Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at a temperature To, while box B contains one mole of helium at temperature (7/3) T 0 . The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then the final temperature of the gases, T f , in terms of T 0 is :
The plot that depicts the behavior of the mean free time τ ( time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)
Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecular of the gas B has an additional vibrational mode, and have a mass m 4 . The ratio of the specific heats ( C V A and C V B ) of gas A and B , respectively is :
What is the ratio of the total energy of all the molecules of one mole of O 2 to the total energy of all the molecules of two moles of helium at the same temperature?
If γ = C P C V , C P being the molar specific heat of a gas at constant pressure and C V its molar specific heat at constant volume, number of degrees of freedom of a molecule of gas can be expressed as:
At room Temperature , a diatomic gas is found to have an rms speed of 1930 m/s. The gas is
The ratio of the specific heats C p C v = γ in terms of degrees of freedom (n) is given by
When the temperature of a gas is raised from 30° C to 90° C, the percentage increase in the r.m.s. velocity of the molecules will be :
Nitrogen gas is at 300ºC temperature. The temperature (in K) at which the rms speed of a H 2 molecule would be equal to the rms speed of a nitrogen molecule, is . (Molar mass of N 2 gas 28 g).
The graph drawn between pressure and volume in Boyle’s law experiment for same mass of gas is shown in figure for different molecular weights, then
Two identical cylinders at same temperature contain Helium at 2.5 atm and Argon at 1 atm respectively. What will be the pressure if both the gases are filled in one of the cylinders ?
A sample of ideal gas is heated from 27 0 C to 327 0 C, initial average kinetic energy of the molecules was E. What will be the average kinetic energy after heating ?
Increase in temperature of a gas filled in a container would lead to
A rigid container contains a mixture of one mole of nitrogen to two moles of He at 0 o C . Then the ratio of rotational kinetic energy per N 2 molecule to the transational kinetic energy per He molecule is
It is required to double the pressure of a gas in a rigid container at 27 0 C by heating it. To what temperature the gas should be raised?
An ideal gas has a volume of 3 V at 2 atmosphere pressure. Keeping the temperature constant, its pressure is doubled. The volume of the gas will be:
Two molecules of a gas have speeds of 9 x 10 6 ms – l and 1 × 10 6 ms – 1 respectively. What is the root mean square speed of these molecules?
The temperature at which the root mean square velocity of the gas molecules would become twice of its value at O o C is
A sample of oxygen is compressed to half of its original volume at constant temperature. If the rms velocity of gas molecules was originally C their new rms velocity is
At a certain temperature, the rms velocity for O 2 is 400 ms – 1 . At the same temperature, the rms velocity for H 2 molecules will be
Two perfect gases at absolute temperature T 1 a n d T 2 are mixed. There is no loss of energy. Find the temperature of the mixture if the masses of the molecules are m m 1 a n d m 2 a n d t h e n u m b e r o f m o l e c u l e s i n t h e g a s e s n 1 a n d n 2 . Then final temperature of the mixture is
Figure shows the pressure P versus volume V graphs for a certain mass of a g as at two constant temperature T 1 and T 2 . Which of the following inference is correct?
The densities at points A and B are ρ 0 and 3 ρ 0 2 . Find the value of x on P-axis.
Average kinetic energy of a gas depends on
If I is the moment of inertia of a rigid diatomic molecule, then calculate the angular mean square velocity of a rotating molecule in the gas sample, if the temperature is T. (k = Boltzmann constant)
The root mean square speed of oxygen molecules ( O 2 )at a certain absolute temperature is V. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the rms speed would be
Two vessels each of volume ‘V’ contains ideal gases at pressure P, temperature T. They are connected by a narrow pipe without changing temperature of 1 st gas . Temperature of 2 nd vessel is increased to 2T. Then , common pressure of gases is
If an air bubble rises from the bottom of a mercury tank to the top, its volume becomes 3 times. If atmospheric pressure is 75 cm of mercury, depth of mercury tank is
A closed hollow insulated cylinder is filled with gas at 0 o C and contains Insulated piston of negligible mass and negligible thickness at middle Point. Without changing temperature on one side, temperature on other Side is heated to 100 o C. If piston moves by 5 cm, Length of hollow cylinder is
Graph is drawn between pressure and volume for a gas at two different temperature T 1 and T 2 as shown , Then
The root mean square velocity of the molecules in a sample of helium is(5/7) times the root mean square velocity of the molecules in a sample of hydrogen at temperature 0 o C The temperature of helium is
What is the rms speed of helium gas molecules at STP?
A vessel of volume V contains an ideal gas absolute temperature T and pressure P. The gas is allowed to leak till its pressure falls to P’. Assuming that the temperature remains constant during leakage, the number of moles of gas that have leaked is
The rms speed of oxygen at room temperature is about 500m/s The speed of hydrogen at the same temperature is about
The temperature at which the rms speed of Oxygen molecules is sufficient for escaping from Earth, is
The gas constant for a molecule is (terms have usual meaning) a) K b) R/N c) R/NT d) R/m
In the equation PV = constant, the numerical value of constant depends upon a) Temperature b) Mass of the gas c) System of units used d) Nature of the gas
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
Figure shows two flasks connected to each other. The volume of the flask 1 is twice that of flask 2. The system is filled with an ideal gas at temperatures 100 K and 200 K, respectively. If the mass of the gas in flask 1 is m, then what is the mass of the gas in flask 2?
If the rms velocity of oxygen molecule at certain temperature is 0.5 km/s, the rms velocity for hydrogen molecule at the same temperature will be:
An ideal gas is initially at temperature T and volume V. Its volume is increased by ΔV due to an increase in temperature ΔT pressure remaining constant. The quantity δ = ΔV / ( VΔT )
The figure below shows the plot of PV nT versus P for oxygen gas at two different temperatures. Read the following statements concerning the above curves ; (i) The dotted line corresponds to the ‘ideal’ gas behaviour. (ii) T 1 > T 2 (iii) The value of PV nT at the point where the curves meet on the y-axis is the same for all gases. Which of the above statement is true
The molecules of a given mass of a gas have r.m.s. velocity of 200 m s – 1 at 27 ° C and 1 . 0 × 10 5 N m – 2 pressure. When the temperature and pressure of the gas are respectively, 127 ° C and 0 . 05 × 10 5 N m – 2 the r.m.s. velocity of its molecules in m s – 1
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. the ratio of the average rotational kinetic energy per O 2 molecule to that per N 2 molecule is
The total KE of all the molecules of helium having a volume V exerting a pressure P is 1500J The total KE in joule of all the molecules of N 2 having the volume 2V and exerting a pressure 2P is
An ideal gas equation can be written as P = ρRT M 0 where ρ and M 0 are respectively,
The root mean square velocity of the gas molecules is 300 m/s. What will be the root mean square speed of the molecules if the atomic weight is double and absolute temperature is halved?
The kinetic energy of molecules of a gas per litre of its volume is found to be 300 joules. Then its pressure will be
Two vessels A and B having equal volume contain equal masses of hydrogen in A and helium in B at 300 K. Then mark the correct statement
An ideal gas is expanded according to the T-V graph shown in figure. Then pressure of the gas
The root mean square velocity at room temperature of an ideal diatomic gas is approximately calculated to be 1918 m/s. The gas may be
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is
In a cylinder there are 60 g Ne and 64 g O 2 . If pressure of mixture of gases in cylinder is 30 bar in this cylinder then partial pressure of O 2 is (in bar)
N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel at temperature T. The mean square of the velocity of molecules of gas B is v 2 and the mean square of x component of the velocity of molecules of gas A is w 2 . The ratio is
The mass of H 2 molecule is 3.32 × 10 –24 g. If 10 23 Hydrogen molecules per second strike 2 cm 2 of wall at an angle of 45° with the normal, when moving with a speed of 10 5 cm/s, the pressure exerted on the wall is nearly.
