- Heat energy absorbed by a system in going through a cyclic process shown in the given figure is
- Calculate the work done by one kilomole of an ideal in gas, in mega joule, in reversibly traversing the cycle shown in figure, ten times. Indicate the direction of traversal around the cycle if the net work is done by the gas.
- The value of γ = C P / C V is 4/3 for an adiabatic process of an ideal gas for which internal energy U = K + nPV . The value of n (K is a constant) is .
- An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P-V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here γ is the ration of heat capacities at constant pressure and constant volume. The number of moles in the gas is n. Column 1 Column 2 Column 3 (I) W 1 2 = 1 γ − 1 P 2 V 2 − P 1 V 1 (i) Isothermal (P) (II) W 1 2 = − P V 2 + P V 1 (ii) Isochoric (Q) (III) W 1 2 = 0 (iii) Isobaric (R) (IV) W 1 2 = − n R T ln ( V 2 V 1 ) (iv) Adiabatic (S) Which one of the following options is the correct combination?
- A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be ? 0 . The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (?−?). For ?≪? the magnitude of the work done in the process is given by (4?? 0 ? 2 ?)X, where X is a constant and γ = C p / C V = 41 / 30 . The value of X is .
- One mole of an ideal monoatomic gas undergo a thermodynamic cyclic process ABCDA as shown in internal energy (U) and density ( ρ ) graph. The corresponding temperature (T) versus pressure (p) graph is
- An ideal gas undergoes a four step cycle as shown in the P – V diagram below. During this cycle, heat is absorbed by the gas in
- One mole of an ideal monatomic gas has initial temperation T 0 , is made to go through the cycle abca shown in the given figure. If U denotes the internal energy, then choose the correct alternative.
- One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PV-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II. LIST–I LIST–II P. In process I 1. Work done by the gas is zero Q. In process II 2. Temperature of the gas remains unchanged R. In process III 3. No heat is exchanged between the gas and its surroundings S. In process IV 4. Work done by the gas is 6 P 0 V 0
- A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be (take the acceleration due to gravity =10 ms −2 and the universal gas constant = 8.3 J mol −1 K −1 ).
- An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P-V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here γ is the ration of heat capacities at constant pressure and constant volume. The number of moles in the gas is n. Column 1 Column 2 Column 3 (I) W 1 2 = 1 γ − 1 P 2 V 2 − P 1 V 1 (i) Isothermal (P) (II) W 1 2 = − P V 2 + P V 1 (ii) Isochoric (Q) (III) W 1 2 = 0 (iii) Isobaric (R) (IV) W 1 2 = − n R T ln ( V 2 V 1 ) (iv) Adiabatic (S) Which one of the following options is the correct combination?
- One mole of an ideal monoatomic gas is taken through process AB given by P = α − βV 2 (where α and β are positive constants) on P-V diagram. Which of the following is the correct statement regarding the given process?
- A gas is taken from state-1 to state-2 along the path shown in figure. If 70 cal of heat is extracted from the gas in the process, calculate the change in internal energy of the system (in J).
- Consider the given cyclic process 1 2 3 4 5 6 7 8 9 10 11 12 1 if the net work done is KP 0 V 0 find the value of K.
- A spherical balloon is filled with an ideal mono-atomic gas. At some instant its pressure was P 0 , volume V 0 and temperature T 0 . If the balloon expanded in such a manner so that the rate of radiation from the balloon remained constant. It was found that the work done by gas inside the balloon was 6 P 0 V 0 1 − 1 n when its volume increased to 8 V 0 .Find the value of n. (Assume ambient temperature to be close to 0 K)
- n moles of an ideal monoatomic gas undergoes a process from 1 4 as shown in the figure. T 1 = 500 K , T 4 = 200 K , P 1 = 10 5 Pa and P 2 = 4 × 10 5 P a . In state 3, 3 V 3 = V 1 . The change in internal energy from state 3 to state 4 is x Joules. The value of ‘x’ is (Take no. of moles n = 1 / R , where R = gas constant)
- An ideal gas is taken through the cycle A B C A , as shown in Fig. If the net heat supplied to the gas in the cycle is 15 J, the work done by the gas in the process C A is J.
