NEET Physics Class 11 Chapter 9 Kinetic Theory Of Gases And Thermodynamics MCQs

NEET Physics Class 11 Chapter 9 Kinetic Theory Of Gases And Thermodynamics Multiple Choice Question And Answers

Question 1. When an ideal gas is compressed isothermally then its pressure increases because :

1. Its potential energy decreases
2. Its kinetic energy increases and molecules move apart
3. Its number of collisions per unit area with walls of container increases
4. Molecular energy increases

Answer: 3. Its number of collisions per unit area with walls of container increases

Question 2. Which of the following quantities is zero on average for the molecules of an ideal gas in equilibrium?

1. Kinetic energy
2. Momentum
3. Density
4. Speed

Answer: 2. Momentum

Question 3. The average momentum of a molecule in a sample of an ideal gas depends on

1. Temperature
2. Number of moles
3. Volume
4. None of these
5. Answer: 4. None of these

Question 4. The volume of air increases by 5% in its adiabatic expansion. The percentage decrease in its pressure will be –

1. 6%
2. 7%
3. 8%

Answer: 3. 7%

Question 5. The equation for an ideal gas is :

1. PV = RT
2. PV^γ = constant
3. C_p– C_V= R
4. None of these

Answer: 1. PV = RT

Question 6. The temperature and pressure of 2g oxygen are 27° C and 76 cm Hg, then the volume of the gas is:

1. 1.53 litre
2. 2.44 litre
3. 3.08 litre
4. 44.2 litre

Answer: 1. 1.53 liter

Question 7. Significance of a and b in van der Waal’s equation :

1. A and b both show the correction in the volume of gas
2. A and b both show cohesive force between molecules
3. A shows cohesive force while b shows correction in volume
4. A shows correction in volume while b shows cohesive force

Answer: 3. A shows cohesive force while b shows correction in volume

Question 8. In which condition a real gas behaves as an ideal gas?

1. At high pressure
2. At low pressure
3. At low temperature
4. All the above

Answer: 2. At low pressure

Question 9. Which of the following parameters does not characterize the thermodynamic state of matter?

1. Temperature
2. Pressure
3. Work
4. Volume

Answer: 3. Work

Question 10. 1 calorie is the heat required to increase the temperature of 1 gm of water by 1°C from

1. 13.5°C to 14.5°C at 76 mm of Hg
2. 14.5 °C to 15.5°C at 760 mm of Hg
3. 6.5 °C to 7.5°C at 76 mm of Hg
4. 98.5 °C to 99.5°C at 760 mm of Hg

Answer: 2. 14.5 °C to 15.5°C at 760 mm of Hg

Question 11. A real gas behaves like an ideal gas if its

1. Pressure and temperature are both high
2. Pressure and temperature are both low
3. Pressure is high and temperature is low
4. Pressure is low and temperature is high

Answer: 4. Pressure is low and temperature is high

Question 12. 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:

1. 1: 4
2. 1: 2
3. 6: 9
4. 8: 9

Answer: 4. 8: 9

Question 13. The degrees of freedom of a stationary rigid body about its axis will be :

1. One
2. Two
3. Three
4. Four

Answer: 3. Three

Question 14. The temperature of an ideal gas at atmospheric pressure is 300 K and the volume is 1 m³. If temperature and volume become double, then the pressure will be :

1. 10⁵ N/m²
2. 2 × 10⁵ N/m²
3. 0.5 × 10⁵ N/m²
4. 4 × 10⁵ N/m²

Answer: 1. 105 N/m²

Question 15. If 2g of helium is enclosed in a vessel at NTP, how much heat should be added to it to double the pressure? (Specific heat of helium = 3 J/gm K)

1. 1638 J
2. 1019 J
3. 1568 J
4. 836 J

Answer: 1. 1638 J

Question 16. At what temperature volume of an ideal gas at 0ºC become triple?

1. 546ºC
2. 182ºC
3. 819ºC
4. 646ºC

Answer: 1. 546ºC

Question 17. Two balloons are filled, one with pure He gas and the other with air, respectively. If the pressure and temperature of these balloons are the same, then the number of molecules per unit volume is

1. More in the He filled balloon
2. Same in both balloons
3. More in an air-filled balloon
4. In the ratio of 1: 4

Answer: 2. Same in both balloons

Question 18. A diatomic molecule has

1. 1 degree of freedom
2. 3 degrees of freedom
3. 5 degrees of freedom
4. 6 degrees of freedom

Answer: 3. 5 degrees of freedom

Question 19. The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be :

1. PV = (5/32) RT
2. PV = 5RT
3. PV = (5/2) RT
4. PV = (5/16) RT

Answer: 1. PV = (5/32) RT

Question 20. Two thermally insulated vessels 1 and 2 are filled with air at temperature (T₁, T₂), volume (V₁, V₂), and pressure (P₁, P₂) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

1. \(T_1+T_2\)
2. \(\left(\mathrm{T}_1+\mathrm{T}_2\right) / 2\)
3. \(\frac{T_1 T_2\left(P_1 V_1+P_2 V_2\right)}{P_1 V_1 T_2+P_2 V_2 T_1}\)
4. \(\frac{T_1 T_2\left(P_1 V_1+P_2 V_2\right)}{P_1 V_1 T_1+P_2 V_2 T_2}\)

Answer: 3. \(\frac{T_1 T_2\left(P_1 V_1+P_2 V_2\right)}{P_1 V_1 T_2+P_2 V_2 T_1}\)

Question 21. A gas behaves more closely as an ideal gas at

1. Low pressure and low temperature
2. Low pressure and high temperature
3. High pressure and low temperature
4. High pressure and high temperature

Answer: 2. Low pressure and high temperature

Question 22. The figure shows graphs of pressure vs density for an ideal gas at two temperatures T₁ and T₂.

1. T₁> T₂
2. T₁= T₂
3. T₁< T₂
4. Any of the three is possible

Answer: 1. T₁> T₂

Question 23. Suppose a container is evacuated to leave just one molecule of gas in it. Let ν_a and ν_rms represent the average speed and the rms speed of the gas.

1. ν_a> ν_rms
2. ν_a< ν_rms
3. ν_a= ν_rms
4. νrms is undefined

Answer: 3. ν_a= ν_rms

Question 24. The rms speed of oxygen molecules in a gas is ν. If the temperature is doubled and the O₂ molecule dissociates into oxygen atoms, the rms speed will become

1. ν
2. ν √2
3. 2ν
4. 4ν

Answer: 3. 2ν

Question 25. Consider a mixture of oxygen and hydrogen kept at room temperature. Compared to a hydrogen molecule an oxygen molecule hits the wall

1. With a greater average speed
2. With a smaller average speed
3. With greater average kinetic energy
4. With smaller average kinetic energy.

Answer: 2. With a smaller average speed

Question 26. Consider the quantity MkT / pV of an ideal gas where M is the mass of the gas. It depends on the

1. Temperature of the gas
2. The volume of the gas
3. The pressure of the gas
4. Nature of the gas

Answer: 4. Nature of the gas

Question 27. If the volume of a gas is decreased by 10% during the isothermal process then its pressure will be –

1. Decrease by 10%
2. Increase by 10%
3. Decrease by 11.11%
4. Increase by 11.11%

Answer: 4. Increase by 11.11%

Question 28. The gases carbon-monoxide (CO) and nitrogen at the same temperature have kinetic energies E₁ and E₂ respectively. Then :

1. E₁= E₂
2. E₁> E₂
3. E₁< E₂
4. E₁ and E₂ cannot be compared

Answer: 1. E₁= E₂

Question 29. In equilibrium, the velocity of molecules of a gas depends on its temperature as

1. \(\mathrm{u} \propto \mathrm{T}\)
2. \(\mathrm{u} \propto \frac{1}{\mathrm{~T}}\)
3. \(\mathrm{u} \propto \sqrt{\mathrm{T}}\)
4. \(\mathrm{u} \propto \mathrm{T}^0\)

Answer: 3. \(\mathrm{u} \propto \sqrt{\mathrm{T}}\)

Question 30. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds \(\left(\frac{v_{\mathrm{rms}}(\text { helium })}{v_{\mathrm{rms}}(\text { argon })}\right)\) is:

1. 0.32
2. 0.45
3. 2.24
4. 3.16

Answer: 4. 3.16

Question 31. The ratio of the average kinetic energy of H₂ and O₂ at a given temperature is :

1. 1: 16
2. 1: 8
3. 1: 4
4. 1: 1

Answer: 4. 1: 1

Question 32. If the temperature of the gas is increased to three times, then its root mean square velocity becomes:

1. 3 times
2. 9 times
3. 12times
4. 3times

Answer: 4. 3times

Question 33. Which of the following statements is incorrect according to assumptions of the kinetic theory of gases?