A gas mixture consists of 2.0 moles of Oxygen and 4.0 moles of Neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system, (Oxygen has two rotational modes)
1 mole of H 2 gas is contained in a box of volume V = 1.00 m 3 at T = 300 K. The gas is heated to a temperature of T = 3000 K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)
1 mole of an ideal gas is contained in a cubical volume 'V'. ABCDEFGH at 300k. One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At a given time
Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass . The ratio of the specific heats of gas A and B, respectively is :
At what temperature is V r m s of hydrogen molecules equal to the escape speed from the Earth’s surface?
Mean free path of the molecules of an ideal gas at pressure p and temperature T is λ . What will be the mean free path of the same gas at pressure p/2 and temperature T?
A rigid container contains some ideal gas. Mean free path of the molecules is λ . If temperature of the gas is now doubled, mean free path of the molecules will be
15 Joule of heat is supplied to a given amount of hydrogen gas at constant volume and its temperature is raised by 5 o C . What amount of heat should be supplied to the same gas at constant pressure to raise its temperature by 5 o C ?
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? Given: Mass of oxygen molecule (m) : 2 . 76 x 10 – 26 kg ; Boltzmann’s constant k B = 1.38x 10 – 23 JK – 1 )
A gas mixture consists of 2 moles of O 2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio C p C v of the mixture is
Statement I : The number of degrees of freedom of triatomic non linear molecule is 6. Statement II : Triatomic nonlinear molecules have three translational degrees of freedom and three rotational degrees of freedom.
Statement I : The rms velocity of gas molecules is doubled, when temperature of gas becomes four times. Statement II : c ∝ T
lf the ratio of specific heat of a gas at constant pressure to that at constant volume is γ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is
When I mole of a monatomic gas is mixed with 3 moles of a diatomic gas, the value of adiabatic exponent γ for the mixture is:
N moles of an ideal diatomic gas are in a cylinder at temperature T. suppose on supplying heat to the gas, its temperature remain constant but n moles get dissociated into atoms. Heat supplied to the gas is
An insulator container contains 4 moles of an ideal diatomic gas at temperature T. Heat Q is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms but temperature of the gas remains constant. Then
At constant pressure V 1 and V 2 are the volumes of a given mass of a gas at temperature 27 o C and 54 o C respectively, then the ratio V 1 V 2 will be
The molar heat capacity in a process of a diatomic gas if it does a work of Q 4 when a heat of Q is supplied to it is
Suppose ideal gas equation follows VP 3 = constant. Initial temperature and volume of the gas are T and V respectively. If gas expand to 27V then its temperature will become
In order to increase the volume of a gas to 3 times at constant pressure at 40 o C , the final temperature should be
A vessel containing 0.1 m 3 of air at 76 cm of Hg is connected to an evacuated vessel of capacity 0.09 m 3 . The resultant air pressure 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 ratio A and B will be
The molecules of a given mass of a gas have root mean square speeds of 100 ms – 1 at 27 0 C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127 0 C and 2.0 atmospheric pressure?
Two perfect monoatomic gases at absolute temperatures T 1 and T 2 are mixed. There is no loss of energy. The masses of the molecules are m l and m 2 .The number of molecules in the gases are n 1 and n 2 .The temperature of the mixture is
Four molecules of a gas have speeds 1,2,3 and4 km s – l respectively. The value of rms speed of the molecules is (in km s – 1 )
The temperature at which rms velocity of helium molecules is equal to the rms velocity of hydrogen molecules at NTP is
An ideal gas is heated at constant volume until its pressure doubles. Which one of the following statements is correct?
20 g of a gas occupies a 100 cc volume at 10 5 dyne/cm 2 . If during an isothermal process, the pressure is changed to 10 4 dyne/cm2, the volume of the gas in cc will be:
If the rms velocity of oxygen molecule at certain temperature is 0.5 km/s, the rms velocity for hydrogen molecule at the same temperature will be:
A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature ‘T’. Neglecting all vibrational mode, the total internal energy of the system is
The air tight and smooth pistons of a cylindrical vessel are connected with a string, as shown. Initially, pressure and temperature of the gas are P 0 and T 0 . The atmospheric pressure is also P 0 . At a later time. tension in the string is 3 8 P 0 A where A is the crosssectional are of the cylinder. At this time, the temperature of the gas has become:
In which of these diagrams, density of an ideal gas remains constant?
The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume?
The pressure P for a gas is plotted against its absolute temperature T for two different volumes V 1 and V 2 , where V 1 > V 2 . If P plotted on Y-axis and T on X-axis, then
A perfect gas at 27 0 C is heated at constant pressure to 627 0 C . if original volume of gas at 27 0 C is V, then volume at 627 0 C .
Real gases obey gas laws at
What is the rms speed of helium gas molecules at STP?
Oxygen is 16 times heavier than hydrogen .If mean Kinetic energy of Oxygen molecules at a certain temperature is E, then the mean Kinetic energy of hydrogen molecules at the same temperature is
In order to increase the temperature of the gas filled in a closed vessel by 1 o C,its pressure is increased by 0.4%.The initial temperature of the gas is
If the root mean square velocity of the molecules of gas enclosed in a vessel is doubled, the pressure becomes
If the temperature of a gas is increased ,while keeping pressure constant, then the number of gas molecules per unit volume
An enclosure of volume V contains a mixture of 8 g of oxygen, 14 g nitrogen and 22 g of carbon dioxide at absolute temperature T. The pressure of the mixture of gases is (R is universal gas constant)
Choose the only correct statement from the following
The ratio of specific heats of gas and number of degrees of freedom (f) has the relation
If the temperature of a gas is increased ,while keeping pressure constant, then the number of gas molecules per unit volume
In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as T q. A good estimate for q is
Oxygen is 16 times heavier than hydrogen .If mean Kinetic energy of Oxygen molecules at a certain temperature is E, then the mean Kinetic energy of hydrogen molecules at the same temperature is
In the given (V-T) diagram, what is the relation between pressure P 1 and P 2 ?
If the root mean square velocity of the molecules of gas enclosed in a vessel is doubled, the pressure becomes
An enclosure of volume V contains a mixture of 8 g of oxygen, 14 g nitrogen and 22 g of carbon dioxide at absolute temperature T. The pressure of the mixture of gases is (R is universal gas constant)
One of the two vessels of same capacity is filled with oxygen and other is with helium of same mass. Both gases are at same temperature. The ration of pressure of these gases is
In order to increase the temperature of the gas filled in a closed vessel by 1 o C,its pressure is increased by 0.4%.The initial temperature of the gas is
The Physical state of a gas is represented by P, V and T in Vessel A and 2P, V 4 2T in vessel B. The ratio of number of molecules in A and B is
Container of equal volumes are filled with hydrogen and oxygen gases of equal masses. At the same temperature the ratio of pressure exerted by the gases is
If two different gases are at the same temperature, which of the following must also be equal?
The rms speed of oxygen molecules (O 2 ) at a certain temperature T (degree absolute) is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, what is its rms speed in atomic form?
An insulated container containing monatomic gas of molar mass m is moving with a velocity v o . If the container is suddenly stopped, find the change in temperature.
If the molar specific heat of a gas at constant pressure is 7R/2, then the atomicity of gas is
The root mean square velocity of a perfect gas is
In fig., if process is isothermal then V C is
The molecules of a given mass of a gas have rms velocity of 200 ms – 1 at 27°C and 10 × 10 5 Nm – 2 pressure. When the temperature and pressure of the gas are respectively, 127°C and 0 . 05 × 10 5 Nm – 2 , the rms velocity of its molecules (in ms – 1 ) is
A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of 320 K, the upper and lower parts are in the ratio 4 : 1. The ratio will become 3 : 1 at a temperature of
The given curve represents the variations of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume?
I. The pressure of an ideal gas depends on the volume of the gas. II. The pressure of an ideal gas depends on the temperature of the gas. Which of the following statement(s) is/are correct?
Two identical containers joined by a small narrow pipe initially contain the same gas at pressure p 0 and absolute temperature T 0 . One container is now maintained at the same temperature while the other is heated to 2T 0 . The common pressure of the gases will be
A molecule of a gas has six degrees of freedom. Then the molar specific heat of the gas at constant volume is
Assertion : The molecules of a monoatomic gas have three degrees of freedom. Reason : The molecules of diatomic gas have five degrees of freedom.
