0 C
A uniform solid brass sphere is rotating with angular speed ω 0 about a diameter. If its temperature is now increased by 100°C, what will be its new angular speed. (Given α B = 2.0 × 10 – 5 per °C)
A closed vessel contains 8 g of oxygen and 7 g of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent, the pressure of the remaining gas in atm will be
Span of a bridge is 2.4 km. At 30°C a cable along the span sags by 0.5 km. Taking a = 12 × 10 – 6 /°C, change in length of cable for a change in temperature from 10°C to 42°C is
The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line (D) Then the expansion of the same ideal gas of mass 2m at a pressure P/2 is given by the straight line
The magnitude of force developed by raising the temperature from 0 o C to 100 o C of an iron bar 1m long and of 1 cm 2 cross section when it is held between two rigid walls so that it is not permitted to expand is α = 10 − 5 / o C and Y = 10 11 N / m 2
Two rods having length l and 2l, made of materials with linear expansion coefficient 2 α and α are soldered together so as to form a single rod of length 3l. The equivalent coefficient of linear expansion for the composite rod is
When the temperature of a body increases
A Brass stopper snuggly fits in the hole of steel plate. To remove the stopper easily, the system
A ball does not pass through a copper ring at room temperature. The same ball, after heating, passes through the same ring. It shows due to heating, the ball
On a hypothetical scale X, the ice point is 40 0 and the steam point is 120 0 . For another scale Y the ice point and steam points are –30 0 and 130 0 respectively. If X-reads 50 0 The reading of Y is
A Fahrenheat thermometer reads 113 0 F while a faulty celsius thermometer reads 44 0 C. The correction to be applied to the celsius thermometer is
Coefficient of cubical expansion of a solid is (0.000027/°C). If the temperature is measured on Fahreheit scale, numerical value of coefficient of linear expansion of solid is
A solid sphere and a hollow sphere of same material have same mass. When they are heated by 50°C, increase in volume of solid sphere is 5 c.c. The expansion of hollow sphere is
A metal meter scale has two holes at the two ends. when the scale is heated the distance between the two holes
If coefficient of cubical expansion is x times the coefficient of superficial expansion, then the value of x is
The ratio of the lengths of two rods is 4:3. The ratio of their coefficients of cubical expansion is 2:3. Then the ratio of their linear expansions when they are heated through same temperature difference is
A wire of length 60 cm is bent into a circle with a gap of 1 cm at its ends. On heating it by 100°C, the length of the gap increases to 1.02 cm.α of material of wire is
If the length of a body is measured in centimeters instead of meters, the coefficient of linear expansion
A metal metre scale gives correct measurement at 0 0 C. It is generally used at a temperature of 40 0 C. The correction to be made for every metre is (α = 10 -6 / 0 C)
A platinum wire can be sealed through glass, but a brass wire cannot be sealed in glass because
The temperature of a thin uniform rod increases by Δt. If moment of inertia be I about an axis perpenducular to its length then its moment of inertia increases by
Two spheres of same size are made of same metal, but one is hollow and the other is solid. They are heated to same temperature then
A metal rod has a length of 1m at 30°C. 'α' of metal is 2.5 ×10 –5 /°C. The temperature at which it will be shortened by 1mm is
Radius of a sphere is 100cm at 0°C and 100.1cm at 100°C. Coefficient of cubical expansion of the sphere is
Upon heating, the length of the side of a cube changes by 2%. The volume of the cube changes by
A length of 2m is measured using a metal tape at 10 0 C. It is calibrated at a temperature 30 0 C. The actual length is (α = 1 x 10 -4 /C 0 )
A steel rod of length 4cm and cross-sectional area 4cm 2 is tightly fixed between two supports and is not allowed to expand. It is heated through 2°C. Thermal stress developed is ….10 6 N/m 2 (Y= 20 ×10 10 N/m 2 = 18 × 10 –6 / 0 C)
A piece of copper wire has a length of 2m at 10°C. Its length at 100°C is (Coefficient of linear expansion of copper = 17×10 -6 /°C)
A piece of steel has a length of 30cm at 15°C. At 90°C its length increases by 0.027 cm. Its coefficient of linear expansion is
The density of lead at 0°C is 11.34 g/cm 3 . The density of lead at 100°C, (if the coefficient of linear expansion of lead = 28 × 10 -6 /°C) is
A steel scale is correct at 0°C. The length of a brass tube measured by it at 40°C is 4.5m. The correct length of the tube at 0°C is (Coefficients of linear expansion of steel and brass are 11×10 -6 /°C and 19×10 -6 /°C respectively).
A steel ball initially at a pressure of 1.0 × 10 5 Pa is heated from 20°C to 120°C keeping its volume constant. Find the pressure inside the ball. Coefficient of line expansion of steel = 12 × 10 -6 /°C and bulk modulus steel = 1.6 × 10 11 N/m 2
A vessel is half filled with a liquid at 0°C. When the vessel is heated to 100°C, the liquid occupies 3/4 volume of the vessel. Coefficient of apparent expansion of the liquid is
A liquid column of height 80cm at 0°C balances the same liquid of height 80.4cm at 100°C. γ R is
Coefficient of real expansion of a liquid is 0.000182/°C. If coefficient of linear expan-sion of vessel is 0.000009/°C, coefficient of apparent expansion of the liqud is
Co-efficient of apparent expansions of a liquid in Gold vessel is G and when heated in a silver vessel is S. If coefficient of linear expansion of Gold is A, coefficient of linear expansion of Silver is
A liquid occupies half of a vessel at a particular temperature. The volume of the unoccupied part remains constant at all temperatures. If α and γ are the coefficients of linear and real expansions of a vessel and liquid, then γ =
The volume of a gas at 20 0 C is 100CC at normal pressure. When it is heated to 100 0 C, its volume is 125CC at the same pressure the volume coeficient of the gas is
If the coefficient of real expansion γ r is 1% more then coefficient of apparent expansion, linear expansion coefficient of the material is
Two samples of Hydrogen and Oxygen of same mass possess same pressure and volume. The ratio of their temperatures is
A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One half of the mass of the gas is removed from the vessel and the temperature of the remaining gas is increased to 87°C. At this temperature the pressure of the gas will be
A glass vessel contains air at 60 0 C. To what temperature must it be heated to expel one third of the air, the pressure remaining constant. (Neglect the expansion of the vessel)
A Steel tank is filled with a gas at 150 atmosphere and at 20 0 C. If the pressure raise to 250 atmospheres, the tank explodes. Find the temperature at which the tank explodes.
The mass of a litre of dry air at N.T.P is 1.293 g. Find the mass of 3 litres of air at 117 0 C and a pressure of 4 atmospheres ?