1. The potential energy of a molecule is zero
2. Molecules move randomly in all directions
3. the kinetic energy of molecules changes when they collide with the wall of a container
4. None of these

Answer: 4. None of these

Question 34. At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at 47º C?

1. 80 K
2. –73 K
3. 3 K
4. 20 K

Answer: 4. 20 K

Question 35. The kinetic energy of one mole gas at 300 K temperature, is E. At 400 K temperature kinetic energy is E’.The value of E’/E is :

1. 1.33
2. \(\sqrt{\left(\frac{4}{3}\right)}\)
3. \(\frac{16}{9}\)
4. 2

Answer: 1. 1.33

Question 36. If the temperature becomes triple, the root mean square velocity of gas molecules will be :

1. \(\text { v } \sqrt{2}\)
2. \(\text { v/ } \sqrt{3}\)
3. \(\sqrt{3} v\)
4. Same

Answer: 3. \(\sqrt{3} v\)

[υ is the root mean square velocity of gas molecules at temperature T]

Question 37. On increasing the temperature of gas contained in a closed vessel by 1°C, the pressure increases by 0.4%. The initial temperature of a gas is:

1. 25 K
2. 250 K
3. 2500° K
4. 250° C

Answer: 2. 250 K

Question 38. When the temperature of a gas is increased then which of the following statements is always true?

1. Work is done on the gas
2. Heat is supplied to a gas
3. The internal energy of the gas is increased
4. The pressure of gas remains unchanged.

Answer: 3. Internal energy of a gas is increased

Question 39. The speed of sound through oxygen at TK is v ms^-1. As the temperature becomes 2T and oxygen gas dissociates into atomic oxygen, the speed of sound :

1. Remains the same
2. Becomes 2v
3. Becomes \(\sqrt{2 v}\)
4. None of these

Answer: 4. None of these

Question 40. When the temperature of an ideal gas is increased from 27ºC to 227ºC, its rms speed is changed from 400 m/s to v_s. The v_s is :

1. 516 m/s
2. 450 m/s
3. 310 m/s
4. 746 m/s

Answer: 1. 516 m/s

Question 41. The root mean square and most probable speed of the molecules in a gas are

1. Same
2. Different
3. Cannot say
4. Depends on the nature of the gas

Answer: 2. Different

Question 42. Hydrogen gas is filled in a container of volume 20 liter. The average translational kinetic energy of all its molecules is 1.5 × 10⁵ J. Pressure of hydrogen in the cylinder is:

1. 2 × 10⁶ N/m²
2. 3 × 10⁶ N/m²
3. 4 × 10⁶ N/m²
4. 5 × 10⁶ N/m²

Answer: 4. 5 × 10⁶ N/m²

Question 43. The root mean square speed of ideal hydrogen gas in a closed chamber at 0°C is 3180 m/s. Its pressure will be (density of hydrogen gas is 8.99 × 10^-2 kg/m³, 1 atm. = 1.01 × 10⁵ N/m²)

1. 1.0 atm.
2. 1.5 atm.
3. 2.0 atm.
4. 3.0 atm.

Answer: 4. 3.0 atm.

Question 44. A flask contains argon and chlorine in the ratio 3: 1 by mass. The temperature of the mixture is 300 K. If the atomic mass of argon = 39.9 u, and the molecular mass of chlorine = 70.9u, then the ratio of average kinetic energy per molecule of argon to chlorine gas is

1. 1: 1
2. 3: 1
3. 1 : 3
4. 39.9: 70.9

Answer: 1. 1: 1

Question 45. At the same temperature and pressure, the densities of two diatomic gases are d₁ and d₂, The ratio of velocities of sound in these gases will be

1. \(\frac{d_1}{d_2}\)
2. \(\sqrt{\frac{d_2}{d_1}}\)
3. \(\sqrt{\frac{d_1}{d_2}}\)
4. \(\frac{d_2^2}{d_1^2}\)

Answer: 2. \(\sqrt{\frac{d_2}{d_1}}\)

Question 46. The ratio of the mean speed of hydrogen molecules to the mean speed of nitrogen molecules in a sample containing a mixture of the two gases.

1. \(\sqrt{14}\)
2. \(\sqrt{7}\)
3. \(\sqrt{28}\)
4. None of these

Answer: 1. \(\sqrt{14}\)

Question 47. Three closed vessels A, B, and C are at the same temperature T, and contain gases that obey the Maxwellian distribution of velocities. Vessel A contains only O₂, B only N_2, and C a mixture of equal quantities of O₂ and N₂. If the average speed of O₂ molecules in vessel A is V₁, that of the N₂ molecules in vessel B is V₂, the average speed of the O₂ molecules in vessel C will be :

1. (V₁+ V₂)/2
2. V₁
3. (V₁V₂)1/2
4. \(\sqrt{3 \mathrm{kT} / \mathrm{M}}\)

Answer: 2. V₁

Question 48. The pressure of an ideal gas is written as P = \(\frac{2 E}{3 V}\). Here E refers to

1. Translational kinetic energy
2. Rotational kinetic energy
3. Vibrational kinetic energy
4. Total kinetic energy.

Answer: 1. Translational kinetic energy

Question 49. Which of the following quantities is the same for all ideal gases at the same temperature?

1. The kinetic energy of 1 mole
2. The kinetic energy of 1 g
3. The number of molecules in 1 mole
4. The number of molecules in 1 g

Answer: 3. The number of molecules in 1 mole

Question 50. Let ΔU₁ and ΔU₂ be the changes in internal energy of the system in the processes A and B then

1. ΔU₁> ΔU₂
2. ΔU₁= ΔU₂
3. ΔU₁< ΔU₂
4. ΔU₁≠ ΔU₂

Answer: 2. ΔU1= ΔU₂

Question 51. The internal energy of a mono-atomic gas is –

1. \(\frac{5 R T}{2}\)
2. \(\frac{3 R T}{2}\)
3. \(\frac{5 R T}{3}\)
4. \(\frac{7 R T}{3}\)

Answer: 2. \(\frac{3 R T}{2}\)

Question 52. The change in internal energy, when a gas is cooled from 927ºC to 27ºC is

1. 100%
2. 200%
3. 75%
4. 400%

Answer: 3. 75%

Question 53. A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes the total internal energy of the system is:

1. 4RT
2. 15RT
3. 9RT
4. 11RT

Answer: 4. 11RT

Question 54. An ideal gas is filled in a closed rigid and thermally insulated container. A coil of 100Ω resistor carrying current 1A for 5 minutes supplies heat to the gas. The change in internal energy of the gas is

1. 10 KJ
2. 20 KJ
3. 30 KJ
4. 0 KJ

Answer: 3. 30 KJ

Question 55. 300 calories of heat is supplied to raise the temperature of 50 gm of air from 20°C to 30°C without any change in its volume. Change in internal energy per gram of air is

1. Zero
2. 0.6 calories
3. 1.2 calories
4. 6.0 calories

Answer: 4. 6.0 calories

Question 56. Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will:

1. Increase
2. Decrease
3. Remain same
4. Decrease for some, while increase for others

Answer: 3. Remain same

Question 57. According to the law of equal distribution of energy, the mean energy of a molecule per degree of freedom is:

1. \(\frac{1}{2} \mathrm{KT}\)
2. KT
3. \(\frac{3}{2} \mathrm{KT}\)
4. \(\frac{5}{2} \mathrm{KT}\)

Answer: 1. \(\frac{1}{2} \mathrm{KT}\)

Question 58. Which of the following statements is correct for any thermodynamic system?