An ideal gas initially at pressure 1 bar is being compressed from 30 m 3 to 10 m 3 volume and its temperature decreases from 320 K to 280 K, then find the value of final pressure of the gas. [AIIMS 2019]
The average kinetic energy per mole of hydrogen at given temperature is [MP PMT 2013]
One mole of a perfect gas in a cylinder fitted with a piston has a pressure ρ , volume V and temperature T . If the temperature is increased by 1 K keeping pressure constant, the increase in volume is
The figure below shows the plot of PV nT versus P for oxygen gas at two different temperatures. Read the following statements concerning the above curves ; (i) The dotted line corresponds to the ‘ideal’ gas behaviour. (ii) T 1 > T 2 (iii) The value of PV nT at the point where the curves meet on the y-axis is the same for all gases Which of the above statement is true
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at 200 K?
Four moles of hydrogen, 2 moles of helium and 1 mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?
The ratio of specific heats at constant pressure & volume of a gas is 9/7, then the number of degrees of freedom of the gas molecules is :
The mean free path of molecules of a gas, (radius r) is inversely proportional to
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given : Mass of oxygen molecule ( m ) = 2 . 76 × 10 – 26 kg , Boltzmann’s constant k B = 1 . 38 × 10 – 23 JK – 1
Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is
Increase in temperature of a gas filled in a container would lead to
The molar specific heats of an ideal gas at constant pressure and volume are denoted by C P a n d C υ respectively. If γ = C p C υ and R is the universal gas constant, then C υ is equal to
In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be
An insulated container containing monoatomic gas of molar mass m is moving with a velocity v 0 . If the container is suddenly stopped, find the change in temperature.
A gas mixture consists of 2 moles of O 2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
The Mean Free Path l for a gas molecule depends upon diameter, d of the molecule as
A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27 O C . Its density is : ( R = 8 . 3 Jmol – 1 K – 1 )
The mean free path for a gas, with molecular diamter d and number density n can be expressed as :
The average thermal energy for a mono-atomic gas is: ( K B is Boltzman constant and T, absoulte temperature)
If two balls of same metal weighing 5 g and 10 g strike with a target with the same velocity. The heat energy so developed is used for raising their temperature alone. Then the temperature will be highe
The r.m.s speed of particle of mass 5 × 10 − 17 k g The r.m.s speed of particle of mass in their random motion in air at NTP will be ( Boltzmann’s constant) K= in their random motion in air at NTP will be ( Boltzmann’s constant) K = 1.38 × 10 − 23 J / K
A light container having a diatomic gas enclosed within is moving with velocity V. mass of the gas is M and number of moles is n. the kinetic energy of gas with respect to ground is
The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 moles of hydrogen and 2 moles of oxygen at STP will be
The value of γ = C p C v for hydrogen, helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to,
If speeds of 10 molecules of a gas are 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 6 km/s, Then the most probable speed is
For certain amount of ideal gas if P be the pressure, V be the volume and E be the total translational kinetic energy. Then the value of E/PV is
A bubble rises from the bottom of a 70 m deep lake and on reaching the surface, its volume becomes (take atmospheric pressure as that of 10 m column of water and assume that the temperature is constant)
When the bulb of a standard gas thermometer is placed in melting ice, the pressure recorded is 83 cm, of mercury and when immersed in boiling water it is 113 cm of mercury. When the bulb is in another boiling liquid, the pressure recorded is 143 cm of mercury. Boiling point of the liquid is
Internal energy of two moles of an ideal gas at a temperature of 127 0 C is 1200 R . Then, the specific heat of the gas at constant pressure is
A ring shaped tube contains two ideal gases with equal masses and relative molar masses M 1 = 32 and M 2 = 28 . The gases are separated by one fixed partition p and another movable stopper S which can move freely without friction inside the ring. The angle α in equilibrium as shown in the figure (in degrees) is
A diatomic gas is at temperature T. The mean rotational kinetic energy of the gas molecules is
The average degrees of freedom per molecule of a gas are 6. The gas performs 25J of work when expands at constant pressure. The heat absorbed by the gas is
Two moles of an ideal gas with C P C V = 5 3 are mixed with 3 moles of another ideal gas with C P C V = 4 3 . The values of C P C V for the mixture is
If the mean free path of atoms of an ideal gas at pressure P is doubled, then the pressure of gas will become
If mass of molecule X is 4 times that of hydrogen. Then mean velocity of X is
If most probable speed of hydrogen molecules at 27 o C is V, then the rms speed of the molecules at 127 o C is
Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C P / C V value will be :
Velocity of sound in a mono atomic ideal gas at 27 o C is 330 m/s. Then the rms speed of molecules of that gas at same temperature is ( Take 5 = 2 .23 )
Two gases-argon(atomic radius 0.07nm, atomic weight 40) and xenon (atomic radius 0.1nm, atomic weight 140 ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closed to
An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time remains unchanged.
Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is :
To raise the temperature of a certain mass of gas by 50 0 C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100 0 C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to ideal)?
Match the C P / C V ratio for ideal gases with different type of molecules : Molecule Type C P / C V (A) Monatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3
Number of molecules in a volume of 4 c m 3 of a perfect mono atomic gas at some temperature T and at a pressure of 2 c m of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 × 10 − 14 e r g , g = 980 c m / s 2 , d e n s i t y o f m e r c u r y = 13 .6 g / c m 3 )
In Boyle’s experiment for a given gas at different temperatures, the graph drawn between pressure and density are straight lines as shown, then
If number of molecules of H 2 are double than that of O 2 , then ratio of kinetic energy of Hydrogen molecule to that of Oxygen molecule at 300 K is
Pressure exerted by a gas at constant temperature is
At a pressure of 24 × 10 5 dyne/cm 2 , the volume of O 2 is 10 litre and mass is 20 gm. The r.m.s velocity will be
The root mean square velocity of the molecules in a sample of Helium is 5/7th that of the molecules in a sample of Hydrogen. If the temperature of Hydrogen sample is 0 °C, then the temperature of the Helium sample is about
A molecule of gas collides with the wall of a container elastically. The expression of pressure due to the collision of molecules of velocity v x is (n=number of molecules per unit volume and m = mass per unit volume )
A molecule of gas collides with the wall of a container elastically. The expression of total pressure to the group of molecules having velocities along the X-axis is
For a gas if ratio of specific heats at constant pressure and volume is then value of degrees of freedom is
The rms velocity of a gas at a given temperature is 300 m/s. What will be the rms velocity of a gas having twice the molecular weight and half the temperature in K.
Three closed vessels A, B and C are at the same temperature T and contain gases which obey Maxwellian distribution of velocities. Vessel A contain O 2 , B only N 2 and C mixture of equal quantities of O 2 and N 2 . If the average speed of the O 2 molecules in the vessel A is V 1 , that of N 2 molecules in the vessel B is V 2 , the average speed of the O 2 molecules in vessel C is
The temperature of an ideal gas is increased from 27 0 C to 927 0 C. The rms speed of its molecules will become
In a jar having a mixture of H 2 and He
At what temperature will the rms speed of Oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given : Mass of oxygen molecule (m) = 2.76×10 –26 kg and Boltzmann’s constant k =1.38×10 –23 JK –1 )
A bulb contains one mole of Hydrogen mixed with one mole of Oxygen at temperature T. The ratio of r.m.s. values of velocity of Hydrogen molecules to that of Oxygen molecules, is
Calculate the number of degrees of freedom of molecules of Hydrogen in 1 cm 3 of Hydrogen gas at NTP,
For a gas at a temperature T the root mean square velocity v rms , the most probable speed v mp , and the average speed v av obey the relationship
Mean kinetic energy (or average energy) per gm mole of a monoatomic gas is given by
The average kinetic energy for the O 2 molecule (rigid rotator) is
Oxygen and Hydrogen are at the same temperature T. The ratio of the mean kinetic energy of Oxygen molecules to that of the Hydrogen molecules will be
A closed vessel A having volume V contains N 2 at pressure P and temperature T. Another closed vessel B having the same volume V contains He at the same pressure P but temperature 2T. The ratio of masses of N 2 and He in the vessels A and B is:
The average thermal energy of a molecule of a diatomic gas is (temperature of gas is T and Boltzmann’s constant is K).