Density of a liquid 'A' is 0.5 g/c.c and that of liquid 'B' is 0.6 g/c.c. Heat capacity of 8 litres of ‘A’ is equal to that of 10 litres of 'B'. Then their specific heats ratio is
A copper rod of length 88 cm and an aluminium rod of unknown length have same increase in length at same increase in temperature. The length of aluminium rod is
A Fahrenheit thermometer reads 113 0 F while a faulty celsius thermometer reads 44 0 C. The correction required to be applied to the celsius thermometer is
There is some change in length when 33000N tensile force is applied on a steel rod of area of cross section 10 –3 m 2 . The change in temperature required to produce the same elongation if the steel rod is heated is (The modulus of elasticity is 3 × 10 11 N/m 2 and the coefficient of linear expansion of steel is 1.1 × 10 –5 / 0 C)
A meter rod made of steel is correct at 0°C and other meter rod of same material is correct at 30°C. If α = 12 × 10 –6 /°C, the difference between their lengths at 20°C is
An iron rod of length 50cm is joined end to end to an aluminium rod of length 100cm. All measurements refer to 20 0 C. The coefficients of linear expansion of iron and aluminium are 12 × 10 –6 / 0 C and 24 × 10 –6 / 0 C respectively. The average coefficient of composite rod is
Two uniform metal rods of length L 1 and L 2 and their linear coefficients of expansion α 1 and α 2 respectively, are connected to form a single rod of length (L 1 +L 2 ). When the temperature of the combined rod is raised by "t°C", the length of each rod increased by the same amount then is
A pendulum clock gives correct time at 20 0 C at a place where g= 10m/s 2 . The pendulum consists of a light steel rod connected to a heavy ball. If it is taken to a different place where g = 10.01m/s 2 at what temperature the pendulum gives correct time (α of steel is 10 –5 / 0 C)
A steel meter scale is to be ruled so that millimeter intervals are accurate within about 5 ×10 –5 m at a certain temperature. The maximum temperature variation allowable during the ruling is [coefficient of linear expansion of steel = 10 ×10 –6 k –1 ]
An iron ball of diameter 6cm and is 0.01 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 200C. The temperature at which (both for ball and plate) the ball just pass through the hole is (α iron = 12 x 10 -6 / 0 C; αbrass = 18 x 10 -6 / 0 C)
A sphere of coefficient of linear expansion α, mass 'm' and radius 'r' is spinning about an axis through its diameter with an angular velocity 'ω' when it is heated such that its temperature increases by Δt, the angular velocity becomes
A thin circular metal disc of radius 500mm is set rotating about a central axis normal to its plane upon raising its temperature gradually, the radius increases to 507.5 mm, the percen-tage change in the rotational KE will be–––
Two thin metal strips, one of brass and the other of iron are fastened together parallel to each other. Thickness of each strip is 1 mm. If the strips are of equal length at 0°C . The inner radius of the arc formed by the bimetallic strip when heated to 80°C is (Coefficient of linear expansion of brass = 19×10 –6 / 0 C & of iron = 12 × 10 –6 / 0 C).
A mercury thermometer contains 2c.c. of Hg. at 0°C. Distance between 0°C and 100°C marks on the stem is 35cm and diameter of the bore is 0.02cm. γ A of liquid is
Coefficient of real expansion of mercury is 0.18 x 10 -3 / 0 C. If the density of mercury at 0 0 C is 13.6 gm/c.c., its density at 573K will be
Volume of mercury in the bulb of a thermo-meter is 10 –6 m 3 . Area of cross section of capillary tube is 2 × 10 –7 m 2 . If the temperature is raised by 100°C, the length of mercury column is (γ Hg =18 × 10 –5 /°C)
A solid whose volume does not change with temperature, floats in a liquid. Fractions f 1 a n d f 2 of its volume remain submerged for two different temperatures t 1 a n d t 2 of liquid. The volume coefficient of expansion of liquid is
One litre of He gas at a pressure of 76cm of Hg and temperature 27 0 C is heated till its pressure and volume are doubled. The final temperature attained by the gas is
An air bubble of volume V 0 is released by a fish at a depth h in a lake. The bubble rises to the surface. Assume constant temperature and standard atmosphric pressure P above the lake. The volume of the bubble just before reaching the surface is (d is the density of water).
A gas obeys PV 2 = constant in addition to PV = RT. If on heating, the temperature is doubled , the volume of the gas is
PQR is a right angled triangle made of brass rod bent as shown. If it is heated to a high temperature the angle PQR.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated, uniformly to raise its temperature slightly
Density of liquid at any temperature ‘t’ is given by d t = d 0 1 + γ t where d 0 is the density at 0°C. This equation applies to
When water is heated from 0°C to 10°C, its volume
In cold countries, water does not freeze at the bottom of a lake in winter, on account of
Among the following , the liquid having negative coefficient of cubical expansion between 273K and 277K is
Pick up the correct statement a) Sun’s temperature is measured by a pyrometer b) Insects temperature is measured by thermo electric thermometer c) Temperature of Human body is measured by mercury thermometer.
The numerical value of coefficient of linear expansion is independent of units of (a) length (b) temperature (c) area (d) mass
Which of the following statements are true a) Rubber contracts on heating b) Water expands on freezing c) Water contracts on heating from 0 0 C to 4 0 C d) Water expands on heating from 4 0 C to 40 0 C
A thin copper wire of length L increases by 1% when heated from 0°C to 100°C. If a thin copper plate of area 2L × L is heated from °C to 100°C. The percentage increase in the area of the plate will be
The coefficient of linear expansion of homogeneous rod changes linearly from α 1 to α 2 from one end to the other end. The effective coefficient of linear expansion is
The variation of length of a substance along three principal directions with temperature is shown in the figure. The average superficial expansivity of the substance is
The given system consists of two springs. If the temperature of the rod is increased by ΔT, the compression in the left spring is
The coefficient of linear expansion of a rod of length 2m varies with distance x from end of the rod as where . Find the increase in length of the rod when heated through 350°C.
A planar lamina is made of thin uniform rods. The length of section AB and EF is L 1 and its coefficient is α 1 . The length of CD is L 2 and its coefficient is α 2 . CB and DE are of same length having coefficient α 1 α 2 = 3 . 5 Points A, B, E and F reside on the same line that is sections AB and EF overlap. Then find the ratio of l 2 l 1 for which the distance between end A and end F remain same at all temperatures
The length of two bars “A” and “B” expand with respect to temperature according to the following graph. Determine “α A ” in terms of “α B “ and “L o ”.
On heating a liquid of coefficient of cubical expansion γ in a container having coefficient of linear expansion γ 3 , the level of liquid in the container will
Statement I : Water expands both when heated or cooled from 4 0 C . Statement II : Density of water is minimum at 4 0 C .
Two metal strips that constitute a thermostat must necessarily differ in their
Statement I : A change in the temperature of a body causes change in its dimension Statement II : The dimension of a body decrease due to the increase in its temperature.
Two rods, one of aluminium and the other made of steel, having initial length l 1 and l 2 are connected together to form a single rod of length l 1 + l 2 . The coefficients of linear expansion for aluminium and steel are α a and α s respectively. If the length of each rod increases by the same amount when their temperature are raised by t 0 C , then find the ratio l 1 ( l 1 + l 2 )
Mercury boils at 367 0 C . However, mercury thermometers are made such that they can measure temperature up to 500 0 C . This is done by
At some temperature T, a bronze pin is a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when
The value of coefficient of volume expansion of glycerin is 5 × 10 – 4 K – 1 . The fractional change in the density of glycerin for a rise of 40 0 C in its temperature is
Statement I : The coefficient of real expansion of the liquid is independent of nature of container. Statement II : γ r = γ a + γ v Where γ a = coefficient of apparent expansion , γ r = coefficient of real expansion and γ v = coefficient of expansion of vessel .
A thin copper wire of length L expands in length by 0.2% when it is heated from 0 0 C to 50 0 C. If a copper plate of area 2 L × L 4 is heated from 0 0 C to 100 0 C. The % increase in its area is
If the length of a cylinder on heating increases by 2%, the area of its base will increase by
A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10 0 C , and the coefficient of linear expansion of the metal of the rod is 2 × 10 – 6 per 0 C , the period of the pendulum will have percentage increase of
On an X temperature scale, water freezes at -125. 0 0 X and boils at 375. 0 0 X. On a Y temperature scale, water freeze at -70. 0 0 Y and boils at -30. 0 0 Y. The value of temperature on X-scale equal to the temperature of 50. 0 0 Y on Y-scale is:
If on heating liquid through 80 0 C , the mass expelled is ( 1 100 ) th of mass still remaining, the coefficient of apparent expansion of liquid is
The difference between volume and pressure coefficients of an ideal gas is :
An insulated chamber at a height h above the earth’s surface and maintained at 30 0 C has a clock fitted with an uncompensated pendulum. The maker of the clock for the chamber mistakenly designs it to maintain correct time at 20 0 C at that height. It is found that if the chamber were brought to earth’s surface the clock in it would click correct time at 30 0 C . The coefficient of linear expansion of the material of pendulum is (earths radius is R)
A piece of metal weighs 46 g in air. When it is immersed in a liquid of specific gravity 1.24 at 27 0 C it weighs 30 g. When the temperature of liquid is raised to 42 0 C the metal piece weighs 30 . 5 g . Specific gravity of liquid at 42 0 C is 1 . 20 . Calculate the coefficient of linear expansion of the metal.