1. The internal energy changes in all processes
2. Internal energy and entropy are state functions
3. The change in entropy can never be zero
4. The work done in an adiabatic process is always zero

Answer: 2. Internal energy and entropy are state functions

Question 59. A system goes from A to B via two processes 1 and 2 as shown in the figure. If ΔU₁ and ΔU₂ are the changes in internal energies in processes 1 and 2 respectively, then:

1. ΔU₁= ΔU₂
2. The relation between ΔU₁ and ΔU₂ cannot be determined
3. ΔU₂> ΔU₁
4. ΔU₂< ΔU₁

Answer: 1. ΔU₁= ΔU₂

Question 60. Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature To, while box B contains one mole of helium at temperature (7/3)To. 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, Tfin terms of T₀ is :

1. \(\mathrm{T}_{\mathrm{f}}=\frac{3}{7} \mathrm{~T}_0\)
2. \(\mathrm{T}_{\mathrm{f}}=\frac{7}{3} \mathrm{~T}_0\)
3. \(T_f=\frac{3}{2} T_0\)
4. \(\mathrm{T}_{\mathrm{f}}=\frac{5}{2} \mathrm{~T}_0\)

Answer: 3. \(T_f=\frac{3}{2} T_0\)

Question 61. An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V₁ and contains ideal gas at pressure p₁ and temperature T₁. The other chamber has volume V₂ and contains ideal gas at pressure p₂ and temperature T₂. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be –

1. \(\frac{T_1 T_2\left(p_1 V_1+p_2 V_2\right)}{p_1 V_1 T_2+p_2 V_2 T_1}\)
2. \(\frac{p_1 V_1 T_1+p_2 V_2 T_2}{p_1 V_1+p_2 V_2}\)
3. \(\frac{p_1 V_1 T_2+p_2 V_2 T_1}{p_1 V_1+p_2 V_2}\)
4. \(\frac{T_1 T_2\left(p_1 V_1+p_2 V_2\right)}{p_1 V_1 T_1+p_2 V_2 T_2}\)

Answer: 1. \(\frac{T_1 T_2\left(p_1 V_1+p_2 V_2\right)}{p_1 V_1 T_2+p_2 V_2 T_1}\)

Question 62. In the following figures to (4), variation of volume by change of pressure is shown. A gas is taken along the path ABCDA. The change in internal energy of the gas will be:

1. Positive in all cases from(1) to (4)
2. Positive in case (1), and but zero in case(4)
3. Negative in cases (1), and but zero in case
4. Zero in all the four cases.

Answer: 4. Zero in all the four cases.

Question 63. An ideal gas changes from state a to state b as shown in Fig. What is the work done by the gas in the process?

1. Zero
2. Positive
3. Negative
4. Infinite

Answer: 1. Zero

Question 64. The process ΔU = 0, for an ideal gas, can be best represented in the form of a graph:

Answer: 2

Question 65. In the following V-T diagram what is the relation between P₁ and P₂:

1. P₂= P₁
2. P₂> P₁
3. P₂< P₁
4. Cannot be predicted

Answer: 3. P₂< P₁

Question 66. In the isothermal expansion of an ideal gas. Select the wrong statement:

1. There is no change in the temperature of the gas
2. There is no change in the internal energy of the gas
3. The work done by the gas is equal to the heat supplied to the gas
4. The work done by the gas is equal to the change in its internal energy

Answer: 4. The work done by the gas is equal to the change in its internal energy

Question 67. In the cyclic process shown on the P – V diagram, the magnitude of the work done is:

1. \(\pi\left(\frac{P_2-P_1}{2}\right)^2\)
2. \(\pi\left(\frac{V_2-V_1}{2}\right)^2\)
3. \(\frac{\pi}{4}\left(P_2-P_1\right)\left(V_2-V_1\right)\)
4. \(\pi\left(P_2 V_2-P_1 V_1\right)\)

Answer: 3. \(\frac{\pi}{4}\left(P_2-P_1\right)\left(V_2-V_1\right)\)

Question 68. A fixed mass of ideal gas undergoes changes in pressure and volume starting at L, as shown in Figure.

Which of the following is correct :

Answer: 2

Question 69. A fixed mass of gas undergoes the cycle of changes represented by PQRSP as shown in Figure. In some of the changes, work is done on the gas, and in others, work is done by the gas. In which pair of the changes work is done on the gas?

1. PQ and RS
2. PQ and QR
3. OR and RS
4. RS and SP.

Answer: 4. RS and SP

Question 70. Consider two processes on a system as shown in Figure. The volumes in the initial states are the same in the two processes and the volumes in the final states are also the same. Let ΔW₁ and ΔW₂ be the work done by the system in the processes A and B respectively.

1. ΔW₁> ΔW₂
2. ΔW₁= ΔW₂
3. ΔW₁< ΔW₂
4. Nothing can be said about the relation between ΔW1 and ΔW₂

Answer: 3. ΔW₁< ΔW₂

Question 71. A mass of an ideal gas undergoes a reversible isothermal compression. Its molecules will then be compared with an initial state, the same

1. Root mean square velocity
2. Mean momentum
3. Mean kinetic energy

1. (1), (2), (3) correct
2. (1), (2) correct
3. (2), (3) correct
4. (1) correct

Answer: 1. (1), (2), (3) correct

Question 72. Find work done by the gas in the process shown in the figure:

1. \(\frac{5}{2} \pi{atm} \mathrm{L}\)
2. \(\frac{5}{2} \mathrm{~atm} \mathrm{~L}\)
3. \(-\frac{3}{2} \pi {atm} \mathrm{L}\)
4. \(-\frac{5}{4} \pi \mathrm{atm} \mathrm{L}\)

Answer: 4. \(-\frac{5}{4} \pi \mathrm{atm} \mathrm{L}\)

Question 73. The change in internal energy of two moles of a gas during adiabatic expansion is found to be –100 joule. The work done during the process is –

1. 100 joule
2. –100 joule
3. Zero
4. 200 joule

Answer: 1. 100 joule

Question 74. The work done in the following figure is –

1. 2 × 10⁵joule
2. 10⁵joule
3. Zero
4. 3 × 10⁵joule

Answer: 2. 105joule

Question 75. The net amount of the work done in the following indicator diagram is –

1. Zero
2. Positive
3. Negative
4. Infinite

Answer: 1. Zero

Question 76. An ideal gas is taken via paths AB, BC, and CA as shown in Fig. The net work done in the whole cycle is-

1. 3P₁V₁
2. –3P₁V₁
3. 6P₁V₁
4. 12P₁V₁

Answer: 2. –3P₁V₁

Question 77. In the indicator diagram shown, the work done along path AB is-

1. Zero
2. 20 joule
3. –20 joule
4. 60 joule

Answer: 2. 20 joule

Question 78. In the above problem work done along path BC is –

1. Zero
2. 40 joule
3. 60 joule
4. None

Answer: 1. Zero

Question 79. In the above problem, the work done along path CA is –

1. 20 joule
2. 30 joule
3. – 30 joule
4. Zero

Answer: 3. –30 joule

Question 80. Starting the same initial conditions, an ideal gas expands from volume V₁ to V₂ in three different ways. The work done by the gas is W₁ if the process is purely isothermal, W₂ if purely isobaric, and W₃ if purely adiabatic. Then:

1. W₂> W₁> W₃
2. W₂> W₃> W₁
3. W₁> W₂> W₃
4. W₁> W₃> W₂

Answer: 1. W₂> W₁> W₃

Question 81. 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 5 J, the work done by the gas in the process C → A is:

1. – 5 J
2. – 10 J
3. – 15 J
4. – 20 J

Answer: 1. – 5 J

Question 82. The work done by a gas taken through the closed process ABCA, see figure is

1. 6P₀V₀
2. 4P₀V₀
3. P₀V₀
4. Zero

Answer: 1. 6P₀V₀

Question 83. A system is given 400 calories of heat and 1000 joule of work is done by the system, then the change in internal energy of the system will be –

1. 680 joule
2. 680 erg
3. 860 joule
4. – 860 joule

Answer: 1. 680 joule

Question 84. If AB and CD are isothermals and AD and BC are adiabatic then the temperatures of

1. B and C are the same
2. A and C are the same
3. B and D are the same
4. The temperature of A is more than that of D

Answer: 4. Temperature of A is more than that of D

Question 85. An ideal gas initially at a state (P₁, V₁) is allowed to expand isothermally to a state (P₂, V₂). Then the gas is compressed adiabatically to its initial volume V₁. Let the final pressure be P₃ and the work done by the gas during the whole process be W, then

1. P₃> P₁ and W < 0
2. P₃> P₁ and W > 0
3. P₃< P₁ and W > 0
4. P₃< P₁ and W < 0

Answer: 1. P₃> P₁ and W < 0

Question 86. An ideal gas is taken through the process shown in the figure:

1. In process AB, work done by the system is positive
2. In process AB, heat is rejected out of the system.
3. In process AB, internal energy increases
4. In process AB internal energy decreases and in process BC internal energy increases.

Answer: 2. In process AB, heat is rejected out of the system.