A rigid container contains helium gas at 150 KPa and 127 o C . If R = 8.3 J − m o l − 1 K − 1 , the density of the gas is
A gas mixture consists of 2 moles of O 2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
The molecules of a given mass of a gas have r.m.s. velocity of 200 ms – 1 at 27 0 C and 1 . 0 × 10 5 Nm – 2 pressure. When the temperature and pressure of the gas are respectively, 127 0 C and 0 . 05 × 10 5 Nm – 2 , the r . m . s . velocity of its molecules in ms – 1 is :
Statement I : Air pressure in a car tyre increases during driving. Statement II : Absolute zero temperature is not zero energy temperature.
An ideal gas has a volume of exactly 1 litre at 1.00 atm and − 20 0 C . To how many atmospheres pressure must it be subjected to be compressed to 0.50 litre when the temperature is 20 0 C ?
If the adiabatic index γ of a gas is 4/3, the gas may be
If 2 moles of an ideal monatomic gas at temperature T o is mixed with 4 moles of another ideal monatomic gas at temperature 2 T o ,then the temperature of the mixture is
Internal energy of n 1 moles of hydrogen of temperature T is equal to the internal energy of n 2 mole of helium at temperature 2T.Then the ratio n 1 n 2 is
I mole of gas having γ = 7 5 is mixed with I mole of a gas having γ = 4 3 . What will be the γ for the mixture?
Certain amount of ideal gas is confined to a rigid container at pressure 8 × 10 5 N / m 2 . Then internal energy per unit volume of the gas is
The molecules of a given mass of a gas have r.m.s. velocity of 200 ms – 1 at 27 o C and 1.0 x 10 5 Nm – 2 pressure. When the temperature and pressure of the gas are respectively, 127 0 C and 0 . 05 × 10 5 Nm – 2 , the r.m.s. velocity of its molecules in ms – l is:
Statement I : The molecules of a monatomic gas has three degrees freedom. Statement II: The molecules of a diatomic gas has five degrees of freedom.
Statement I: All molecular motion ceases at – 273 0 C Statement II: Temperature – 273 0 C cannot be attained.
Suppose a diatomic gas gets ionised to a certain extent without any expenditure of heat energy. If the fractional change in the number of moles of the gas be η , then ignoring any energy loss, the fractional change in the temperature of the gas will be
Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?
If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is
When heat in given to a gas in an isobaric process, then
Internal energy of an ideal gas depends upon
One litre of helium gas at a pressure 76 cm. of Hg and temperature 27 o C is heated till its pressure and volume are double. The final ternperature attained by the gas is:
A vessel of volume 1660 cm 3 contains 0.1 mole of oxygen and 0.2 mole of nitrogen. If the temperature of the mixture is 300 K, find its pressure.
The volume of a given mass of a gas at 27 o C , I atm is l00cc. What will be its volume at 327 0 C ?
The initial temperature of a gas is 100 0 C . The gas is contained in closed rigid vessel. If the pressure of the gas is increased by 5%. calculate the increase in temperature of the gas:
A sample of a perfect gas occupies a volume V at a pressure P and obsolete temperature T. The mass of each molecule is m, which of the following expressions given the number of molecules in the sample?
Two gases A and B having the same temperature T, same pressure P and same volume V are mixed. lf the mixture is at the same temperature and occupies a volume V. the pressure of the mixture is
During an experiment an ideal gas is found to obey an additional law V 2 P = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2V, the temperature becomes
An insulated container containing monoatomic gas of molar mass m is moving with a velocity v o . If the container is suddenly stopped, find the change in temperature.
A cylinder contains a mixture of helium and argon gas in equilibrium at 150 0 C . what is the rms speed of each type of molecule?
A light container having a diatomic gas enclosed with in is moving with velocity v. Mass of the gas is M and number of moles is n. The kinetic energy of gas w.r.t. ground is
The rms speed of particle of mass 5 x 10 – 17 kg. in their random motion in air at NTP will be (Boltzmann’s constant K = 1 . 38 x l 0 – 23 J / K )
Two vessels A and B contain ideal gases with the temperature of B double that of A. Both gases are heated, so that they attain the same temperature. It is found that the fractional increase in the most probable speed of gas in vessel ,A is double that of the mean speed of gas in B. The ratio of the final to the initial temperature of gas in vessell is
Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contains only 0 2 , B only N 2 and C a mixture of equal quantities of 0 2 and N 2 . If the average speed of the O 2 molecules in vessel A is V 1 that of the N 2 molecules in vessel B is V 2 the average speed of the O 2 molecules in vessel C is (where M is the mass of an oxygen molecule)
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O 2 molecule to that per N 2 molecule is
At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 20 0 C ?
Which of the following statements is true?
The molecules ofa given mass of a gas have a rms velocity of 200 m,/sec at 27 0 C and 1 . 0 x 10 5 N / m 2 pressure. When the temperature is 127 0 C and pressure is 0 . 5 x 10 5 N / m 2 , the rms velocity in m./sec will be
The root mean square speed.of the rnolecules of a diatomic gas is v. When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is
At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at 47 0 C ?
N molecules, each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of molecules of .B type is denoted by v 2 and the mean square velocity of A type is denoted by ω 2 , the ω 2 v 2 is
A cylinder contains a mixture of helium and argon gas in equilibrium at 150 0 C . What is the average kinetic energy for each type of gas molecule?
At a pressure of 24 × 10 5 dyne cm – 2 , the volume of O 2 is l0 litre and mass is 20 g. The rms velocity will be
The ratio of the vapour densities of two gases at the same temperature is 8 : 9. The ratio of the rms velocities of their molecules is
The rms speed of oxygen molecules at a certain temperature T is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, then the rms speed
At what temperature is the K.E. of a gas molecule half that of its value at 27 0 C ?
The energy density U V of an ideal gas is related to its pressure P as
On the basis of kinetic theory of gases, the mean K.E. of I mole per degree of freedom is
The ratio of the number of moles of a monoatomic to a polyatomic gas in a mixture of the two, behaving as an diatomic gas is : (vibrational modes of freedom is to be ignored)
Four molecules of a gas are having speeds of l, 4, 8 and 16 ms – 1 . The root mean square velocity of the gas molecules is
When the temperature of a gas is raised from 27 0 C to 90 0 C , the percentage increase in the rms velocity of the molecules will be
At what temperature, rms velocity of O 2 molecules will be 1 3 of t h a t o f H 2 molecules at – 3 0 C ?
An assembly of smoke particles in air at NTP is under consideration. If the mass of each particle is 5 x l 0 – 17 kg , then the rms speed is (Given: k = 1.38 ×19 – 23 JK – 1 )
The rms velocity of hydrogen gas molecules at NTP is V m s – 1 . The gas is heated at constant volume till the pressure becomes four times. The final rms velocity is
Oxygen and hydrogen in two enclosures have same mass, volume and pressure. The ratio of the temperatures of the two gases is
250 litre of an ideal gas is heated at constant pressure from 27 0 C such that its volume becomes 500 litres. The final temperature is
The molecular weights of oxygen and hydrogen are 32 and 2 respectively. The root mean square velocities of oxygen and hydrogen at NTP are in the ratio
Molecular hydrogen at one atmosphere and helium at two atmospheres occupy volume V each at the same temperature. The rms velocity of hydrogen molecules is x times the rms velocity of helium molecules. What is the value of x?
The average kinetic energy of H 2 molecule at 300 K is E. At the same temperature the average kinetic energy of O 2 molecule is
The ratio of average translational KE to rotational KE of a linear polyatomic molecule at temperature T is
In the given (V-T) diagram, what is the relation between pressure P 1 and P 2 ?
A gas mixture consists of 2 moles of O 2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:
Consider the following statements. (A) The pressure exerted by an enclosed ideal gas does not depend on the shape of the container. (B) The pressure of an ideal gas depends on the number of moles, temperature and volume of the enclosure. 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.
A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature ‘T’. Neglecting all vibrational mode, the total internal energy of the system is
Which of the following is not an assumption of KTG?