Coefficients of linear expansion of two rods A and B are in the ratio 2 : 3. The rods are fixed between two rigid walls. If the young’s modulii of the materials of the rod are in the ratio 2:1 and temperatures of the rods are increased by 15 o C , the thermal stresses developed in the rods will be in the ratio
The correct value of 0°C on the Kelvin scale is :
The temperature in the Fahrenheit scale corresponding to 253 K is:
The reading of Centigrade thermometer coincides with that of Fahrenheit thermometer in a liquid. The temperature of the liquid is
The Fahrenheit and Kelvin scales of temperature will give the same reading at :
The temperature of a substance increases by 27C 0 . On the Kelvin scale this increase is equal to:
A Centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers 140°. What is the fall in temperature as registered by the Centigrade thermometer ?
Mercury thermometers can be used to measure temperature up to :
Mercury boils at a temperature of 367°C; however mercury thermometers are made which can measure up to 500°C. This is done by:
Two thermometers are constructed in the same way except that one has a spherical bulb and the other a cylindrical bulb; which one will respond quickly to temperature changes ?
Two thermometers are used to record the temperature of a room. If the bulb of one is wrapped in wet hanky :
The standard scale of temperature is :
In a constant volume gas thermometer, the temperature of a bath is measured by :
The temperature range measured by hydrogen gas thermometer is :
In a resistance thermometer, the resistances at 0°C and 100°C are 6.74 ohm and 7.74 ohm respectively. The temperature corresponding to 6.53 ohm resistance is :
Which instrument will you most conveniently employ to measure a temperature of 400°C?
A thermoelectric thermometer is made . of copper-iron thermocouple. One junction is placed in melting ice and the other end is placed in a bath, whose temperature is continuously increased from 0°C to 600°C. The current in the galvanometer :
Which of the following statements are not true? (i) Size of degree is smallest on Celsius scale (ii) Size of degree is smallest on Fahrenheit scale (iii) Size of degree is equal on Fahrenheit and Kelvin scale (iv) Size of degree is equal on Celsius and Kelvin scale
Reading of temperature may be same on : (i) Celsius and Kelvin scale (ii) Fahrenheit and Kelvin scale (iii) Celsius and Fahrenheit scale (iv) All the three scales
To measure a temperature say around 400°C which of the following thermometers can be used most conveniently : (i) gas thermometer (ii) mercury thermometer (iii) platinum thermometer (iv) thermocouple
The temperature range that can be measured by thermocouple thermometer is :
The study of physical phenomena at low temperatures (below liquid nitrogen) is called:
On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39°W and 239°W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39°C on the Celsius scale ?
Expansion during heating :
When a metal rod is heated it expands because :
When a strip made of iron ( α 1 ) and copper α 2 ( > α 1 ) is heated:
If the length of a cylinder on heating increases by 2%, the area of its base will increase by :
A beaker is filled with water at 4°C at one time; the temperature is increased by a few °C above 4°C and at another time it is decreased by few °C below 4°C. One shall observe that :
A beaker is completely filled with water at 4°C. It will overflow if:
A composite rod made of copper ( α = 1.8 x 10 -5 K -1 ) and steel ( α = 1.2 x 10 -5 K -1 ) is heated, then it:
A uniform solid sphere of copper is rotating about a diameter with an angular speed ω . Its temperature is increased by 80°C. α Cu being the coefficient of linear expansion of Cu,new angular speed of the sphere will be :
At some temperature T, a bronze pin is a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when :
Absolute coefficient of expansion of a liquid is 10 times the volume coefficient of expansion of the vessel. Ratio of absolute and apparent expansion of liquid is :
Coefficient of apparent expansion of mercury in a glass vessel is 153 x 10 -6 / o C and in a steel vessel is 144 x 10 -6 /°C. If α for steel is 12 x 10 -6 /°C, then that of glass is
Coefficients of linear expansion of an isotropic solid along three rectangular axes in the solid are α x , α y and α z . Coefficient of cubical expansion of the solid for small change in temperature can be expressed as : ( assume α x , α y and α z to be small quantities)
Consider the following statements (A) A common model of a solid assumes the atoms executing SHM about mean lattice positions. This model cannot explain thermal expansion of solids. (B) The average distance over a time period of oscillation between the particles remains constant.
Consider the following statements (A) A brass disc is just fitted in a hole in steel plate. The system must be cooled to loosen the disc from the hole. (B) The coefficient of linear expansion for brass is greater than the coefficient of linear expansion for steel.
Consider the following statements (A) Fahrenheit is the smallest unit measuring temperature. (B) Fahrenheit was the first temperature scale used for measuring temperature. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) A temperature change which increases the length of a steel rod by 1 % will increase its volume by 3%. (B) The coefficient of volume expansion is nearly three times the coefficient of linear expansion. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
There are two spheres of same material and radius. One is solid and the other is hollow. If they are heated to the same temperature the expansion of :
The relation between the volume and temperature of a sample of water in the range 0°C to 100°C is best represented by:
Which of the following curves represents variation of density of water with temperature best ?
A solid ball of metal has a spherical cavity inside it. If the ball is heated, the volume of the cavity will:
Three metal rods of the same length and area of cross section form an equilateral triangle as shown in Fig. D is the mid-point of side BC. If AD is independent for small change in temperature, then ( α 1 is the coefficient of linear expansion for rod BC and α 2 for rods AB and AC).
‘A’ is a steel rod of length I A and ‘B’ a copper rod of length l B . Values of l A and l B such that l A -l B = 5 cm at all temperatures, are : (Given α Cu = 1 . 7 × 10 – 5 / C o , α st e e l = 1 . 1 × 10 – 5 / C o )
It is required to prepare a steel metre scale such that the millimetre intervals are to be accurate within 0.0005 mm at a certain temperature. Maximum temperature variation allowable during the rulings of millimetre marks is : ( α steel = 13 . 22 × 10 – 6 / C o )
A rod of length 40 cm has the coefficient of linear expansion α 1 = 6 × 10 – 6 / C o . The other rod has coefficient of linear expansion, α 2 = 4 × 10 – 6 / C o . If the difference in their lengths at all temperatures remains the same, the length of the other rod is:
A U-tube contains mercury with one limb at 0°C and the other at 100°C. The heights of the mercury columns are 60 cm at 0°C and 62 cm at 100°C. The coefficient of volume expansion of mercury per °C is :
Which of the following statements is true about anomalous expansion of water?
The density of a substance at 0°C is l0 g/cc and at l00°C, its density is 9.7 g/cc. The coefficient of linear expansion of the substance is
A rail tack made of steel having length l0 m is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by 20°C. It is deformed as shown in figure. Find x (displacement of the centre) if α steel = 1 . 2 × 10 – 5 / 0 C
Water has maximum density at:
A rod of length 20 cm is made of metal A. It expands by 0.075 cm when its temperature is raised from 0°C to 100°C. Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature. In the composite rod, the portion made of metal A has length
Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of n moles having pressure P 0 , volume V 0 and temperature T 0 is
A rod of length 1000 mm and co-efficient of linear expansion α = 10 – 4 per degree is placed symmetrically between fixed walls separated by l00l mm. The Young’s modulus of the rod is 10 11 N / m 2 . If the temperature is increased by 20°C, then the stress developed in the rod is (in N / m 2 )
When a rod is heated but prevented from expanding, the compressional force developed is independent of :
A brass wire 1.8 m long at 27°C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of -39°C, what is the tension developed in the wire, if its diameter is 2.0 mm? Coefficient of linear expansion of brass = 2.0 x 10 – 5 / 0 C , Young’s modulus of brass = 0.91 x 10 11 Pa.