Question 87. If heat is supplied to an ideal gas in an isothermal process,

1. The internal energy of the gas will increase
2. The gas will do positive work
3. The gas will do negative work
4. The said process is not possible

Answer: 2. The gas will do positive work

Question 88. A system can be taken from the initial state p₁, V₁ to the final state p₂, V₂ by two different methods. Let ΔQ and ΔW represent the heat given to the system and the work done by the system. Which of the following must be the same in both methods?

1. ΔQ
2. ΔW
3. ΔQ + ΔW
4. ΔQ – ΔW

Answer: 4. ΔQ – ΔW

Question 89. In changing the state of a system from state A to state B adiabatically the work done on the system is 322 joule. If 100 calories of heat are given to the system in bringing it from state B to state A, then the work done on the system in this process will be –

1. 98 joule
2. 38.2 joule
3. 15.9 calorie
4. 15.9 joule

Answer: 1. 98 joule

Question 90. An ideal gas heat engine operates in a Carnot cycle between 227ºC and 127ºC. It absorbs 6 kcal at a higher temperature. The amount of heat (in kcal) converted into work is equal to:

1. 1.6
2. 1.2
3. 4.8
4. 3.5

Answer: 2. 1.2

Question 91. In a closed container of 44.8 liter, the volume of monoatomic gas is filled up. The heat required to raise the temperature by 10°C will be :

1. R
2. 10R
3. 20R
4. 30R

Answer: 4. 30R

Question 92. Two moles of an ideal gas are taken in a cyclic process abcda. During the process, ab and cd temperatures are 500 K and 300 K respectively. Calculate heat absorbed by the system (In 2 = 0.69 and R = 8.3 J/mol-K)

Answer: 2290.3j

Question 93. If Q, E, and W denote respectively the heat added, change in internal energy, and the work done in a closed cycle process, then

1. W = 0
2. Q = W = 0
3. E = 0
4. Q = 0

Answer: 3. E = 0

Question 94. Which of the following is incorrect regarding the first law of thermodynamics?

1. It does not apply to any cycle process
2. It is a restatement of the principle of conservation of energy
3. It introduces the concept of the internal energy
4. It introduces the concept of the entropy

Answer: (1,4)

Question 95. When a system is taken from state I to state f along the path, it is found that Q = 50 cal and W = 20 cal. Along the path ibf Q = 36 cal. W along the path ibf is:

1. 6 cal
2. 16 cal
3. 66 cal
4. 14 cal

Answer: 1. 6 cal

Question 96. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is.

1. \(\frac{2}{5}\)
2. \(\frac{3}{5}\)
3. \(\frac{3}{7}\)
4. \(\frac{5}{7}\)

Answer: 4. \(\frac{5}{7}\)

Question 97. Boiling water is changing into steam. Under this condition, the specific heat of water is

1. Zero
2. One
3. Infinite
4. Less than one

Answer: 3. Infinite

Question 98. Supposing the distance between the atoms of a diatomic gas to be constant, its specific heat at constant volume per mole (gram mole) is

1. \(\frac{5}{2} R\)
2. \(\frac{3}{2} R\)
3. R
4. \(\frac{7}{2} R\)

Answer: 1. \(\frac{5}{2} R\)

Question 99. A gas is formed of molecules each molecule possessing f degrees of freedom, then the value of γ = \(\frac{C_p}{C_V}\)is equal to:

1. \(\frac{2}{\mathrm{f}}\)
2. \(1+\frac{2}{f}\)
3. \(1+\frac{f}{2}\)
4. \(\mathrm{f}+\frac{1}{2}\)

Answer: 2. \(1+\frac{2}{f}\)

Question 100. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio C_p/C_V for the gas is:

1. 4/3
2. 2
3. 5/3
4. 3/2

Answer: 4. 3/2

Question 101. Some students find values of C_V and C_P for gas in calorie/gm–mol K. Which pair is most correct?

1. C_V= 3, C_P= 5
2. C_V= 4, C_P= 6
3. C_V= 3, C_P= 2
4. C_V= 3, C_P= 4.2

Answer: 1. C_V= 3, CP= 5

Question 102. The thermal capacity of anybody is:

1. A measure of its capacity to absorb heat
2. A measure of its capacity to provide heat
3. The quantity of heat required to raise its temperature by a unit degree
4. The quantity of heat required to raise the temperature of a unit mass of the body by a unit degree

Answer: 3. The quantity of heat required to raise its temperature by a unit degree

Question 103. 1 mole of a gas with γ = 7/5 is mixed with 1 mole of a gas with γ = 5/3, then the value of γ for the resulting mixture is:

1. 7/5
2. 2/5
3. 24/16
4. 12/7

Answer: 3. 24/16

Question 104. The molar heat capacity at a constant volume of oxygen gas at STP is nearly 2.5 R. As the temperature is increased, it gradually increases and approaches 3.5 R. The most appropriate reason for this behavior is that at high temperatures

1. Oxygen does not behave as an ideal gas
2. Oxygen molecules dissociate in atoms
3. The molecules collide more frequently
4. Molecular vibration gradually becomes effective

Answer: 3. The molecules collide more frequently

Question 105. The amount of heat required to raise the temperature of 100 gm water from 20ºC to 40ºC will be –

1. 100 calorie
2. 2000 calorie
3. 4000 calorie
4. Zero

Answer: 2. 2000 calorie

Question 106. Two moles of ideal helium gas are in a rubber balloon at 30° C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)

1. 62J
2. 104 J
3. 124 J
4. 208 J

Answer: 4. 208 J

Question 107. The molar specific heat at constant pressure of an ideal gas is \(\left(\frac{7}{2}\right)\) R. The ratio of specific heat at constant pressure to that at constant volume is:

1. \(\frac{7}{5}\)
2. \(\frac{8}{7}\)
3. \(\frac{5}{7}\)
4. \(\frac{9}{7}\)

Answer: 1. \(\frac{7}{5}\)

Question 108. One mole of ideal monoatomic gas (γ = 5/3) is mixed with one mole of diatomic gas (γ = 7/5). What is γ for the mixture? γ denotes the ratio of specific heat at constant pressure, to that at constant volume.

1. 3/2
2. 23/15
3. 35/23
4. 4/3

Answer: 1. 3/2

Question 109. A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio
Cof the mixture is:

1. 1.59
2. 1.62
3. 1.4
4. 1.54

Answer: 2. 1.62

Question 110. If C_P and CV denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

1. C_P – C_V = R / 28
2. C_P – C_V = R / 14
3. C_P – C_V = R
4. C_P – C_V = 28R

Answer: 1. C_P – C_V = R/28

Question 111. A gas is contained in a metallic cylinder fitted with a piston. The piston is suddenly moved in to compress the gas and is maintained at this position. As time passes, after this pressure of the gas in the cylinder

1. Increases
2. Decreases
3. Remains constant
4. Increases or decreases depending on the nature of the gas.

Answer: 2. Decreases

Question 112. Two samples A and B are initially kept in the same state. Sample A is expanded through an adiabatic process and sample B through an isothermal process upto the same final volume. The final pressures in A and B are p_A and p_B respectively.

1. p_A> p_B
2. p_A= p_B
3. p_A< p_B
4. The relation between p_A and p_B cannot be deduced.

Answer: 3. p_A< p_B

Question 113. Let T_a and T_b be the final temperature of the samples A and B respectively in the previous question then:

1. T_a< T_b
2. T_a= T_b
3. T_a> T_b
4. The relation between T_a and T_b cannot be deduced.

Answer: 1. T_a< T_b

Question 114. Let ΔW_a and ΔW_b be the work done by the systems A and B respectively in the previous question then:

1. ΔW_a> ΔW_b
2. ΔW_a= ΔW_b
3. ΔW_a< ΔW_b
4. The relation between W_a and W_b cannot be deduced

Answer: 3. ΔW_a< ΔW_b

Question 115. Four curves A, B, C, and D are drawn in Figure. for a given amount of gas. The curves that represent adiabatic and isothermal changes are

1. C and D respectively
2. D and C respectively
3. A and B respectively
4. B and A respectively

Answer: 3. A and B respectively

Question 116. For an ideal gas, the heat capacity at constant pressure is larger than that at constant volume because

1. Positive work is done during the expansion of the gas by the external pressure
2. Positive work is done during expansion by the gas against external pressure
3. Positive work is done during expansion by the gas against intermolecular forces of attraction
4. More collisions occur per unit of time when volume is kept constant.