2 g of Hydrogen is mixed with 22.4 litre of Helium at STP in a container of volume 20 litre. If the final temperature is 300 K, find the pressure.
Which of the following types of kinetic energies contribute to internal energy?
In the V-T graph shown in figure: Column-I Column-II i. Gas A is … and gas B is … p. monoatomic, diatomic ii. P A P B is q. diatomic, monoatomic iii.. n A n B is r. > 1 s. < 1 t. cannot say any thing Now, match the given columns and select the correct option from the codes given below. Codes
Two identical vessels contain the same gas at pressures P 1 and P 2 at absolute temperatures T 1 and T 2 , respectively. On joining the vessels with a small tube as shown in the figure, the gas reaches a common temperature T and a common pressure P. Determine the ratio P T .
Two spherical vessel of equal volume, are connected by a narrow tube. The apparatus contains an ideal gas at one atmosphere and 300 K. Now if one vessel is immersed in a bath of constant temperature 600K and the other in a bath of constant temperature 300 K. Then the common pressure will be
According to kinetic theory of ideal gases,
Which of the following is in accordance with assumptions of kinetic theory of ideal gases?
According to kinetic theory of ideal gases,
A real gas behaves more closely as an ideal gas at
According to kinetic theory of gases, which of the following statement(s) is wrong?
According to kinetic theory of gases, for a given gas at a given temperature,
Upon collision in a closed container, the gas molecules
According to kinetic theory of gases, at absolute zero temperature,
If E is total energy, U is potential energy and k is kinetic energy of a mole of an ideal gas
An ideal gas at temperature T 0 is taken in a container. The walls of the container are also at same temperature. If gas molecules undergo elastic collisions with the walls of the container
Mixture of oxygen and hydrogen gas is taken in a vessel at room temperature. When an oxygen molecule and a hydrogen molecule collide
As per kinetic theory of gases, suppose a molecule of a gas strikes a particular wall of a cubical vessel at t = 0
Select the correct alternative
If pressure of a gas is increased without changing its density, then
Some gas at 300 K is enclosed in a container. Now the container is placed on a fast moving train. While the train is in motion, the temperature of the gas
Why moon does not have atmosphere?
A gas is allowed to expand isothermally. The root mean square velocity of the molecules
The root mean square (rms) speed of oxygen molecules (O 2 ) at a certain absolute temperature is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, rms speed would be
The most probable speed of molecules in a gas at a temperature is given by (P is the pressure exerted by the gas and r is its density)
When temperature of a gas is increased, fraction of gas molecules travelling with most probable speed
An electric fan is switched on in a closed room. The air in the room is
Let v A V G , v R M S and v M P denote mean speed, rms speed and most probable speed, respectively, of the molecules in an ideal monatomic gas at absolute temperature T. The mass of a molecule is m. Then,
According to kinetic theory of gases, at absolute zero temperature,
Two monatomic gases A and B having atomic masses M A , M B respectively are kept at the same temperature. The ratio of r.m.s. velocity and average velocity of gas A is R A and corresponding value for gas B is R B . Then R A = R B
A gas is enclosed inside a cylindrical vessel fitted with a piston. When the piston is moved in, gas heats up. It is because
Hydrogen and Oxygen gases at the same temperature have
The temperature of a gas is a measure of
If the volume of a gas is doubled at constant pressure, the average translational kinetic energy of its molecules will
In the case of hydrogen and oxygen, at NTP which of the following quantities is / are same? (1) Average momentum per molecule (2) Average kinetic energy per molecule (3) Kinetic energy per unit volume (4) Kinetic energy per unit mass
The average kinetic energy of a helium atom at 30 o C is
As per law of equipartition of energy, energy associated with each molecule having f degrees of freedom is
Law of equipartition of energy is valid for
How many degrees of freedom does a monoatomic gas have?
How many degrees of freedom does a diatomic gas have at ordinary temperatures?
Molar specific heat at constant volume (C V ) for a monoatomic gas is
Supposing the distance between the atoms of a diatomic gas to be constant, its specific heat at constant volume per mole (gram mole) is
If a molecule can acquire energy in N different independent ways, how many degrees of freedom does it have?
The mean free path of a molecule of a gas depends
If a molecule has N vibrational modes, then how many total degrees of freedom does it have?
The collision frequency of the molecules of a gas at a temperature is
The mean free path of gas molecules depends on
The average collision period in a gas undergoing isobaric process is
Three perfect gases at absolute temperatures T 1 , T 2 a n d T 3 are mixed. The masses of the molecules are m 1 , m 2 a n d m 3 and number of molecules are n 1 , n 2 a n d n 3 respectively. Assuming no loss of energy, the final temperature of the mixture is
As per Maxwell’s law of distribution of velocities of molecules of an ideal gas,
If the mean free path is doubled, then the pressure of the gas at constant temperature becomes
If RMS velocity of gas molecules increases,
Number of degrees of freedom of a gas A are higher compared to that of gas B at the same temperature. It means
For a gas, the rms speed at 800 K is
At a certain absolute temperature T, an ideal diatomic gas has total energy U. Energy E is supplied to the gas and its temperature increases by t on Kelvin scale. If an additional energy E is supplied to the gas, find the final temperature of the gas on Kelvin scale.
Kinetic theory of ideal gases can be used to predict
The rms speed of helium at 27 o C and 1 atm pressure is 900 m s − 1 . Then the rms speed of the helium molecules at 27 o C and 2 atm pressure is
A closed vessel of fixed volume contains a mass m of an ideal gas. The RMS speed is v. Additional mass m of the same gas is pumped into the vessel and the pressure rises to 2p, temperature remaining the same as before. RMS speed now is
The molecules of a given mass of a gas have RMS speed 200 m s − 1 at 27 ºC and 10 N m − 2 pressure. When the absolute temperature is doubled and the pressure is halved, then find RMS speed of the molecules of the same gas i n m s − 1 .
A flask contains hydrogen and helium in the ratio 2 : 1 by mass. The temperature of the mixture is 27 o C. Obtain the ratio of rms speeds of the molecules of the two gases. Molecular mass of hydrogen = 2, molecular mass of helium = 4.
At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at 200 K?
At what absolute temperature T is the root mean square speed of a hydrogen molecule equal to its escape velocity from the surface of the moon? Radius of moon is R, g is acceleration due to gravity on moon’s surface, m is mass of hydrogen molecule and k is Boltzmann constant.
The rms speed of the molecules of a gas in a vessel is 400 m s − 1 . If half of the gas leaks out at constant temperature, the rms speed of the remaining molecules will be
At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth? v e = 11.2 k m s − 1 , m a s s o f o x y g e n m o l e c u l e = 2.76 × 10 − 26 k g a n d k = 1.38 × 10 − 23 J k − 1
If V S is velocity of sound in air, and V R is RMS velocity of gas molecules
At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be 1930 m s − 1 . The gas possibly is
The rms velocity of the molecules in a sample of helium is 5 7 t h of that of the molecules in a sample of hydrogen. If the temperature of hydrogen gas is 0 ° C , the temperature of the helium sample is nearly equal to
A gas molecule at the surface of earth happens to have rms speed for the gas at 0 o C. Suppose it went straight up without colliding with other molecules, how high would it rise? Mass of the molecule is 4.65 × 10 − 26 k g . Boltzmann’s constant = 1.38 × 10 − 23 J K − 1 .
The average speed v and r.m.s. speed V RMS of the molecules are related as
A container contains helium gas at 0 ° C . What is the average linear momentum of a helium molecule of mass 6 . 64 × 1 0 – 27 kg in the container?
Three closed vessels A, B and C are at the same temperature. Vessel A contains only O 2 , B only N 2 and C a mixture of equal quantities of O 2 and N 2 . If the average speed of O 2 molecule in vessel A is v 1 , that of N 2 molecules in vessel B is v 2 , the average speed of O 2 molecules in vessel C is
Three gas molecules have velocities 0 . 3 km s − 1 , 0 . 6 km s − 1 and 1 . 5 km s − 1 . Calculate rms velocity and average velocity.