An isosceles triangle is formed with a thin rod of length l 1 and coefficient of linear expansion α 1 , as the base and two thin rods each of lenglh /, and coefficient of linear expansion α 2 , as the two sides. The distance between the apex and the midpoint of the base remain unchanged as the temperature is varied. The ratio of lengths l 1 l 2 is
A brass rod of length 50 cm and diameter 3.0 cm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°C, if the original lengths are at 40.0°C? (Coefficient of linear expansion of brass = 2.0 x 10 – 5 /°C, steel = 1.2 x 10 – 5 /°C)
In the shown planar frame made of thin uniform rods, the’ length of section AB and EF is l 1 and its thermal linear coefficient of expansion is α 1 . The length of section CD is l 2 and its thermal linear coefficient of expansion is α 2 . CB and DE are of same length having thermal linear coefficient of expansion α 2 . Points A, B, E and F reside on same line, that is, sections AB and EF overlap. Then the ratio l 1 l 2 for which the distance between end A and end F remains the same at all temperatures, is:
A steel rod of length 1m is heated from 25°C to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given: Coefficient of linear expansion of steel = 12 x 10 – 6 / 0 C )
The lengths of two metallic rods at temperatures θ are L A and L B and their linear coefficient of expansion are α A and α B respectively. If the difference in their lengths is to remain constant at any temperature then
A 30.0 cm long metal rod expands by 0.0650 cm when its temperature is raised from 0 0 C to 100°C. A second rod of different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third composite rod, also 30.0 cm long, is made-up of pieces of each of the above metals placed end to end and expands by 0.0580 cm when temperature is increased from O°C to 100°C. The length of the longer portion of the composite bar in cm at 0°C is
The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = aT , where a is a positive constant and T in °C. If the length of the rod is l at temperature 0°C, then the temperature at which the length will be 2l is:
On an X temperature scale, water freezes at -125 .0° X and boils at 375.0° X. On a Y temperature scale, water freezes at -70.0°Y and boils at -30.0°Y. The value of temperature on X-scale equal to the temperature of 50.0°Y on Y-scale is:
A piece of metal weight 46 gm in air, when it is immersed in the liquid of specific gravity 1.24 at 27°C it weighs 30 gm. When the temperature of liquid is raised to 42°C the metal piece weight 30.5 gm, specific gravity of the liquid at 42°C is 1.20, then the linear expansion of the metal will be
A glass flask of volume one litre at 0 0 C is filled, level full of mercury at this temperature. The flask and mercury are now heated to l00°C. How much mercury will spill out, if coefficient of volume expansion of mercury is 1 .82 x 10 – 4 / 0 C and linear expansion of glass is 0.1 x 10 – 4 / 0 C respectively?
A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10°C, and the coefficient of linear expansion of the metal of the rod is 2 × 10 – 6 per 0 C , the period of the pendulum will have percentage increase of
Two wires A and B of the same cross sectional areas, Young’s moduli Y 1 and Y 2 and coefficients of linear expansion α 1 and α 2 respectively are joined together and fixed between rigid supports at either ends. The tension in the compound wire when wire A is heated and wire B is cooled at different temperature is same when wire A alone is cooled at the same temperature as wire B earlier. Find correct option.
Why can any low density gas be used in a constant volume gas thermometer?
The temperature of a substance increases by 27°C. On the Kelvin scale this increase is equal to
If the temperature of a patient is 40°C his temperature in the Fahrenheit scale will be
A Celsius thermometer and a Fahrenheit thermometer are put in a hot bath. The reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer. The temperature of the hot bath is
The freezing point on a thermometer is marked as 20° and the boiling point as 150°. A temperature of 60°C on this thermometer will be read as
The reading of Centigrade thermometer coincides with that of Fahrenheit thermometer in a liquid. The temperature of the liquid is
The length of each steel rail is 10m in winter. The coefficient of linear expansion of steel is 0.000012/°C and the temperature increases by 15°C in summer. The gap to be left between the rails
The length of a metal rod at 0°C is 0.5m.When it is heated, its length increases by 2.7mm. The final temperature of rod is (coeff. of linear expansion of metal = 90 × 10 -6 /°C)
A metal plate of area 1.2 m 2 increases its area by 2.4 × 10 -4 m 2 when it is heated from 0°C to 100°C. The coefficient of cubical expansion of the metal expressed in per °C is
A clock while keeps correct time at 30° C has a pendulum rod made of brass. The number of seconds it gains (or) looses per second when the temperature falls to 100 C is [ a of brass= 18 × 10 -6 /°C ]
The inner diameter of a brass ring at 273 K is 5 cm. To what temperature should it be heated for it to accommodate a ball 5.01 cm in diameter. ( α = 2 × 10 -5 /°C)
A metal sheet having size of 0.6 × 0.5 m 2 is heated from 293 K to 520°C. The final area of the hot sheet is {a of metal = 2 × 10 -5 /°C]
A wire of length 60 cm is bent into a circle with a gap of 1 cm. At its ends, on heating it by 100°C, the length of the gap increases to 1.02 cm. α of material of wire is
A faulty thermometer has its fixed points marked at 6° and 96°. What is the correct temperature on the Centigrade scale when this thermometer reads 87°
The temperature at which Celsius reading is half the Fahrenheit reading
A Fahrenheit thermometer registers 107° while a faulty Celsius thermometer registers 42°. Find the error in the later.
The pressure of hydrogen gas in a constant volume gas thermometer is 80.0cm at 0°C, 110cm at 100°C and 95.0 cm at unknown temperature t. Then t is equal to
A faulty thermometer has 90.5°C and 0.5°C as upper and lower fixed points respectively. What is the correct temperature if this faulty thermometer reads 15.5°C
A metal rod having a linear coefficient of expansion 2 × 10 -5 /°C has a length 1m at 25°C, the temperature at which it is shortened by 1 mm is (1983 E)
The variation of density of a solid with temperature is given by the formula
A crystal has a coefficient of linear expansion 12 × 10 -6 /°C in one direction and 244 × 10 -6 /°C in every direction at right angles to it . Then the coefficient of cubical expansion of crystal is
The resistance of a certain platinum resistance thermometer is found to be 2.56 Ω at 0°C and 3.56 Ω at 100°C . When the thermometer is immersed in a given liquid, its resistance is observed to be 5.06 Ω . The temperature of the liquid
A constant volume gas thermometer shows pressure readings of 50 cm and 90 cm of mercury at 0°C,100°C respectively, The temperature of the bath when pressure reading is 60 cm of mercury.
On a hypothetical scale A the ice point is 42° and the steam points is 182° For another scale B. The ice point is –100 and steam point in 90°. If B reads 60°. The reading of A is.
The upper and lower fixed points of a faulty mercury thermometer are 210°F and 34°F respectively. The correct temperature read by this thermometer is
A Fahrenheit thermometer registers 110° F while a faulty Celsius thermometer registers 44°C . Find the error in the later
When a rod is heated from 25°C to 75°C, it expands by 1 mm. When a rod of same material but with 4 times the length is heated from 25°C to 50°C. The increase in length is
Two metal rods have coefficients of linear expansion 1.1 × 10 -5 /°C and 1.65 × 10 -5 /°C respectively. The difference in lengths is 10cm at all temperatures. Their initial lengths must be respectively.