- During the process AB of an ideal gas
- A massless piston divides a closed, thermally insulated cylinder into two equal parts. One part contains m=28 gram of nitrogen at temperature T 0 . At this temperature one- third of molecules are dissociated into atoms and the other part is evacuated. The piston is released and the gas fills the whole volume of the cylinder. Then the piston is slowly displaced back to its initial position. The increase in internal energy of the gas is: (Neglect further dissociation of molecules during motion of the piston)
- Figure shows variation of internal energy U with the density ρ of one mole of ideal mono – atomic gas for a thermodynamic cycle ABCA. Here process AB is a part of rectangular hyperbola. Incorrect diagram for the above process among the following is
- Answer the following by appropriately matching the lists based on the information given in the paragraph. In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T Δ X , where T is temperature of the system and Δ X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas X = 3 2 Rln T T A + Rln V V A . Here R is gas constant, V is volume of gas and T A and V A are constants. The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities. List-I List-II I) Work done by the system in process 1 2 3 P) 1 3 R T 0 ln 2 II) Change in internal energy in process 1 2 3 Q) 1 3 R T 0 III) Heat absorbed by the system in process 1 2 3 R) R T 0 IV) Heat absorbed by the system in process 1 2 S) 4 3 R T 0 T) 1 3 R T 0 3 + ln 2 U) 5 6 R T 0 If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with P 0 V 0 = 1 3 R T 0 , the correct match is,
- Answer the following by appropriately matching the lists based on the information given in the paragraph. In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T Δ X , where T is temperature of the system and Δ X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas X = 3 2 Rln T T A + Rln V V A . Here R is gas constant, V is volume of gas and T A and V A are constants. The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities. List-I List-II I) Work done by the system in process 1 2 3 P) 1 3 R T 0 ln 2 II) Change in internal energy in process 1 2 3 Q) 1 3 R T 0 III) Heat absorbed by the system in process 1 2 3 R) R T 0 IV) Heat absorbed by the system in process 1 2 S) 4 3 R T 0 T) 1 3 R T 0 3 + ln 2 U) 5 6 R T 0 If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with P 0 V 0 = 1 3 R T 0 , the correct match is,
- Answer the following by appropriately matching the lists based on the information given in the paragraph. In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T Δ X , where T is temperature of the system and Δ X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas X = 3 2 R ln T T A + R ln V V A . Here R is gas constant, V is volume of gas and T A and V A are constants. The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities. List-I List-II I) Work done by the system in process 1 2 3 P) 1 3 R T 0 ln 2 II) Change in internal energy in process 1 2 3 Q) 1 3 R T 0 III) Heat absorbed by the system in process 1 2 3 R) R T 0 IV) Heat absorbed by the system in process 1 2 S) 4 3 R T 0 T) 1 3 R T 0 3 + ln 2 U) 5 6 R T 0 If the process carried out on one mole of monatomic ideal gas is as shown in figure in the PV-diagram with P 0 V 0 = 1 3 R T 0 , the correct match is,
- Answer the following by appropriately matching the lists based on the information given in the paragraph. In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by T Δ X , where T is temperature of the system and Δ X is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas X = 3 2 Rln T T A + Rln V V A . Here R is gas constant, V is volume of gas and T A and V A are constants. The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities. List-I List-II I) Work done by the system in process 1 2 3 P) 1 3 R T 0 ln 2 II) Change in internal energy in process 1 2 3 Q) 1 3 R T 0 III) Heat absorbed by the system in process 1 2 3 R) R T 0 IV) Heat absorbed by the system in process 1 2 S) 4 3 R T 0 T) 1 3 R T 0 3 + ln 2 U) 5 6 R T 0 If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with P 0 V 0 = 1 3 R T 0 , the correct match is,
- An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P-V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here γ is the ration of heat capacities at constant pressure and constant volume. The number of moles in the gas is n. Column 1 Column 2 Column 3 (I) W 1 2 = 1 γ − 1 P 2 V 2 − P 1 V 1 (i) Isothermal (P) (II) W 1 2 = − P V 2 + P V 1 (ii) Isochoric (Q) (III) W 1 2 = 0 (iii) Isobaric (R) (IV) W 1 2 = − n R T ln ( V 2 V 1 ) (iv) Adiabatic (S) Which one of the following options is the correct combination?
- One mole of an ideal diatomic gas undergoes a process AB as shown. Pressure at A and B are 5 P 0 and P 0 while volumes are V 0 and 5 V 0 respectively. On the basis of the given information answer the following question (s).
- n moles of an ideal monoatomic gas undergoes a process from 1 4 as shown in the figure. T 1 = 500 K , T 4 = 200 K , P 1 = 10 5 Pa and P 2 = 4 × 10 5 P a . In state 3, 3 V 3 = V 1 . The change in internal energy from state 3 to state 4 is x Joules. The value of ‘x’ is (Take no. of moles n = 1 / R , where R = gas constant)
- An ideal gas is taken through the cycle A B C A , as shown in Fig. If the net heat supplied to the gas in the cycle 15J, the work done by the gas in the process C A is J.