Answer: 2. Positive work is done during expansion by the gas against external pressure

Question 117. A gas has:

1. One specific heat only
2. Two specific heats only
3. An infinite number of specific heats
4. No specific heat

Answer: 3. Infinite number of specific heats

Question 118. For a solid with a small expansion coefficient,

1. C_p– C_v= R
2. C_p– C_v= R
3. C_p is slightly greater than C_v
4. C_p is slightly less than C_v

Answer: 3. C_p is slightly greater than C_v

Question 119. When an ideal gas undergoes an adiabatic change causing a temperature change ΔT

1. There is no heat gained or lost by the gas
2. The work done by the gas is equal to the change in internal energy
3. The change in internal energy per mole of the gas is Cv ΔT, where Cvis the molar heat capacity at constant volume.

1. (1), (2), (3) correct
2. (1), (2) correct
3. (1), (3) correct
4. (1) correct

Answer: 3. (1), (3) correct

Question 120. The adiabatic bulk modulus of hydrogen gas (γ = 1.4) at NTP is:

1. 1 × 10⁵ N/m²
2. 1 × 10^-5 N/m²
3. 1.4 N/m²
4. 1.4 × 10⁵ N/m²

Answer: 4. 1.4 × 10⁵ N/m²

Question 121. A given quantity of a gas is at pressure P and absolute temperature T. The isothermal bulk modulus of the gas is:

1. \(\frac{2}{3} P\)
2. P
3. \(\frac{3}{2} P\)
4. 2P

Answer: 2. P

Question 122. A and B are two adiabatic curves for two different gases. Then A and B correspond to:

1. Ar and He respectively
2. He and H₂ respectively
3. O₂ and H₂ respectively
4. H₂ and He respectively

Answer: 2. He and H₂ respectively

Question 123. In a cyclic process shown in the figure an ideal gas is adiabatically taken from B and A., the work done on the gas during the process B → A is 30 J, and when the gas is taken from A → B the heat absorbed by the gas is 20 J. The change in internal energy of the gas in the process A → B is:

1. 20 J
2. – 30 J
3. 50 J
4. – 10 J

Answer: 2. –30 J

Question 124. An ideal gas is allowed to expand freely against a vacuum in a rigid insulated container. The gas undergoes:

1. An increase in its internal energy
2. A decrease in its internal energy
3. Neither an increase nor decrease in temperature or internal energy
4. An increase in temperature

Answer: 1. An increase in its internal energy

Question 125. For free expansion of a gas in an adiabatic container which of the following is true?

1. Q = W = 0 and ΔU = 0
2. Q = 0, W > 0 and ΔU = Q
3. W = 0, Q > 0 and ΔU = Q
4. W = 0, Q < 0 and ΔU = 0

Answer: 1. Q = W = 0 and ΔU = 0

Question 126. In an adiabatic process on a gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about

1. 0.36%
2. 0.5%
3. 0.7&
4. 1%

Answer: 1. 0.36%

Question 127. A fixed mass of an ideal gas undergoes the change represented by XYZX below. Which one of the following sets could describe these changes?

Answer: 4

Question 128. Starting with the same initial conditions, an ideal gas expands from volume V₁ to V₂ in three different ways. The work done by the gas is W₁ if the process is isothermal, W₂ if isobaric and W₃ if adiabatic, then :

1. W₂> W₁> W₃
2. W₂> W₃> W₁
3. W₁> W₂> W₃
4. W₁> W₃> W₂

Answer: 1. W₂> W₁> W₃

Question 129. A gas is expanded from volume V₀ to 2V₀ under three different processes. Process 1 is isobaric, process 2 is isothermal and process 3 is adiabatic. Let ΔU₁, ΔU₂, and ΔU₃ be the change in internal energy of the gas in these three processes. Then:

1. ΔU₁> ΔU₂> ΔU₃
2. ΔU₁< ΔU₂< ΔU₃
3. ΔU₂< ΔU₁< ΔU₃
4. ΔU₂< ΔU₃< ΔU₁

Answer: 1. ΔU₁> ΔU₂> ΔU₃

Question 130. The molar heat capacity for the process shown in fig. is

1. C = C_p
2. C = C_v
3. C > C_v
4. C = 0

Answer: 4. C = 0

Question 131. Find the amount of work done to increase the temperature of one mole of ideal gas by 30ºC. if it is expanding under the condition V ∝ T^2/3 (R = 8.31 J/mol – K):

1. 16.62 J
2. 166.2 J
3. 1662 J
4. 1.662 J

Answer: 2. 166.2 J

Question 132. A gas undergoes a process in which its pressure P and volume V are related as VPⁿ = constant. The bulk modulus of the gas in the process is:

1. no
2. P^1/n
3. P/n
4. Pⁿ

Answer: 3. P/n

Question 133. V = \(k\left(\frac{P}{T}\right)^{0.33}\) where k is constant. It is a,

1. Isothermal process
2. Adiabatic process
3. Isochoric process
4. Isobaric process

Answer: 3. Isochoric process

Question 134. For the adiabatic process of an ideal gas the value of \(\frac{d P}{P}\) is equal to –

1. \(-\gamma \frac{d V}{V}\)
2. \(-\gamma \frac{V}{d V}\)
3. \(\frac{d V}{V}\)
4. \(-\gamma^2 \frac{d V}{V}\)

Answer: 1. \(-\gamma \frac{d V}{V}\)

Question 135. The isobaric modulus of elasticity is –

1. ∞
2. Zero
3. 1
4. \(\frac{C_p}{C_v}\)

Answer: 2. Zero

Question 136. Two samples of a gas A and B initially at the same temperature and pressure, are compressed to half their initial volume, A isothermally and B adiabatically. The final pressure in –

1. A and B will be the same
2. A will be more than in B
3. A will be less than B
4. A will be double that in B

Answer: 3. A will be less than in B

Question 137. The isothermal bulk modulus of elasticity of a gas is 1.5 × 10⁵ N/m². Its adiabatic bulk modulus of elasticity will be if γ = 1.4 –

1. 1.5 × 10⁵ N/m²
2. 3 × 10⁵ N/m²
3. 2.1 × 10⁵ N/m²
4. ∞

Answer: 3. 2.1 × 10⁵ N/m²

Question 138. The pressure and volume of a diatomic gas are P and V respectively. It is compressed suddenly to 1/32 of its initial volume then its final pressure will be –

1. 32 P
2. 128 P
3. P/128
4. P/32

Answer: 2. 128 P

Question 139. The work done by gas in an adiabatic process depends on –

1. Change in temperature
2. Change in volume
3. Change in pressure
4. Change is heat

Answer: 1. Change in temperature

Question 140. The volume of a gas is reduced to 1/4 of its initial volume adiabatically at 27ºC. The final temperature of the gas will be if γ = 1.4 –

1. 300 × (4)0.4 K
2. 100 × (4)0.4 K
3. 27 × (4)0.4 K
4. 300 × (1/4)0.4 K

Answer: 1. 300 × (4)0.4 K

Question 141. 1 m³ of gas is compressed suddenly at atmospheric pressure and temperature 27ºC such that its temperature becomes 627ºC. The final pressure of the gas will be (γ = 1.5)-

1. 27 × 10⁶ N/m²
2. 7.2 × 10⁵ N/m²
3. 2.7 × 10⁵ N/m²
4. 27 × 10⁵ N/m²

Answer: 4. 27 × 105 N/m²

Question 142. If 1 kg air (γ = 1.4) is heated adiabatically from 0ºC to 10ºC then the increase in its internal energy will be (C_v= 0.172 cal/gmºC) –

1. 1720 joule
2. 7224 joule
3. 172 calorie
4. 7224 calorie

Answer: 2. 7224 joule

Question 143. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The value of γ for the gas is –

1. \(\frac{5}{3}\)
2. \(\frac{7}{5}\)
3. \(\frac{3}{2}\)
4. \(\frac{11}{9}\)

Answer: 3. \(\frac{3}{2}\)

Question 144. 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T₁, the work done in the process is:

1. \(\frac{9}{8} \mathrm{RT}_1\)
2. \(\frac{3}{2} \mathrm{RT}_1\)
3. \(\frac{15}{8} R T_1\)
4. \(\frac{9}{2} R T_1\)

Answer: 1. \(\frac{9}{8} \mathrm{RT}_1\)

Question 145. An ideal gas is expanding such that PT₂ = constant. The coefficient of volume expansion of the gas is

1. \(\frac{1}{\mathrm{~T}}\)
2. \(\frac{2}{\mathrm{~T}}\)
3. \(\frac{3}{\mathrm{~T}}\)
4. \(\frac{4}{\mathrm{~T}}\)

Answer: 3. \(\frac{3}{\mathrm{~T}}\)

Question 146. One mole of an ideal gas at an initial temperature of T K does 6R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and constant volume is 5/3, the final temperature of the gas will be :

1. (T + 2.4) K
2. (T – 2.4) K
3. (T + 4) K
4. (T – 4) K

Answer: 4. (T – 4) K

Question 147. 2 moles of He gas γ = 5/3 of 20-litre volume at 27ºC subjected to constant pressure is expanded to double the initial volume. Then, it is adiabatically taken to an initial temperature of 27ºC. What will be the work done in the isobaric process? Also find the final pressure, final volume, and work done in the adiabatic process.