Two rods of same length and same diameter are drawn from equal masses and same quantity of heat is supplied to the two rods. Find the ratio of expansions if specific heats of the material is 2/3 and that of coefficient of linear expansion is 1/2
Two uniform metal rods one of aluminium of length l 1 and another made of steel of length l 2 and linear coefficients of expansion α a and α s respectively are connected to form a single rod of length l 1 +l 2 . When the temperature of the combined rod is raised by t°C, the length of each rod increases by the same amount. Then l 1 l 1 + l 2 is
A pendulum clock gives correct time at 20°C at a place where g= 10m/s 2 . The pendulum consists of a light steel rod connected to a heavy ball. If it is taken to a different place where g = 10.01m/s 2 at what temperature the pendulum gives correct time (α of steel is 10 –5 /°C)
A thin brass sheet at 10°C and a thin steel sheet at 20°C have the same surface area. The common temperature at which both would have the same area is (Coefficient of linear expansion for brass and steel are respectively, 19 × 10 − 6 / ∘ C are 11 × 10 − 6 / ∘ C
A clock pendulum made of invar has a period of 0.5sec at 20°C. If the clock is used in a climate where the temperature averages to 30°C, how much time does the clock loose in each oscillation. For invar α = 9 × 10 − 70 C − 1
The ratio of lengths of two rods is 1 : 2 and the ratio of coefficient of expansions is 2 : 3. The first rod is heated through 60°C. Find the temperature through which the second rod is to be heated so that its expansion is twice that of first is
On a hypothetical scale X, the ice point is 40° and the steam point is 120°. For another scale Y the ice point and steam points are –30° and 130° respectively. If X-reads 50° The reading of Y is
The initial lengths of two rods A and B are in the ratio 3:5 and coefficients of linear expansion are in the ratio 5:3. If the rods are heated from 34°C to 65°C, the ratio of their expansion will be
A pendulum clock is 5 seconds fast at temperature of 15 °C and 10 seconds slow at a temperature of 30 °C. Per day At what temperature does it give the correct time?
A thin brass sheet at 20°C and a thin steel sheet at 30°C have the same surface area. The common temperature at which both would have the same area is (Coefficient of linear expansion for brass and steel are respectively, 19 × 10 –6 /°C are 11 × 10 –6 /°C)
Two thin metal strips, one of brass and the other of iron are fastened together parallel to each other. Thickness of each strip is 2 mm. If the strips are of equal length at 0°C. The radius of the arc formed by the bimetallic strip when heated to 80°C is (Coefficient of linear expansion of brass = 19 × 10 -6 /°C & of iron = 12 × 10 -6 /°C).
Two rods of the same length, have radii in the ratio 3:4. Their densities are respectively 8000 and 9000 kg/m 3 . Their specific heats are in the ratio of 2:3. When the same amount of heat is supplied to both, the changes in their lengths are in the ratio. (If their linear coefficients are in the ratio 5:6)
Two rods of different materials and identical cross sectional area, are joined face to face at one end and their free ends are fixed to the rigid walls. If the temperature of the surroundings is increased by 30°C, the magnitude of the displacement of the joint of the rod is (length of rods l 1 =l 2 =1unit, ratio of their young’s moduli, Y 1 /Y 2 =2, coefficients of linear expansion are α 1 and α 2 )
An iron rod of length 50 cm is joined to an aluminium rod of length 100cm. All measurements refer to 20°C. The coefficient of linear expansion of iron and aluminium are 12 × 10 − 6 / ∘ C and 24 × 10 − 6 / ∘ C respectively. The average linear expansion coefficient of composite system is :
An equilateral triangle ABC is formed by joining three rods of equal length and D is the mid-point of AB. The coefficient of linear expansion for AB is α 1 and for AC and BC is α 2 . The relation between α 1 and α 2 , if distance DC remains constant for small changes in temperature is
An iron ball of diameter 6cm and is 0.01 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 20°C. The temperature at which (both for ball and plate) the ball just passes through the hole is α iron = 12 × 10 − 6 / 0 C ; α brass = 18 × 10 − 6 / 0 C
A rod of length 2 m is at a temperature of 20°C . The free expansion of the rod is 0.9mm. If the temperature is increased to 50°C , the stress produced when the rod is fully prevented to expand Y = 2 × 10 11 N / m 2 , α = 15 × 10 − 6 / 0 C
A cube of edge (L) and coefficient of linear expansion (α ) is heated by 1°C. Its surface area increases by
A steel tape is placed around the earth at the equator. When the temperature is 0°C neglecting the expansion of the earth, the clearance between the tape and the ground if the temperature of the tape rises to 30°C, is nearly α stteel = 11 × 10 − 6 / K
The variation of lengths of two metal rods A and B with change in temperature are shown in figure. The coefficients of linear expansion α A for the metal A and the temperature T will be : (Given α B = 9 × 10 − 6 / ∘ C
A rod of steel is 5m long and 3cm diameter at a temperature of 20°C. Find the free expansion of the rod when the temperature is raised to 65°C. Find the respective pulls exerted if (i) the ends do not yield and (ii) the ends yield by 0.12 cm. Y = 2 × 10 5 MN / m 2 and α = 12 × 10 − 6 per ° C
Two bars are unstressed and have lengths of 25cm and 30cm at 20° as shown in Figure. Bar (1) is of aluminium and bar (2) is of steel. The cross-sectional area of bars are 20cm 2 for aluminium and 10cm 2 for steel. Assuming that the top and bottom supports are rigid, stress in Al and steel bars in N mm 2 when the temperature is 70 0 C. (Nearly ) Y a = 0 .70 × 10 5 N / mm 2 ⋅ Y s = 2 .1 × 10 5 N / mm 2 α a = 24 × 10 − 6 / ∘ C and α s = 12 . × 10 − 6 / ∘ C
The density of a substance at 0 o C is 10 g/c.c. and at 100°C its density is 9.7g/c.c. The coefficient of linear expansion of the substance is.
Express 0K on Fahrenheit scale
The steam point and the ice point of a mercury thermometer are marked as 80 0 and 20 0 . What will be the temperature in centigrade mercury scale when this thermometer reads 32 0
A centrigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers 176 0 F. What is the fall in temperature as registered by the Centigrade thermometer
The pressure of a gas filled in the bulb of a constant volume gas thermometer at 0 0 C and 100 0 C are 28.6 cm and 36.6 cm of mercury respectively. The temperature of bulb at which pressure will be 35.0 cm of mercury will be
A Fahrenheit thermometer reads 113 0 F while a faulty celsius thermometer reads 44 0 C. The correction to be applied to the celsius thermometer is
A fixed mass of an ideal gas is maintained at constant volume the pressure of the gas at triple point of water is ptr then thermodynamic temperature of the gas when the pressure is P
Which of the curves in figure represents the relation between celsius and Fahrenheit temperature?
If two temperatures differ by 25 degrees on celsius scale, the difference of temperature on Fahrenheit scale is
Two rods, one of aluminium and the other made of steel, having initial length l 1 and l 2 respectively are connected together to form a single rod of length l 1 + l 2 . The coefficient of linear expansion for aluminium and steel are α a and α s respectively. If the length of each rod increases by the same amount when their temperature t 0 C are raised by , then find the ratio l 1 l 1 + 2
A brass disc fits simply in a hole of a steel plate. the disc from the hole can be loosened if the system
A clock with a metal pendulum beating seconds keeps correct time at 0°C . If it loses 12.5s a day at 25°C , the coefficient of linear expansion of metal pendulum is
The ratio among coefficient of volume expansion, superficial expansion and linear expansion is
Two holes of unequal diameters d 1 and d 2 d 1 > d 2 are cut in metal sheet. If the sheet is heated
The coefficient of linear expansion of steel and brass are 11 × 10 − 6 / o C and 19 × 10 − 6 / o C respectively. If their difference in lengths at all temperatures has to be kept constant at 30 cm, their lengths at 0 0 C should be
A metal sheet with a circular hole is heated. The hole
The correct value of 0 ° C on the Kelvin scale is
When the temperature of a rod increases from t to t + Δt , its moment of inertia increases from I to I + ΔI . If be the coefficient of linear expansion of the rod, then the value of ΔI I is
The coefficient of linear expansion of crystal in one direction is α 1 and that in every direction perpendicular to it is α 2 . The coefficient of cubical expansion is
A metal rod has a length of 1m at 30 ∘ C . α of metal is 2.5 × 10 − 5 / 0 C . The temperature at which it will be shortened by 1mm is
Two bars of copper having same length but unequal diameter are heated to the same temperature. The change in length will be
If a thermometer reads freezing point of water as 20°C and boiling point as 150°C. What will thermometer read when the actual temperature is 60°?