- For one mole of a mono atomic gas, match the following Column – 1 [Thermo dynamic process] Column – 2 [Bulk modulus] Column-3 Slope of P – V graph (I) Isothermal (i) Infinity (P) − R T V 2 (II) Adiabatic (ii) 5 R T 3 V (Q) zero (III) Isobaric (iii) R T V (R) Infinity (IV) Isochoric (iv) zero (S) − 5 R T 3 V 2 Pick correct combination for the given matrix
- For one mole of a mono atomic gas, match the following Column – 1 [Thermo dynamic process] Column – 2 [Bulk modulus] Column-3 Slope of P – V graph (I) Isothermal (i) Infinity (P) − R T V 2 (II) Adiabatic (ii) 5 R T 3 V (Q) zero (III) Isobaric (iii) R T V (R) Infinity (IV) Isochoric (iv) zero (S) − 5 R T 3 V 2 Pick correct combination for the given matrix
- For one mole of a mono atomic gas, match the following Column – 1 [Thermo dynamic process] Column – 2 [Bulk modulus] Column-3 Slope of P – V graph (I) Isothermal (i) Infinity (P) − R T V 2 (II) Adiabatic (ii) 5 R T 3 V (Q) zero (III) Isobaric (iii) R T V (R) Infinity (IV) Isochoric (iv) zero (S) − 5 R T 3 V 2 Pick correct combination for the given matrix
- The molar heat capacity C for an ideal gas going through a processs which is given by C = a T , where ‘a’ is a constant and T is absolute temperature. If γ = C P C V , the work done by one mole of gas during heating from temperature T 0 to η T 0 through the given process will be
- Consider one mole of helium gas enclosed in a container at initial pressure P 1 and volume V 1 . It expands isothermally to volume 4V 1 . After this, the gas expands adiabatically and its volume becomes 32V 1 . The work done by the gas during isothermal and adiabatic expansion processes are W ??? and W ???? , respectively. If the ratio W iso W adia = f ln 2 , then ? is
- One mole of an ideal monoatomic gas undergo a thermodynamic cyclic process ABCDA as shown in internal energy (U) and density ( ρ ) graph. The corresponding temperature (T) versus pressure (p) graph is
- One mole of an ideal diatomic gas undergoes a process AB as shown. Pressure at A and B are 5 P 0 and P 0 while volumes are V 0 and 5 V 0 respectively. On the basis of the given information answer the following question (s). During the process from A B , pressure and volume of the gas, where the direction of flow of heat is reversed, is
- One mole of an ideal diatomic gas undergoes a process AB as shown. Pressure at A and B are 5 P 0 and P 0 while volumes are V 0 and 5 V 0 respectively. On the basis of the given information answer the following question (s). During the process from A B , pressure and volume of the gas, where the direction of flow of heat is reversed, is
- The molar specific heat of the process P = a T for a monoatomic gas, a being constant , is b 2 R . The value of b is
- One mole of monoatomic gas is taken through cyclic process shown below. T A = 300 K. Process AB is defined as PT = constant.
- A container closed by a freely moving piston contains a mixture of hydrogen and helium gases of total mass 12 gm. A heat of 150 kJ is transferred to the gas at constant pressure and in this process gas performs 50 kJ work. Find mass of hydrogen (in gm) in the mixture.
- Three moles of an ideal gas C P = 7/2R at pressure P A and temperature T A is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally the gas is compressed at constant volume to the original pressure P A . The correct P-V and P-T diagrams indicating the process are
- A system undergoes three quasi-static processes sequentially as indicated in the given figure. 1-2 is an isobaric process, 2-3 is a polytropic process with γ = 4/3 and 3-1 is a process in which PV= constant. P 2 = P 1 = 4 x 10 5 N/m 2 , P 3 =1 x 10 5 N/m 2 and V 1 = 1 m 3 . The heat transfer for the cycle is Δ Q , the change in internal energy is Δ U and the work done is Δ W . Then
- Logarithms of readings of pressure and volume for an ideal gas were plotted on a graph as shown in the given figure. By measuring the gradient, it can be shown that the gas may be
- n moles of an ideal gas undergo a thermodynamic process in which pressure of gas varies linearly with the volume of gas as shown in figure. If P 0 V 0 nR = 200 K , find the maximum temperature of the gas during the process (in K).
- Find work done by the gas in the process shown in figure:
- n moles of an ideal gas undergo a thermodynamic process in which pressure of gas varies linearly with the volume of gas as shown in figure. If P 0 V 0 nR = 200 K , find the maximum temperature of the gas during the process (in K).
- Temperature versus pressure graph of an ideal gas is shown in the given figure. During the process AB,
- P-V diagram of a cyclic process ABCA is as shown in the given figure. Choose the correct alternative.
- Figure shows a cyclic process performed on one mole of an ideal gas. A total of 1000 J of heat is withdrawn from the gas in a complete cycle. Find the work done on/by the gas, in joule, during the process B C. Given R = 8.3 J mol -1 K -1
- One mole of oxygen undergoes a cyclic process in which volume of the gas change 10 times within the cycle, as shown in the figure. Process: AB and CD are adiabatic. Find the efficiency of the process, in percent. Take (10) 0.4 =2.5.
- During the process AB of an ideal gas
- n moles of an ideal gas undergo a thermodynamic process in which pressure of gas varies linearly with the volume of gas as shown in figure. If P 0 V 0 nR = 200 K , find the maximum temperature of the gas during the process (in K).
- P-V diagram of a cyclic process ABCA is as shown in figure. Select the correct statement(s).
- One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P 0 . Choose the correct option(s) from the following
- A monatomic gas of n moles undergoes a cyclic process ABCDA as shown in figure. Process AB is isobaric, BC is adiabatic, CD is isochoric and DA is isothermal. The maximum and minimum temperature in the cycle are 4T 0 and T 0 respectively. Then