1. 7470 J
2. 7074 J
3. 7070 J
4. 7474 J

Answer: 1. 7470 J

Question 148. A Carnot engine works between 600 K and 300 K. In each cycle of operations, the engine draws 1000 joules of energy from the source at 600 K. The efficiency of the engine is –

1. 20%
2. 50%
3. 70%
4. 90%

Answer: 2. 50%

Question 149. In the above problem, the useful work done by the engine is –

1. 100 joule
2. 500 joule
3. 1000 joule
4. 150 joule

Answer: 2. 500 joule

Question 150. In the above problem, the energy rejected by the sink is –

1. 100 joule
2. 500 joule
3. 1000 joule
4. 300 joule

Answer: 2. 500 joule

Question 151. A Carnot engine works between the ice point and the steam point. Its efficiency will be –

1. 26.81 %
2. 53.36 %
3. 71.23 %
4. 85.42 %

Answer: 1. 26.81 %

Question 152. In the above problem, to increase the efficiency of the engine by 20%, its sink temperature will have to be changed by –

1. Increase by 20 K
2. Decrease by 293 K
3. Increase by 20ºC
4. Decrease by 20ºC

Answer: 4. Decrease by 20ºC

Question 153. In the above problem, to increase the efficiency by 20%, its source temperature will have to be changed by –

1. 402.5 K increase
2. 129.5 K decrease
3. 129.5 ºC increase
4. 129.5 ºC decrease

Answer: 3. 129.5 ºC increase

Question 154. A Cannot engine work between 200ºC and 0ºC. Another Carnot engine works between 0ºC and –200ºC. In both cases, the working substance absorbs 4 kilocalories of heat from the source. The efficiency of the first engine will be –

1. \(\frac{100}{473}\)
2. \(\frac{200}{473}\)
3. \(\frac{200}{273}\)
4. \(\frac{273}{373}\)

Answer: 2. \(\frac{200}{473}\)

Question 155. In the above problem, the efficiency of the second engine will be –

1. \(\frac{100}{273}\)
2. \(\frac{173}{273}\)
3. \(\frac{200}{273}\)
4. \(\frac{273}{373}\)

Answer: 3. \(\frac{200}{273}\)

Question 156. In the above problem, the ratio of efficiencies of two engines will be –

1. 0.18
2. 0.38
3. 0.58
4. 0.78

Answer: 3. 0.58

Question 157. In the above problem, the amount of useful work done by the first engine is –

1. 7.1 × 10³ Joule
2. 3.8 × 10⁴ Joule
3. 5.9 × 10⁵ Joule
4. 9.3 × 10⁶ Joule

Answer: 1. 7.1 × 10³ Joule

Question 158. In the above problem, the output work of the second engine is

1. 2.93 × 10³ calorie
2. 12.3 × 10³ calorie
3. 12.3 × 10³ joule
4. 2.93 × 10³ calorie

Answer: 1. 2.93 × 10³ calorie

Question 159. In the above problem, the ratio of outputs of two engines is –

1. 0.577
2. 0.377
3. 0.777
4. 0.177

Answer: 1. 0.577

Question 160. The efficiency of the Carnot engine is 50% and the temperature of the sink is 500 K. If the temperature of the source is kept constant and its efficiency is to be raised to 60%; then the required temperature of the sink will be:

1. 600 K
2. 500 K
3. 400 K
4. 100 K

Answer: 3. 400 K

Question 161. Even the Carnot engine cannot give 100% efficiency because we cannot:

1. Prevent radiation
2. Find ideal sources
3. Reach absolute zero temperature
4. Eliminate friction

Answer: 3. Reach absolute zero temperature

Question 162. “Heat cannot be itself flow from a body at a lower temperature to a body at a higher temperature” is a statement or consequence of :

1. Second law of thermodynamics
2. Conservation of momentum
3. Conservation of mass
4. The first law of thermodynamics

Answer: 1. Second law of thermodynamics

Question 163. A Carnot engine takes 3 × 10⁶ cal of heat from a reservoir at 627ºC and gives it to a sink at 27ºC. The work done by the engine is:

1. 4.2 × 10⁶ J
2. 8.4 × 10⁶ J
3. 16.8 × 10⁶ J
4. Zero

Answer: 2. 8.4 × 106 J

Question 164. In a Carnot engine, the reservoir temperature is 7°C. Its efficiency is 50%. To increase efficiency to 70% by how much temperature of the source is to be raised.

1. 840 K
2. 280 K
3. 560 K
4. 373 K

Answer: 4. 373 K

Question 165. Which statement is incorrect?

1. All reversible cycles have the same efficiency
2. A reversible cycle has more efficiency than an irreversible one
3. Carnot cycle is a reversible one
4. Carnot cycle has the maximum efficiency in all cycles

Answer: 1. All reversible cycles have the same efficiency

Question 166. An ideal gas heat engine operates in cannot cycle between 227ºC and 127ºC. It absorbs 6 × 10⁴ cal of heat at higher temperatures. The amount of heat converted to work is:

1. 2.4 × 10⁴ cal
2. 6 × 10⁴ cal
3. 1.2 × 10⁴ cal
4. 4.8 × 10⁴ cal

Answer: 3. 1.2 × 10⁴ cal

Question 167. A Carnot engine whose sink is at 300 K has an efficiency of 40% By how much should the temperature of the source be increased to increase its efficiency by 50% of the original efficiency:-

1. 275 K
2. 325 K
3. 250 K
4. 380 K

Answer: 3. 250 K

Question 168. An engine has an efficiency of \(\frac{1}{6}\). When the temperature of the sink is reduced by 62ºC, its efficiency is doubled. The temperature of the source is:

1. 124ºC
2. 37ºC
3. 62ºC
4. 99ºC

Answer: 4. 99ºC

Question 169. The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is:

1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(\frac{1}{3}\)
4. \(\frac{2}{3}\)

Answer: 3. \(\frac{1}{3}\)

Question 170. A Carnot engine, having an efficiency of η = 1/10 as a heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at a lower temperature is

1. 99 J
2. 90 J
3. 1 J
4. 100 J

Answer: 2. 90 J

Question 171. The work of 146 kJ is performed to compress one-kilo mole of a gas adiabatically and in this process the temperature of the gas increases by 7C. The gas is (R = 8.3 J mol^-1 K^-1)

1. Diatomic
2. Triatomic
3. A mixture of monoatomic and diatomic
4. Monoatomic

Answer: 1. Diatomic

Question 172. A Carnot working between 300K and 600K has a work output of 800 J per cycle. What is the amount of heat energy supplied to the engine from the source per cycle

1. 1800 J/cycle
2. 1000 J/cycle
3. 2000 J/cycle
4. 1600 J/cycle

Answer: 4. 1600 J/cycle

Question 173. The coefficient of performance of a Carnot refrigerator working between 30° C and 0° C is

1. 10
2. 1
3. 9
4. 0

Answer: 3. 9

Question 174. If the door of a refrigerator is kept open then which of the following is true

1. Room is cooled
2. Room is heated
3. The room is either cooled or heated
4. The room is neither cooled nor heated

Answer: 2. Room is heated

Question 175. An Ideal gas heat engine operated in a Carnot’s cycle between 227° C and 127° C. It absorbs 6 × 10⁴ J at high temperatures. The amount of heat converted into work is

1. 4.8 × 10⁴ J
2. 3.5 × 10⁴ J
3. 1.6 × 10⁴ J
4. 1.2 × 10⁴ J

Answer: 4. 1.2 × 10⁴ J

Question 176. An ideal gas heat engine exhausting heat at 77° C does not have a 30% efficiency. It must take the heat at