A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown. The metal X has a higher coefficient of expansion compared to that for metal Y. When bimetallic strip is placed in a cold bath
The volume of a metal sphere increases by 0.24% when its temperature is raised by 40 o C . The coefficient of linear expansion of the metal is
When a metal sphere is heated, its volume increases by 50c.c and its surface area increases by 25cm 2 . Its initial radius is
If a thermometer reads freezing point of water as 20 o C and boiling point as 150 o C , how much will thermometer read when the actual temperature is 60 o C ?
A metal rod of Young’s modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by t o C , the linear stress developed in it is
The coefficient of linear expansion of a metal is 1 x 10 -5 / o C. The percentage increase in area of a square plate of that metal when it is heated through 100 o C is
A solid sphere and a hollow sphere of same material have same mass. When they are heated by 50 o C, increase in volume of solid sphere is 5 cc. The expansion of hollow sphere is
The length of a steel rod is 5 cm longer than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are 12 x 10 -6 / o C and 18 x 10 -6 / o C respectively)
A glass flask of volume 360 cc. is completely filled with a liquid of real expansion coefficient 17 .7 × 10 − 5 / 0 C α glass = 9 × 10 − 6 / 0 C . When it is heated from 20 o C to 100 o C, volume of liquid expelled is
A vessel of volume ‘V’ is half filled with a liquid of density ‘2d’ and coefficient of apparent expansion ‘x’ and the other half is filled with another liquid of density ‘d’ but coefficient of apparent expansion ‘2x’. The temperature is risen through 2 o C , the mass of the liquid expelled out
The temperature at which density of a liquid is 1% less than that of its density at 0 o C ( γ is coefficient of absolute expansion)
A cube continues to float in water when the system is heated from 10 o C to 40 o C. Buoyant force acting on it
How much mercury must be placed inside a glass flask, having an internal volume 300 cc so that the volume of the remaining space inside the flask remains constant at all temperatures ? γ Hg = 1 .8 × 10 − 4 0 C − 1 , α g = 1 × 10 − 5 0 C − 1
A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown. The metal X has a higher coefficient of expansion compared to that for metal Y. When bimetallic strip is placed in a cold bath
The volume of a metal sphere increases by 0.24% when its temperature is raised by 40 o C . The coefficient of linear expansion of the metal is
When a metal sphere is heated, its volume increases by 50c.c and its surface area increases by 25cm 2 . Its initial radius is
If a thermometer reads freezing point of water as 20 o C and boiling point as 150 o C , how much will thermometer read when the actual temperature is 60 o C ?
A correct thermometer in Fahrenheit is introduced in a water bath along with a Celsius thermometer. The readings observed are 86 o F and 32 o C. The correction to be made to the Celsius reading will be
A thermometer is graduated in millimeters. It registers –3 mm when the bulb of thermometer is in pure melting ice and 22 mm when the thermometer is in steam at a pressure of 1 atmosphere. The temperature in o C when the thermometer registers 13 mm is
If two rods of length L and 2L having coefficients of linear expansion α and 2 α respectively are connected so that total length becomes 3L. The average coefficient of linear expansion of the composite rod equals:
The length of a steel rod is 5cm more than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (Coefficient of linear expansion for steel and brass are 12 x 10 -6 / o C and 18 x 10 -6 / o C respectively)
pendulum clock goes slow by 10 sec/day when atmospheric temperature is 40°C and goes fast by 8 sec/day when temperature is 20°C. The temperature at which the clock gives correct time is
Two rods of same mass and same length lo but having different coefficient of expansions α and 3 α are joined at P (see figure). System is placed on frictionless surface. If temperature of whole system is changed by ∆ T , the displacement of junction point is
A clock pendulum made of invar has a period of 0.5s at 20 0 C . If the clock is used in a climate where average temperature is 30 0 C , approximately. How much fast or slow will the clock run in 10 6 s α i n var = 1 × 10 − 6 / 0 C ?
A metal rod of Young’s modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by the linear stress developed in it is
A faulty thermometer reads freezing point and boiling point of water as − 5 0 C a n d 95 0 C respectively. What is the correct value of temperature as it reads 60 0 C on faulty thermometer?
A bimetallic strip consists of metals X and Y. it is mounted rigidly at the base as shown. The metal X has a higher coefficient of expansion to that for metal Y. when the bimetallic strip is place in a cold bath
Two rods of lengths l 1 and l 2 are made of materials whose coefficients of linear expansion are α 1 and α 2 respectively. If the difference between the two lengths is independent of temperature, then
There is a rectangular metal plate in which two cavities in the shape of rectangle and circle are made, as shown with dimensions. P and Q are the centres of these cavities. On heating the plate, which of the following quantities increase?
A clock pendulum made of invar has a period of 0.5s at 20 0 C . If the clock is used in a climate where average temperature is 30 0 C , approximately. How much fast or slow will the clock run in 10 6 s α invar = 1 × 10 − 6 / 0 C ?
Two rods having length l 1 and l 2 , made of materials with the linear coefficient of expansion α 1 and α 2 , were welded together. The equivalent coefficient of linear expansion for the composite rod is
Two identical beakers with negligible thermal expansion are filled with water to the same level at 4 o C. If one says A is heated while the other says B is cooled, then
A metal rod of Young’s modulus Y and coefficient of thermal expansion a is held at its two ends such that its length remains invariant. If its temperature is raised by t 0 C , the linear stress developed in it is
A steel rod of length 1m is heated from 25 0 C to 75 0 C keeping its length constant. The longitudinal strain developed in the rod is (Given : Coefficient of linear expansion of steel = 12 × 10 − 6 / 0 C )
A difference of temperature of 25 0 C is equivalent to a difference of
A faulty thermometer reads freezing point and boiling point of water as − 5 0 C and 95 0 C respectively. What is the correct value of temperature as it reads 60 0 C on faulty thermometer?
A centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers 140 0 F . What is the temperature as registered by the centigrade thermometer?
If a graph is plotted taking the temperature in Fahrenheit along the Y-axis and the corresponding temperature in Celsius along the x-axis, it will be a straight line
A bimetallic strip consists of metals X and Y. it is mounted rigidly at the base as shown. The metal X has a higher coefficient of expansion to that for metal Y. when the bimetallic strip is place in a cold bath
A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10 0 C , and the coefficient of linear expansion of the metal of the rod is 2 × 10 − 6 per 0 C , the period of the pendulum will have percentage increase of
The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = aT , where a is a positive constant and T in 0 C . If the length of the rod is l at temperature 0 0 C , then the temperature at which the length will be 2 l is
Temperature remaining constant, the pressure of gas is decreased by 40%. The percentage change in volume
The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = aT , where a is a positive constant and T in 0 C . If the length of the rod is l at temperature 0 0 C , then the temperature at which the length will be 3 l is
A solid floats submerged in a liquid. When the liquid is heated, which of the following is most likely to happen?