The figure below shows the plot of P V n T versus P for oxygen gas at two different temperatures. Read the following statements concerning the curves given below and identify correct statements. (i) The horizontal line corresponds to the ideal gas (ii) T 1 > T 2 (iii) The value of P V n T at the point where the curves meet on the y-axis is the same for all gases
A vessel contains 0.5 g of hydrogen and 0.8 g of oxygen. The volume of vessel is 5 28 m 3 while its temperature is maintained at 300 K. Then the pressure of the mixture is M H 2 = 2 , M O 2 = 32 , R = 25 3 J − m o l − 1 K − 1 .
According to kinetic theory of gases, pressure of an ideal gas (p) and its energy density (u) are related as
E 0 and E h respectively represent average translatory kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at the same temperature, which of the following statements is true?
A sealed container with a negligible linear coefficient of thermal expansion contains Helium. When heated from 300 K to 600 K, the average kinetic energy of Helium atom is
The average translational kinetic energy of oxygen molecules is 0.05 eV. Calculate the temperature of the oxygen. Use 1eV = 1 . 6 × 1 0 – 19 J .Boltzmann’s constant, k = 1 . 38 × 1 0 – 23 J K – 1 .
Two gases are at absolute temperatures 300 K and 350 K respectively. The ratio of average kinetic energy of their molecules is
Find the change in translational kinetic energy per molecule of the gas if its pressure changes by 0.25 atm (volume of the gas = 1.5 litre).
The total kinetic energy of translatory motion of all the molecules of 5 litres of nitrogen exerting a pressure P is 3000 J.
A cubical box of side 1 m contains helium gas (atomic weight 4) at a pressure of 100 Nm – 2 . During an observation time of 1 second, an atom travelling with root- mean-square speed parallel to one of the edges of the cube was found to make 500 hits with a particular wall, without any collision with other atoms. Take R = 25 3 J mol – 1 K – 1 and k = 1 . 38 × 1 0 – 23 J K – 1 . Evaluate average kinetic energy.
3 moles of an ideal monoatomic gas at a temperature of 27 o C are mixed with 2 moles of an ideal monoatomic gas at a temperature 227 o C. Determine the equilibrium temperature of the mixture, assuming no loss of energy.
One kilogram of a diatomic gas is at a pressure of 8 × 10 4 N m − 2 . The density of the gas is 4 k g m − 3 . What is the energy of the gas due to its thermal motion?
For a gas, γ = 9 7 . What is the number of degrees of freedom of the molecules of this gas?
A vessel of volume 33.2 × 10 − 3 m 3 contains an ideal gas at 300K and 200 kPa. The gas is allowed to leak until the pressure falls to 125 kPa. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.
Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2:3. The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature is 4:3. The ratio of their densities is
Five grams of Helium having rms speed of molecules as 1000 m/s and 24 g of oxygen having rms speed of 1000 m/s are introduced into a thermally isolated vessel. The ratio of rms speeds of Helium and oxygen when thermal equilibrium is attained is N 2 . Find N. Neglect the heat capacity of the vessel.
N molecules, each of mass m of gas A, and 2N molecules, each of mass 2m of gas B, are contained in the same vessel which is maintained at a temperature T. The mean square of the velocity of the molecules of B type is denoted by v B 2 and the mean square of the x-component of the velocity of A type is denoted by v A 2 . The ratio v B 2 v A 2 = N 3 . Find N.
An adiabatic vessel contains n 1 moles of diatomic gas. Moment of inertia of each molecule is I = 2.76 × 10 − 46 k g m 2 and root mean square angular velocity is ω 0 = 5 × 10 12 r a d s − 1 . Another adiabatic vessel contains n 2 = 5 moles of a monoatomic gas at a temperature 470K. Assume gases to be ideal, calculate root-mean square angular velocity of diatomic molecules (in multiple of 10 12 r a d s − 1 ) when the two vessels are connected by a thin tube of negligible volume.
The highest vacuum attained so far is of the order of 10 -11 mm of Hg. How many molecules are there in 1m 3 of a vessel under such a high vacuum at 0 º C ?
The mean free path of the molecules of two gases having molecular diameters 1 A o and 2 A o is N: 1. Gases are under identical conditions of temperature, pressure and volume. Find N.
We have 0.5 g of hydrogen gas in a cubic chamber of side 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant until a final pressure of 100 atm is reached. What is the volume of gas in final state as per ideal gas assumption? Is one justified in assuming the ideal gas law, in the final state? (Hydrogen molecules can be considered as spheres of radius 1 A o ) .
Ten small planes are flying at a speed of 150kmph in total darkness in an air space that is 20 × 20 × 1.5 k m 3 in volume. You are in one of the planes, flying at random within this space, with no way of knowing where the other planes are. On an average, about 25 × N hours time will elapse between collision of a plane with your plane. Assume a safety region as a sphere of radius 10 m around every plane. Find N.
Consider a rectangular block of wood moving with a velocity v 0 in a gas of mass density ρ and at temperature T. Assuming the velocity is along x-axis and the area of cross-section of the block perpendicular to v 0 is A.The drag force acting on the block is N ρ A v 0 k T m , where m is mass of each molecule. Find N.
The total number of degrees of freedom of molecules of hydrogen of volume 1 cc at NTP is 1.34 × 10 ( 5 × N ) . Find N.
A light container having a monoatomic ideal gas enclosed within is moving with speed v 1 . Its speed is suddenly reduced to v 2 . Find the resulting change in temperature. (Mass of each molecule of gas = m, k = Boltzmann constant).
A light container having a diatomic gas enclosed within is moving with velocity v. Mass of the gas is M and number of moles is n and temperature is T. Find kinetic energy of the gas with respect to centre of mass and with respect to ground.
Nitrogen of mass 15 g is enclosed in a vessel at temperature 300 K so that it does not lose any energy to external system. The amount of heat required to double the root mean square velocity of these molecules is N times 2000 J. Find N. (Round off answer to nearest multiple of 10).
Number of degrees of freedom of an ideal gas is 5 and velocity of sound in the gas is V. Then rms speed of the molecules of the gas is
A spherical balloon of volume V contains Helium gas at a pressure P. How many moles of Helium are there in the balloon if the average kinetic energy of the Helium atoms is K − .
A hypothetical gas sample has its molecular speed distribution graph as shown in the figure. Speed u and d N d u have appropriate limits. The root mean square speed of the molecules is N 3 . Find N. (Do not worry about units).
The mean free path of nitrogen molecules at a pressure of 1 atm and temperature 0 º C is 0.8 × 10 − 7 m . If the number density of molecules is 2.7 × 10 25 p e r m 3 , then the molecular diameter is 3.2 × N A o . Find N.
Helium and oxygen gases are contained in two identical vessels at temperatures T 0 and respectively. Their respective pressures are P 0 and 4P 0 . They are connected by a thin pipe and are allowed to diffuse without any loss of energy. The equilibrium pressure of the gaseous mixture is 69 P 0 13 N . Find N.