1. 127° C
2. 227°C
3. 327° C
4. 673°C

Answer: 2. 227°C

Question 177. The efficiency of the Carnot engine is 100% if

1. T₂= 273 K
2. T₂= 0 K
3. T₁= 273 K
4. T₁= 0 K

Answer: 2. T₂= 0 K

Question 178. The efficiency of Carnot’s engine operating between reservoirs, maintained at temperatures 27°C and 123°C, is

1. 50%
2. 24%
3. 0.75%
4. 0.4%

Answer: 1. 50%

Question 179. A Carnot engine operates between 227°C and 27°C. The efficiency of the engine will be

1. \(\frac{1}{3}\)
2. \(\frac{2}{5}\)
3. \(\frac{3}{4}\)
4. \(\frac{3}{5}\)

Answer: 2. \(\frac{2}{5}\)

Question 180. A Carnot engine has the same efficiency between 800 K to 500 K and x K to 600 K. The value of x is

1. 1000 K
2. 960 K
3. 846K
4. 754 K

Answer: 2. 960 K

Question 181. A scientist says that the efficiency of his heat engine which operates at source temperature 127°C and sink temperature 27°C is 26% then

1. It is impossible
2. It is possible but less probable
3. It is quite probable
4. Data are incomplete

Answer: 1. It is impossible

Question 182. A Carnot’s engine is made to work between 200°C and 0°C first and then between 0°C and –200°C. The ratio of efficiencies of the engine in the two cases is

1. 1.73 :1
2. 1:1.73
3. 1:1
4. 1: 2

Answer: 1. 1.73 :1

Question 183. The efficiency of a Carnot engine is 50% when the temperature of the outlet is 500 K. To increase up to 60% keeping the temperature of intake the same what is the temperature of the outlet

1. 200K
2. 400 K
3. 600K
4. 800 K

Answer: 2. 400 K

Question 184. If an ideal flask containing hot coffee is shaken, the temperature of the coffee will:

1. Decrease
2. Increase
3. Remain same
4. Decrease if temperature is below 4ºC and increase if temperature is equal to or more than 4ºC

Answer: 2. Increase

Question 185. An electric fan is switched on in a closed room. The air in the room is

1. Cooled
2. Heated
3. Maintains its temperature
4. Heated or cooled depending on the atmospheric pressure

Answer: 2. Heated

Question 186. A heat engine employing a Carnot cycle with an efficiency of η = 10% is used as a refrigerating machine, the thermal reservoirs being the same. The refrigerating efficiency ∈ is

1. 12
2. 8
3. \(\frac{1}{10}\)
4. 9

Answer: 4. 9

Question 187. An ideal gas is initially at temperature T and volume V. Its volume is increased by ΔV due to an increase in temperature ΔT, with pressure remaining constant. The quantity \(\delta=\frac{\Delta \mathrm{V}}{\mathrm{V} \Delta \mathrm{T}}\) varies with temperature as:

Answer: 3

Question 188. A monoatomic ideal gas, initially at temperature T₁, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If L₁ and L₂ are the length of the gas column before and after expansion respectively, Then T₁/T₂ is given by:

1. \(\left(\frac{L_1}{L_2}\right)^{2 / 3}\)
2. \(\frac{\mathrm{L}_1}{\mathrm{~L}_2}\)
3. \(\frac{L_2}{L_1}\)
4. \(\left(\frac{L_2}{L_1}\right)^{2 / 3}\)

Answer: 4. \(\left(\frac{L_2}{L_1}\right)^{2 / 3}\)

Question 189. Which of the following graphs correctly represents the variation of β = –(dV/dP)/V with P for an ideal gas at constant temperature?

Answer: 1

Question 190. An ideal gas undergoes a cyclic process as shown in the given P–T diagram, where the process AC is adiabatic. The process is also represented by :

Answer: 2

Question 191. Statement – 1

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and volume. because

Statement – 2

The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

1. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
2. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
3. Statement-1 is True, Statement-2 is False
4. Statement-1 is False, and Statement-2 is True.

Answer: 2. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Question 192. One mole of a monatomic ideal gas is taken along two cyclic processes E → F → G → E and E → F → H → E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal, or adiabatic.

Match the paths in List 1 with the magnitudes of the work done in List 2 and select the correct answer using the codes given below the lists.

Codes:

Answer: 1.

Question 193. Two containers of equal volume contain the same gas at pressure p₁ and p₂ and absolute temperature T₁ and T₂ respectively. On joining the vessels the gas reaches a common pressure p and common temperature T. The ratio p/T is equal to

1. \(\frac{p_1}{T_1}+\frac{p_2}{T_2}\)
2. \(\frac{p_1 T_1+p_2 T_2}{\left(T_1+T_2\right)^2}\)
3. \(\frac{p_1 T_2+p_2 T_1}{\left(T_1+T_2\right)^2}\)
4. \(\frac{\mathrm{p}_1}{2 \mathrm{~T}_1}+\frac{\mathrm{p}_2}{2 \mathrm{~T}_2}\)

Answer: 4. \(\frac{\mathrm{p}_1}{2 \mathrm{~T}_1}+\frac{\mathrm{p}_2}{2 \mathrm{~T}_2}\)

Question 194. If a diatomic gas is supplied heat Q in a process, it performs work \(\frac{Q}{4}\). What is the molar heat capacity of the gas in this process?

1. \(\frac{2}{5} R\)
2. \(\frac{5}{2} R\)
3. \(\frac{10}{3} R\)
4. \(\frac{6}{7} R\)

Answer: 3. \(\frac{10}{3} R\)

Question 195. Two samples of air A and B having the same composition and initially at the same temperature T, pressure P, and volume V are taken. A and B are made to undergo the following process :

Case 1: A and B are compressed from volume V to volume V/2. A is compressed isothermally while B is compressed adiabatically. The final pressures are P_AC and P_BC respectively.

Case: 2 A and B are allowed to undergo expansion from volume V to volume 2V. A undergoes while B undergoes adiabatic expansion. The final pressure of A and B are P_AE and P_BE respectively.

1. P_AC = P_BC and P_AE = P_BE
2. P_AC = P_AE and P_BC = P_BE
3. P_AC > P_BC and P_AE < P_BE
4. P_AC < P_BC and P_AE> P_BE

Answer: 4. P_AC < P_BC and P_AE > P_BE

Question 196. 4 moles of an ideal monoatomic gas occupying volume V is adiabatically expanded from temperature 300 K to a volume of \(2 \sqrt{2} \mathrm{~V}\). Find:

1. Final temperature.
2. Change in internal energy (R = 8.3 J/mol K)

Answer:

1. 150K
2. -7500 J

Question 197. The internal energy change in a system that has absorbed 2 kcal of heat and done 500 J of work is

1. 8900 J
2. 6400 J
3. 5400 J
4. 7900 J

Answer: 4. 7900 J

Question 198. If ΔU and ΔW represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

1. ΔU = – ΔW, in a adiabatic process
2. ΔU = ΔW, in a isothermal process
3. ΔU = ΔW, in a adiabatic process
4. ΔU = – ΔW, in an isothermal process

Answer: 1. ΔU = – ΔW, in a adiabatic process

Question 199. If Cpand Cvdenote the specific heats (per unit) mass of an ideal gas of molecular weight M, where R is gas constant, then (Mains)]

1. C_p– C_v= R/M²
2. C_p– C_v= R
3. C_p– C_v= R/M
4. C_p– C_v= MR

Answer: 3. C_p– C_v= R/M

Question 200. A monoatomic gas at pressure P₁ and volume V₁ is compressed adiabatically to \(\frac{1}{8} \text { th }\) of its original volume. What is the final pressure of the gas

1. 64P₁
2. P₁
3. 16P₁
4. 32P₁

Answer: 4. 32P₁

Question 201. A mass of diatomic gas (γ = 1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27ºC to 927ºC. The pressure of the gas in a final state is:

1. 28 atm
2. 68.7atm
3. 256 atm
4. 8 atm

Answer: 3. 256 atm

Question 202. A thermodynamic system is taken through the cycle ABCD as shown in the figure. Heat rejected by the gas during the cycle is:

1. 2 PV
2. 4 PV
3. 12PV
4. PV

Answer: 1. 2 PV

Question 203. One mole of an ideal gas goes from an initial state A to final state B via two processes: It first undergoes isothermal expansion from volume V to 3V and then its volume is reduced from 3V to V at constant pressure. The correct P-V diagram representing the two processes is:

Answer: 4

Question 204. An ideal gas goes from state A to state B via three different processes as indicated in the P-V diagram:

If Q₁, Q₂, Q₃ indicate the heat absorbed by the gas along the three processes and ΔU₁, ΔU₂, and ΔU₃ indicate the change in internal energy along the three processes respectively, then

1. Q₁> Q₂> Q₃ and ΔU₁= ΔU₂= ΔU₃
2. Q₃> Q₂> Q1and ΔU₁= ΔU₂= ΔU₃
3. Q₁= Q₂= Q₃ and ΔU₁> ΔU₂> ΔU₃
4. Q₃> Q₂> Q₁ and ΔU₁> ΔU₂> ΔU₃

Answer: 1. Q₁> Q₂> Q₃ and ΔU₁= ΔU₂= ΔU₃

Question 205. A gas is taken through the cycle A → B → C → A, as shown. What is the net work done by the gas?