Two rods, one of aluminium and the other made of steel, having initial lengths l 1 and l 2 are connected together to form a single rod of length l 1 + l 2 .The coefficient of linear expansion for aluminium and steel are α a and α s respectively. If the length of each rod increases by the same amount when their temperature are raised by t° C, then find the ratio l 1 l 1 + l 2
Expansion during heating :
Absolute coefficient of expansion of a liquid is 10 times the volume coefficient of expansion of the vessel. Ratio of absolute and apparent expansion of liquid is :
When water is heated from 0°C to 10°C, its volume :
Coefficient of apparent expansion of mercury in a glass vessel is 153 x 10 -6 / o C and in a steel vessel is 144 x 10 -6 /°C. If α for steel is 12 x 10 -6 /°C, then that of glass is
It is required to prepare a steel metre scale such that the millimetre intervals are to be accurate within 0.0005 mm at a certain temperature. Maximum temperature variation allowable during the rulings of millimetre marks is : ( α steel = 13 . 22 × 10 – 6 / C o )
A brass sphere is heated to give it a small increase of temperature. Percentage change will be maximum in its :
A U-tube contains mercury with one limb at 0°C and the other at 100°C. The heights of the mercury columns are 60 cm at 0°C and 62 cm at 100°C. The coefficient of volume expansion of mercury per °C is :
A rod of length 40 cm has the coefficient of linear expansion α 1 = 6 × 10 – 6 / C o . The other rod has coefficient of linear expansion, α 2 = 4 × 10 – 6 / C o . If the difference in their lengths at all temperatures remains the same, the length of the other rod is:
The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = aT , where a is a positive constant and T in 0 C . If the length of the rod is l at temperature 0 0 C , then the temperature at which the length will be 3 l is
A vessel of volume V is half filled with a liquid of density 2d and coefficient of apparent expansion 2x. The other half is filled with another liquid of density ‘d’ and coefficient of apparent expansion ‘x’. When temperature is increased by 4 o C, mass of liquid expelled is
Coefficient of apparent expansion of same liquid in glass vessel is ‘G’ and in silver vessel is ‘S’. If coefficient of linear expansion of glass is ‘A’, coefficient of linear expansion of silver is
A long vessel having coefficient of linear expansion ‘α’ contains a liquid up to certain height. On heating , it is found that the height of liquid column remains constant at all temperature. Volume coefficient of Expansion of liquid is
When copper rod of length ‘ l ’ is heated by ∆ t , percentage increase in length is 1% . If copper plate of area ( 2 l × l ) is heated by ( 2 ∆ t ) , percentage increase in area is
When a solid metal sphere is heated, its volume increases by 50cc and surface area increases by 25 c m 2 . Radius of that sphere is
A vessel contains a liquid filled with 1/5 th of its volume. Another vessel contains same liquid up to 1/4 th of its volume. In both cases, the volume of empty space remains constant at all temperatures. Then ratio of coefficient of linear expansions of two vessels is
For a crystal, coefficient of linear expansion in one direction is 12 × 10 − 6 / 0 C and along the 2 mutually perpendicular directions are 6 × 10 − 6 / 0 C , 6 × 10 − 6 / 0 C . Coefficient of cubical expansion of that crystal is
A pendulum clock runs 10 seconds slow per day when room temperature is 30 ∘ C . It runs 20 seconds fast per day when room temperature is 15 ∘ C . The temperature at which clock shows correct time is
Length of steel rod is 50 cm more than length of brass rod at all temperatures . If α st = 12 × 10 − 6 / ∘ C , α B r = 18 × 10 − 6 / ∘ C . Length of steel rod is
A steel stopper snuggly fits in the hole of brass plate. To remove the stopper easily, the system
A liquid occupies 1/3 rd of a vessel at a particular temperature. The volume of unoccupied part remains constant at all temperatures. If α is coefficient of linear expansion of vessel and ‘ γ ’ is coefficient of real expansion of liquid, then
A thin rod and a thick rod same length and same metal are heated. A) If both are heated by same temperature difference, both will expand equally B) If both are heated by giving equal amounts of heat, thick rod expands more.
If coefficient of real expansion γ R is 3 % more than coefficient of apparent expansion, coefficient of linear expansion of material is
A bimetal strip made of brass and steel is straight at room temperature. When it is heated , it bends
Coefficient of apparent expansion of same liquid in glass vessel is ‘G’ and in silver vessel is ‘S’. If coefficient of linear expansion of glass is ‘A’, coefficient of linear expansion of silver is
A long vessel having coefficient of linear expansion ‘ α ‘ contains a liquid up to certain height. On heating, it is found that the height of liquid column remains constant at all temperature. Volume coefficient of expansion of liquid is
A rotating solid metal sphere is heated by 100 ∘ C . If α = 2 × 10 − 5 / 0 C then percentage change in its moment of inertia is
A vessel having coefficient of cubical expansion γ g contains liquid Of coefficient of real expansion r R up to certain level. When Vessel Is heated, match column I and column II. Column – I Column – II a γ g < γ R p liquid level rises continuously from beginning b γ g = γ R q liquid level falls continuously from beginning c γ g > γ R r liquid level remains same d γ g = 0 s liquid level first falls and then rises a b c d 1 s r q p 2 s r p q 3 q r s p 4 r q p s
The graph drawn with absolute temperature T on X-axis and pressure of an ideal gas P on Y-axis is as shown. As the temperature of the gas increases, the volume
Two 10.0 m long iron rails are separated by 1.0 cm. The value of α for iron is 1 × 10 − 5 / C ° . If the initial temperature is 0 ° C , the temperature at which the rails will touch is
Two metal rods A and B have lengths L 1 and L 2 and same radius. The coefficients of linear expansions of the materials of A and B are α 1 and α 2 respectively. If the two rods are joined to form a longer rod of length L 1 + L 2 , the equivalent coefficient of linear expansion of the composite rod will be
A horizontal narrow glass tube of 100 cm length closed at both ends contains a gas divided in to equal parts by a mercury pellet 10 cm long with the system at 127 ° C . Now one side is heated to 227 ° C , while the other side is cooled to 27 ° C . The distance moved by the mercury pellet in cm is nearly (neglect expansion of glass and mercury)
List – I List – II a Isotropic solids e Expands on melting b Ice f Equal expansion in all directions c Anisotropic solids g contracts on melting d Copper h unequal expansion in different directions a b c d 1 f h g e 2 f g h e 3 g h e f 4 e f g h
The temperature corresponding to the mid-point of the fundamental interval in the Fahrenheit scale expressed in Kelvin scale is
A cylindrical metal rod of length L 0 is shaped into a ring with a small gap as shown in figure. On heating the system.
Three temperatures are given A = 10 ° F , B = 10 ° C and C = 10 K . Which of the following is correct ascending order of these temperatures?
A sample of an ideal gas is heated so that its volume as well as pressure are doubled. The percent increase in its absolute temperature must be
For one mole of an ideal gas, the temperature of the gas expressed in centigrade scale is plotted on the X – axis and the product “PV” is plotted on the Y – axis. The graph is
Two 10.0 m long iron rails are separated by 1.0 cm. The value of α for iron is 1 × 10 − 5 / C ° . If the initial temperature is 0 ° C , the temperature at which the rails will touch is
It is said that the original Centigrade thermometer designed by Celsius had upper fixed point (steam point) as 0° and lower fixed point (ice point) as 100° . This temperature scale we label as Tuglak scale and temperatures in this scale represented by °T . A temperature of 50 ° T is equivalent to x ° C , then x is
The temperature corresponding to the mid-point of the fundamental interval in the Fahrenheit scale expressed in Kelvin scale is
A clock has a long pendulum made of brass. Due to a temperature change of 20 ° C the time period of oscillation of the pendulum is found to change by 0.02 %. The coefficient of linear expansion of brass is
A rectangular metal plate has two circular holes drilled in it in a symmetric manner as shown in the figure. If the metal plate is uniformly heated, which of the shown distances “A”, “B” or “C” increases?
Three temperatures are given A = 10 ° F , B = 10 ° C and C = 10 K . Which of the following is correct ascending order of these temperatures?
Examine the two statements A and B, and choose the correct option from those given below. A: For a given gas at constant pressure, the density is directly proportional to its absolute temperature. B: For a given gas at constant temperature, the density is inversely proportional to its pressure.
For one mole of an ideal gas, the temperature of the gas expressed in centigrade scale is plotted on the X – axis and the product “PV” is plotted on the Y – axis. The graph is
If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young’s modulus of copper may be taken to the equal to that of iron) is
Two rods of different materials having coefficients of thermal expansion α 1 and α 2 and Young’s moduli Y 1 and Y 2 are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided
A wire of cross-sectional area A at temperature T is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature ( T − ΔT ) , what tension is developed in the wire ? The coefficient of linear expansion is α and Young’s modulus of the wire is Y
A steel scale measures the length of a copper rod as L cm when both are at 20 o C, the calibration temperature for the scale. If the coefficients of linear expansion for steel and copper are α s and α c respectively, what would be the scale reading (in cm) when both are at 27 o C ?