One mole of monoatomic gas is brought from state A to state B. The initial temperature at A is T 0 . The temperature at B will
At a depth of 40 m, the temperature of the lake is 12 °C and an air bubble has a volume of 1.0 cm 3 . The air bubble is rising up to reach the surface of the lake, where the temperature is 35 °C. Find the volume of the air bubble when it reaches the surface of the lake
When an air bubble of radius ‘r’ rises from the bottom to the surface of a lake, its radius becomes 5r/4 (the pressure of the atmosphere is equal to the 10m height of water column). If the temperature is constant and the surface tension is neglected, the depth of the lake is
Two identical containers connected by a fine capillary tube contain air at N.T.P. if one of those containers is immersed in pure water, boiling under normal pressure then new pressure is
During an experiment an ideal gas is found to obey an additional law VP 2 = constant. The gas is initially at a temperature ‘T’ and volume ‘V’. When it expands to a volume 2V, the temperature becomes
At constant temperature, a 1 L vessel is filled with 125 ml of a gas at 0.6 atm and 150 ml of another gas at 0.8 atm. Now, if the temperature remains constant, find the total pressure of the mixture at equilibrium:
A cycle tube has volume 2000 cm 3 . Initially the tube is filled to (3/4) th of its volume by air at pressure of 10 5 N/m 2 . It is to be inflated to a pressure of 6 × 10 5 N/m 2 under isothermal conditions. The number of strokes of pump, which gives 500 cm 3 air in each stroke, to inflate the tube is
The average transnational kinetic energy of the molecules of a gas will be doubled if at constant :
A closed container of volume 0.02m 3 contains a mixture of neon and argon gases, at a temperature of 27°C and pressure of 1 × 10 5 Nm -2 . The total mass of the mixture is 28g. If the gram molecular weights of neon and argon are 20 and 40 respectively. Find the masses of the individual gases in the container, assuming them to be ideal. (Universal gas constant R = 8.314 J/mol.k)
Two identical vessels A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The masses of gas in A and B are m A and m B respectively. The gases are allowed to expand isothermally to the same final volume 3 V. The change in pressure of the gas in A and B are found to be ∆ P and 1.5 ∆ P respectively. Then
Two thermally insulated vessels 1 and 2 are filled with air at temperature (T 1 , T 2 ), volume (V 1 , V 2 ) and pressure (P 1 , P 2 ) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
Match List I and List II List-I List-II A) Barometer E) Charles’s law B) specific gas constant F) J mole -1 K -1 C) gas thermometer G) Boyle’s law D) universal gas constant H) J Kg -1 K -1
Assertion (A): Real gases do not obey the ideal gas equation. Reason (R): In the ideal gas equation, the volume occupied by the molecules as well as the inter molecular forces are ignored.
Assertion (A): PV/T=constant for 1 gram of gas. This constant varies from gas to gas. Reason (R): 1 gram of different gases at NTP occupy different volumes.
Assertion (A): PV/T=constant for 1 mole of gas. This constant is same for all gases. Reason (R): 1 mole of different gases at NTP occupy same volume of 22.4 litres.
Assertion (A): Pressure of gas is same every where inside a closed container Reason (R): The gas molecules under go elastic collisions among themselves and with walls of the container
Assertion (A): Volume of gas at 50°C is ‘V’. Keeping the pressure constant, the temperature is doubled. Volume becomes 2V. Reason (R): At constant pressure, the volume of gas is directly proportional to its absolute temperature.
Assertion (A): The air pressure in a car tyre increases during driving Reason (R): Temperature of air in the tyre increases due to friction of tyre with road. Increase in temperature results in an increase in pressure according to Charles’s law
At a pressure of 24 × 10 5 dyn cm − 2 , the volume of O 2 is 10 1 and mass is 20 g. The rms velocity will be
The average translational energy and the rms speed of molecules of a sample of oxygen gas at 300 K are 6.21 × 10 − 21 J and 484 ms -1 respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)
0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27 °C. Find the amount of heat energy to be supplied to the gas to double the rms speed of its molecules.
Four molecules of a gas have speeds 1, 2, 3 and 4 km s -1 . The value of the root mean square speed of the gas molecule is
We write the Boyle’s Law as PV=C, when the temperature remain constant. In this relation the magnitude of C depends upon
An ideal gas obeys an additional law PV 2 = constant. Initially the gas is at 400 K. What is the temperature if it expands to 2V
An open vessel contains a gas at 60°C. To what temperature should the gas be heated so that 1/4 th of the mass of gas is expelled ?
Two samples of nitrogen and oxygen of same mass possesses same pressure and volume. The ratio of their temperature is
A closed vessel of capacity 1m 3 contains 0.9 kg of water and 1.6 kg of oxygen. The pressure in the vessel at a temperature of 500 K is (R = 8 J mol -1 k -1 )
Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point A is ρ 0 . Density at B will be
Two flasks of capacity 4 litres and 8 litres connected by a narrow tube contain a gas at a pressure of 60cm of Hg and at a temperature of 27 o C. When the larger flask alone is dipped in a bath at 127 o C, keeping the temperature of the smaller flask constant at 27 o C, then the resultant pressure is
If P is the pressure, V the volume, R the gas constant, k the Boltzmann constant and T the absolute temperature, then the number of molecules in the given mass of the gas is given by
Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of B being twice that of A. under such conditions. The density of A is found to be one-third of the density of B. the ratio of molecular weight of A and B is
If both temperature and the volume of an ideal gas are doubled, the pressure
During an experiment an ideal gas is found to obey an additional law VP 2 = constant. The gas is initially at temperature T and volume V, when it expands to volume 2V, the resulting temperature is
An ideal gas obeys additional law PV 2 = Constant . Initial temperature of gas is T . If volume of gas is doubled, temperature becomes
An opened vessel contains air at 27 o C. It is heated until half of air is expelled. If expansion of vessel is negligible. The final temperature to which vessel heated is
For a gas pressure, volume and temperature all are changing. But graph is drawn between pressure and temperature and straight line AB is obtained as shown in figure While going from A to B , volume of gas is
When pressure of gas in a closed vessel is increased by 1% , temperature is increased by 2 o C. Initial temperature of gas is
Volume coefficient of oxygen is ‘x’ and pressure coefficient of Nitrogen is ‘y’. Then
One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is
When the temperature of a gas is raised from 27°C to 90°C, the percentage increase in the r.m.s. velocity of the molecules will be
In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as T q. A good estimate for q is
At room Temperature , a diatomic gas is found to have an rms speed of 1930 m/s. The gas is
At what temperature, the mean kinetic energy of O 2 will be the same for H 2 molecules at – 73°C
The r.m.s. velocity of a gas at a certain temperature is 2 times than that of the oxygen molecules at that temperature. The gas can be
The rms speed of oxygen at room temperature is about 500m/s The speed of hydrogen at the same temperature is about
The Velocities of four molecules of a gas are 3 m / s , 3m/s, 4m/s and 6m/s. the root mean square velocity V rms is
The temperature of an ideal gas is increased from 120K to 480K.The rms Velocity of the gas molecules is v at 120K.At 480k ,it becomes
Pressure versus temperature graphs of an ideal gas are as shown in figure. Choose the wrong statement
The temperature at which the rms speed of Oxygen molecules is sufficient for escaping from Earth, is
Certain amount of an ideal gas are contained in a closed vessel. The vessel is moving with a constant velocity v. The molecular mass of gas is M. The rise in temperature of the gas when the vessel is suddenly stopped is ( γ = C P / C V )
Considering the gases to be ideal, the value of γ = C P C V for a gaseous mixture consisting of = 3 moles of carbon dioxide and 2 moles of oxygen will be ( γ O 2 = 1 .4 , γ CO 2 = 1 .3 )
A jar has a mixture of hydrogen and oxygen gas in the ratio of 1 : 5. The ratio of mean kinetic energies of hydrogen and oxygen molecules is
Two vessels having equal volumes contain molecular hydrogen at 1 atm and helium at 2 atm , respectively . What is the ratio of the rms speeds of hydrogen molecule to that of helium molecule if both are at the same temperature?
One Kilogram of a diatomic gas is at pressure of 8 x10 4 N/m 2 The density of the gas is 4kg/m 3 . What is the energy of the gas due to its thermal motion?
Statement 1. The total translation K.E.of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its Volume. Statement 2. The Molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
The ratio of most probable speed and the rms speed of gas molecules at a given temperature is
The ratio of specific heats of gas and number of degrees of freedom (f) has the relation
The Physical state of a gas is represented by P, V and T in Vessel A and 2P, V 4 2T in vessel B. The ratio of number of molecules in A and B is
A Vessel is filled with a gas at one atmospheric pressure .At the same temperature, the mass of that gas is increased by 25% the pressure of gas in the vessel is
Container of equal volumes are filled with hydrogen and oxygen gases of equal masses. At the same temperature the ratio of pressure exerted by the gases is
A vessel of volume V contains an ideal gas absolute temperature T and pressure P. The gas is allowed to leak till its pressure falls to P’. Assuming that the temperature remains constant during leakage, the number of moles of gas that have leaked is
A vessel contains 1 mole of O 2 (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing 1 mole of He gas (molar mass 4) at a temperature 2T has a pressure of
One of the two vessels of same capacity is filled with oxygen and other is with helium of same mass. Both gases are at same temperature. The ration of pressure of these gases is
Consider the following statements. (A) The pressure exerted by an enclosed ideal gas does not depend on the shape of the container. (B) The pressure of an ideal gas depends on the number of moles, temperature and volume of the enclosure. 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.