A pendulum clock is 5 second fast at temperature of 15 o C and 10 second slow at a temperature of 300 o C At what temperature does it give the correct time ?
The apparent coefficient of expansion of a liquid, when heated in a copper vessel is C and when heated in a silver vessel is S. If A is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is
A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The coefficients of linear expansion of the two metals are α C and α B . On heating, the temperature of the strip goes up by ∆ T and the strip bends to form an arc of radius of curvature R. Then R is
The coefficient of linear expansion of glass is α g / ∘ C and cubical expansion of mercury is γ m / ∘ C . The volume of the bulb of mercury thermometer at 0°C is V 0 and cross section of the capillary is A o . What is the length of mercury column in capillary at T ∘ C , if the mercury just fills the bulb at O°C ?
At temperature To, two metal strips of length /o and thickness d is bolted so that their ends coincide. The upper strip is made up of metal A and have coefficient of expansion α A and lower strip is made up of metal B with coefficient of expansion α B α A > α B . When temperature of their blastic strip is increased from To to T 0 + ΔT , one stop becomes longer than the other and the blastic strip is bend in the form of a circle as shown in . The radius of curvature fi of the strip is
A glass flask of volume 1 litre is fully filled with mercury at 0°C. Both the flask and mercury are now heated to 100°C. If the coefficient of volume expansion of mercury is 1 ⋅ 82 × 10 − 4 / ∘ C , volume coefficient of linear expansion of glass is 10 x 10 – 6 /°C, the amount of mercury which is spilled out is
A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are γ 1 and γ 2 respectively. If the temperature of both mercury and metal are increased by an amount ΔT , the fraction of the volume of the metal submerged in mercury changes by the factor
45 gm of alcohol are needed to completely fill up a weight thermometer at 15°.C. The weight of alcohol which will overflow when the weight thermometer is heated to 33°C is (Take γ a = 121 × 10 − 5 / ∘ C )
A weight thermometer contains 20 gm of mercury at 0°C and when its temperature is raised to 100°C. 315 gm of mercury is expelled. If the coefficient of linear expansion of glass is 0.0000066 per °C, the coefficient of absolute expansion of mercury is
A steel wire of length 2o cm and uniform cross-section 1mm 2 is tied rigidly at both the ends. The temperature of the wire is altered from 40°C to 20°C. Coefficient of linear expansion for steel α =1.1 x 10 -5 /°C and f for steel is 2 .0 x 10 11 N/m 2 . The change in tension of the wire is
A metallic bar is heated from 0°C to 100°C. The coefficient of linear expansion is 10 -5 K -1 . What will be the percentage increase in length ?
A rectangular block is heated from 0°C to 100°C. The percentage increase in its length is 0.10%. What will be the percentage increase in its volume ?
When a rod is healed but prevented from expanding, the stress developed is independent of
A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C ? (Given : α for steel =11 x10 -6 per °C and α for Cu = 17 x 10 -6 per °C)
Two rods of lengths l 1 and l 2 are made of materials whose coefficients of linear expansions are α 1 and α 2 . If the difference between two lengths is independent of temperature.
A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10°C, and the coefficient of linear expansion of the metal of the rod is 2 x 10 -6 per °C, the period of the pendulum will have percentage increase of
The density of water at 20°C is 998 kg/m 3 and that at 40°C is 992 kg/m 3 . The coefficient of cubical expansion of water is
A glass flask of volume 1000 cm 3 is completely filled with mercury at 0°C. The coefficient of cubical expansion of mercury is 182 x 10 -6 /°C and that of glass is 30 x 10 -6 /°C. If the flask is now placed in boiling water at 100°C, how much mercury will overflow ?
Two rods one of aluminum length I 1 , having coefficient of linear expansion α 1 and other of steel of length l 2 having coefficient of linear expansion α 2 are joined end to the end. The expansion in both the rods is same for the same variation in temperature. Then the value l 1 / l 1 + l 2 is
A solid cube with coefficient of linear expansion o floats in a liquid whose coefficient of volume expansion is γ . When both the solid and liquid are heated, then the solid does not sink or lift when
The coefficient of apparent expansion of mercury in a glass vessel is 153 x 10 – 6 / 0 C and in a steel vessel is 144 x 10 – 6 / ° C. If α for steel is 12 x 10 -6 /°C, then that of glass is
Above neutral temperature, thermo e.m.f.
A thermocouple is made from two metals, Antimony and Bismuth. lf one junction of the couple is kept hot and the other is kept cold, then electric current wiII
Which of the graphs shown in fig. represents the variation of thermo emf (e) of a thermocouple with temperature T of the hot Junction ? The cold junction is maintained at 0°C.
The thermo e.m.f. of a thermocouple varies with the temperature θ of the hot junction as E = aθ – bθ 2 volt where the ratio (a / b) is 700°C. If the cold junction is kept at 0°C, then the neutral temperature is
The absolute zero temperature in Fahrenheit scale is
On which of the following scales of temperature, the temperature is never negative?
A clock with a metal pendulum beating seconds keeps correct time at 0°C. If it loses 12.5 s a day at 25°C, the coefficient of linear expansion of metal pendulum is
A bimetallic strip is made of aluminium and steel ( α Al > α steel ) . On heating, the strip will [NCERT Exemplar]
Two uniform brass rods A and B of lengths l and 2l and radii 2r and r respectively are heated to the same temperature. The ratio of the increase in volume of A to that of B is
The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is α . The sphere is heated a little by a temperature ∆ T, so that its new temperature is T + ∆ T. The increase in the volume of the sphere is approximately, {NCERT Exemplar]
The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel, it is S. If A is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is
Directions This question consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following four responses. Assertion : In summers, a metallic scale will read more than the actual. Reason : In summers, length of metallic scale increases.
A copper rod of length 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is (Here α c u = 17 × 10 – 5 p e r K a n d α A l = 22 × 10 – 5 p e r K ) . [NEET (National) 2019]
The coefficient of volume expansion of glycerine is 49 × 10 – 5 ∘ C – 1 . What is the fractional change in density for a 30 o C rise in temperature?
Coefficient of linear expansion of brass and steel rods are ( α 1 and α 2 . Lengths of brass and steel rods are l 1 and l 2 , respectively. If ( l 2 – l 1 ) is maintained same at all temperatures, which one of the following relations holds good? [NEET 2016]
Two metal rods of lengths L 1 and L 2 and coefficients of linear expansion α 1 and α 2 respectively are welded together to make a composite rod of length (L 1 + L 2 ) at 0°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET 2015]
Water is heated from 0°C to 100°C, then its volume. [KCW 2015]
In anomalous expansion of water, at what temperature, the density of water is maximum? [KCET 2014]
A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L, α and Y respectively denote the length of the rod, coefficient of linear thermal expansion and Young’s modulus of its material, then for an increase in temperature of the rod by ∆ T, the longitudinal stress developed in the rod is [AMU 2014]
A horizontal uniform tube, open at both ends, is containing a liquid of certain length at some temperature. When the temperature is changed, the length of the liquid in the tube is not changed. If α is the coefficient of linear expansion of the material of the tube and γ is the coefficient of volume expansion of the liquid, then [EAMCET 2013]
Two temperature scales A and B are related by A – 42 100 = B – 72 220 . At which temperature, two scales have the same readings? [WB JEE 2011]
There is some change in length when a 33000 N tensile force is applied on a steel rod of area of cross- section 10 -3 m -2 . The change of temperature required to produce the same elongation, if the steel rod is heated is (Take, modulus of elasticity is 3 x 10 11 Nm -2 and coefficient of linear expansion of steel is 11 X 10 -5 / 0 C)
The equation of state corresponding to 8 g of O 2 is