The Velocities of four molecules of a gas are 3 m / s , 3m/s, 4m/s and 6m/s. the root mean square velocity V rms is
The temperature of an ideal gas is increased from 120K to 480K.The rms Velocity of the gas molecules is v at 120K.At 480k ,it becomes
Two vessels having equal volumes contain molecular hydrogen at 1 atm and helium at 2 atm , respectively . What is the ratio of the rms speeds of hydrogen molecule to that of helium molecule if both are at the same temperature?
Statement 1. The total translation K.E.of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its Volume. Statement 2. The Molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
One Kilogram of a diatomic gas is at pressure of 8 x10 4 N/m 2 The density of the gas is 4kg/m 3 . What is the energy of the gas due to its thermal motion?
The ratio of most probable speed and the rms speed of gas molecules at a given temperature is
A Vessel is filled with a gas at one atmospheric pressure .At the same temperature, the mass of that gas is increased by 25% the pressure of gas in the vessel is
The root mean square velocity of the molecules in a sample of helium is(5/7) times the root mean square velocity of the molecules in a sample of hydrogen at temperature 0 o C The temperature of helium is
Choose the only correct statement from the following
A vessel contains 1 mole of O 2 (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing 1 mole of He gas (molar mass 4) at a temperature 2T has a pressure of
When a gas in a cylinder is compressed at constant temperature by a piston, the pressure of the gas increases. Consider the following three statements. a) The rate at which the molecules collide with the piston increases b) The average speed of the molecules increases c) The molecules collide with each other more often Which statement(s) correctly explain the increase in pressure?
The kinetic energy of a given sample of an ideal gas depends only on its
The graph drawn between pressure and volume in Boyle’s law experiment is shown in figure for different masses of same gas at same temperature then
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
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)
Mean kinetic energy per gram molecule for diatomic gas is
The average speed of molecules of oxygen gas is 450 m/s. If the mean free path is 1.1 × 10 -7 m, then the average number of collisions per second is
A vessel contains a mixture of 1 mole of oxygen and two moles of nitrogen at 300 K. The ratio of the rotational kinetic energy per O 2 molecule to that per N 2 molecule is
The root mean square velocity of the molecules of a gas is 1260 m/s. The average speed of the molecules is
A closed vessel of fixed volume contains a mass m of an ideal gas, the root mean square speed being v. Additional mass m of the same gas is pumped into the vessel and the pressure rises to 2 P, the temperature remaining the same as before. The root mean square speed of the molecule now is
The specific heat of argon at constant volume and at constant pressure are 315 JK and 525 JK respectively. Its density at NTP will be
An ideal gas is initially at temperature T and volume V. Its volume is increased by ∆ V due to an increase in temperature ∆ T , pressure remaining constant. The quantity δ = ( ΔV / VΔT ) varies with temperature as
If a gas has n degrees of freedom, the value of γ is
Gas at pressure P o is contained in a vessel. If the masses of all the molecules are halved and their speed doubled, the resulting pressure P will be equal to
The temperature of an ideal gas increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is y, at 480 K it becomes
Ifat N.T.P., velocity of sound in a gas is 1150 m/s, then the r.m.s. velocity of gas molecules at N.T.P. is : (Given R = 8.3 J/mol K and C P = 4.8 cal/mol K)
At what temperature is the rms velocity of hydrogen molecule equal to that of an oxygen molecule at 47 o C?
An ideal gas is initially at temperature T and volume V. Its volume is increased by ∆ V due to an increase in temperature ∆ T, pressure remaining constant. The quantity δ = ∆ V / ( V ∆ T ) varies with temperature as
The molecules of a given mass of gas have rms speed 200 m s -1 at 27 °C and 10 5 N m -2 pressure. When the absolute temperature is doubled and the pressure is halved, then rms speed (in m s -1 ) of the molecules of the same gas is .
Variation of internal energy with density of one mole of monoatomic gas is depicted in the adjoining figure. Corresponding variation of pressure with volume can be depicted as (Assuming the curve is rectangular hyperbola)
Which one of the following is not an assumption of kinetic theory of gases?
According to equipartition law of energy each particle in a system of particles have thermal energy E equal to
A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (see figure). If the temperature is increased, then [NCERT Exemplar)
A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is p 0 and temperature is T 0 , atmospheric pressure is also p 0 . Now, the temperature of the gas is increased to 2T 0 , the tension in the wire will be
In the V-T graph shown in the figure. Match the Column I with Column II and mark the correct option from the codes given below. Column I Column II (A) Gas A is (p) Monoatomic (B) p A /p B is (q) Diatomic (C) n A /n B is (r) > 1 (D) Gas B is (s) < 1 (t) Cannot say anything Codes A B C D
A graph between pressure p (along Y-axis) and absolute temperature T(along X-axis) for equal moles of two gases has been drawn. Given that volume of second gas is more than volume of first gas. Which of the following statement(s) is/are correct? [JIPMER 2017]
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?
An ideal gas equation can be written as p = ρ R T M 0 where, ρ and M 0 are respectively, [NEET 2020]
From the following statements, concerning ideal gas at any given temperature T, which of the following statement is incorrect?
Directions (Q. Nos. 1-4) These questions 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 : Degree of freedom of a monoatomic gas is always three, whether we consider vibrational effects or not. Reason : At all temperatures (low or high), vibrational kinetic energy of an ideal gas is zero.
Directions (Q. Nos. 1-4) These questions 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 : Degree of freedom of a monoatomic gas is always three, whether we consider vibrational effects or not. Reason : At all temperatures (low or high), vibrational kinetic energy of an ideal gas is zero.
A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C. Its density is (Take, R = 8 . 3 J mol – 1 K – 1 ) [NEET 2020]
Assertion : Vibrational degree of freedom of a diatomic gas molecule appears at every high temperature. Reason : Diatomic gas has two vibrational degree of freedom in one direction. [AIIMS 2019]
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the earth’s atmosphere? (Take, mass of oxygen molecule, m = 2.76 × 10 – 26 kg and Boltzmann’s constant, k B = 1 . 38 × 10 – 23 J K – 1 )
The rms speed of oxygen molecule in a gas at 27°C would be given by [UK PMT 2015]
The pressure of an ideal gas is directly proportional to [UK PMT 2015]
The ratio of rms speed of an ideal gas molecules at pressure p to that at pressure 2p at const volume is
The rms speed of oxygen is v at a particular temperature. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed becomes [WB JEE 2015]
At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its volume is [Manipal 2015]
The average kinetic energy of a gas molecule at absolute temperature T is
The number of molecules in a litre of a gas at temperature of 27°C and a pressure of 10 6 dyne cm – 2 is [UP CPMT 2013]
In kinetic theory of gases, it is assumed that molecular collisions are [UP CPMT 2013]
During an experiment an ideal gas is found to obey an additional law Vp 2 = constant. The gas is initially at temperature T and volume V. When it expands to volume 2V, the resulting temperature is [UP CPMT 2012]
Heat Q = 3 2 RT is supplied to 4 moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms is .
1 mole of H 2 gas is contained in a box of volume V=1.00 m 3 at T 1 = 300 K. The gas is heated to a temperature of T 2 = 3000 K and the gas gets converted into a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal)
An ideal gas is initially at temperature T and volume V. Its volume is increased by ΔV due to an increase in temperature ∆ T , pressure remaining constant. The quantity δ = ΔV / ( VΔT )
If four molecules of a gas have speed 2, 4, 6, 8 kms -1 respectively, then root mean square speed (in kms -1 ) will be .. and respectively.
The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 ms -1 . The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is x 3 ms − 1 . The value of x will be
The translatory kinetic energy of a gas per g is
The equation of state corresponding to 8 g of O 2 is
The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 ms -1 The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is x 3 ms − 1 The value of x will be