1. 1000 J
2. Zero
3. –2000 J
4. 2000 J

Answer: 1. 1000 J

Question 206. In the given (V–T) diagram, what is the relation between pressure P₁ and P₂?

1. P₂> P₁
2. P₂< P₁
3. Cannot be predicted
4. P₂= P₁

Answer: 2. P₂< P₁

Question 207. The molar-specific heats of an ideal gas at constant pressure and volume are denoted by C_p and C_v, respectively. If γ = \(\frac{C_p}{C_v}\) and R is the universal gas constant, then C_v is equal to:

1. \(\frac{R}{(\gamma-1)}\)
2. \(\frac{(\gamma-1)}{R}\)
3. \(\gamma R\)
4. \(\frac{1+\gamma}{1-\gamma}\)

Answer: 1. \(\frac{R}{(\gamma-1)}\)

Question 208. The amount of heat energy required to raise the temperature of 1g of Helium at NTP, from T₁K to T₂K is:

1. \(\frac{3}{2} \mathrm{~N}_{\mathrm{a}} \mathrm{k}_{\mathrm{B}}\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
2. \(\frac{3}{4} \mathrm{~N}_{\mathrm{a}} \mathrm{k}_{\mathrm{B}}\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
3. \(\frac{3}{4} N_a k_B \frac{T_2}{T_1}\)
4. \(\frac{3}{8} N_a k_B\left(T_2-T_1\right)\)

Answer: 4. \(\frac{3}{8} N_a k_B\left(T_2-T_1\right)\)

Question 209. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is:

1. 2
2. \(\frac{5}{3}\)
3. \(\frac{3}{2}\)
4. \(\frac{4}{3}\)

Answer: 3. \(\frac{3}{2}\)

Question 210. The mean free path of molecules of a gas (radius ‘r’) is inversely proportional to:

1. r³
2. r²
3. r
4. \(\sqrt{r}\)

Answer: 2. r2

Question 211. One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure,

The change in internal energy of the gas during the transition is:

1. –20 kJ
2. 20 J
3. – 12 kJ
4. 20 kJ

Answer: 1. –20 kJ

Question 212. A Carnot engine, having an efficiency of η=\(\frac{1}{10}\) as a heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at a lower temperature is:

1. 99 J
2. 90 J
3. 1 J
4. 100 J

Answer: 2. 90 J

Question 213. The ratio of the specific heats \(\frac{C_P}{C_v}\)= γin terms of degrees of freedom (n) is given by:

1. \(\left(1+\frac{n}{3}\right)\)
2. \(\left(1+\frac{2}{n}\right)\)
3. \(\left(1+\frac{n}{2}\right)\)
4. \(\left(1+\frac{1}{n}\right)\)

Answer: 2. \(\left(1+\frac{2}{n}\right)\)

Question 214. The figure below shows two paths that may be taken by a gas to go from a state A to a state C.

In process AB, 400J of heat is added to the system, and in process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process of AC will be:

1. 500 J
2. 460 J
3. 300 J
4. 380 J

Answer: 2. 460 J

Question 215. An ideal gas is compressed to half its initial volume using several processes. Which of the processes results in the maximum work done on the gas?

1. Isobaric
2. Isochoric
3. Isothermal
4. Adiabatic

Answer: 4. Adiabatic

Question 216. The coefficient of performance of a refrigerator is 5 if the temperature inside the freezer is –20°C, and the temperature of the surroundings to which it rejects heat is

1. 41°C
2. 11°C
3. 21°C
4. 31°C

Answer: 4. 31°C

Question 217. 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:

1. \(\frac{3}{4}\)
2. 2
3. \(\frac{1}{2}\)
4. \(\frac{2}{3}\)

Answer: 1. \(\frac{3}{4}\)

Question 218. A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:

1. Which of the cases (whether compression through isothermal or through an adiabatic process) requires more work will depend upon the atomicity of the gas
2. Compressing the gas isothermally will require more work to be done
3. Compressing the gas through an adiabatic process will require more work to be done
4. Compressing the gas isothermally or adiabatically will require the same amount of work

Answer: 3. Compressing the gas through adiabatic process will require more work to be done

Question 219. The molecules of a given mass of a gas have r.m.s. velocity of 200 ms^-1 at 27ºC and 1.0×10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are respectively, 127ºC and 0.05×10⁵ Nm², the r.m.s. velocity of velocity of its molecules in ms^-1 is;

1. \(\frac{100}{3}\)
2. \(100 \sqrt{2}\)
3. \(\frac{400}{\sqrt{3}}\)
4. \(\frac{100 \sqrt{2}}{3}\)

Answer: 3. \(\frac{400}{\sqrt{3}}\)

Question 220. One mole of an ideal monatomic gas undergoes a process described by the equation PV³ = constant. The heat capacity of the gas during this process is :

1. R
2. \(\frac{3}{2} R\)
3. \(\frac{5}{2} R\)
4. 2R

Answer: 1. R

Question 221. The temperature inside a refrigerator is t₂ ºC and the room temperature is t₁ ºC. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be

1. \(\frac{t_1+t_2}{t_1+273}\)
2. \(\frac{t_1}{t_1-t_2}\)
3. \(\frac{t_1+273}{t_1-t_2}\)
4. \(\frac{t_2+273}{t_1-t_2}\)

Answer: 3. \(\frac{t_1+273}{t_1-t_2}\)

Question 222. 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?

1. mkT
2. P / (kT)
3. Pm / (kT)
4. P / (kTV)

Answer: 3. Pm / (kT)

Question 223. Thermodynamic processes are indicated in the following diagram:

Match the following :

1. 1 → A 2 → C, 3 → D, 4 → B
2. 1 → C, 2 → A, 3 → D, 4 → B
3. 1 → C, 2 → D, 3 → B, 4 → A
4. 1 → D, 2 → B, 3 → A, 4 → C

Answer: 2. 1 → C, 2 → A, 3 → D, 4 → B

Question 224. A gas mixture consists of 2 moles of O₂ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. 4 RT
2. 15 RT
3. 9 RT
4. 11 RT

Answer: 4. 11 RT

Question 225. A Carnot engine having an efficiency of \(\frac{1}{10}\) as a heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at a lower temperature is:

1. 1 J
2. 90 J
3. 99 J
4. 100 J

Answer: 2. 90 J

Question 226. The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

1. \(\frac{2}{5}\)
2. \(\frac{2}{7}\)
3. \(\frac{1}{3}\)
4. \(\frac{2}{3}\)

Answer: 1. \(\frac{2}{5}\)

Question 227. The efficiency of an ideal heat engine working between the freezing point and boiling point of water is

1. 26.8 %
2. 12.5 %
3. 6.25 %
4. 20 %

Answer: 1. 26.8 %

Question 228. 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 kB =1.38×10^-23 JK^-1

1. 2.508×10⁴ K
2. 1.254×10⁴ K
3. 5.016×10⁴ K
4. 8.360×10⁴ K

Answer: 4. 8.360×10⁴ K

Question 229. In which of the following processes, heat is neither absorbed nor released by a system?

1. Isochoric
2. Isothermal
3. Adiabatic
4. Isobaric

Answer: 3. Adiabatic

Question 230. An increase in the temperature of a gas-filled container would lead to the:

1. Decrease in intermolecular distance
2. Increase in its mass
3. Increase in its kinetic energy
4. Decrease in its pressure

Answer: 3. Increase in its kinetic energy

Question 231. The value of \(\gamma\left(=\frac{C_p}{C_v}\right)\), for hydrogen helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to,

1. \(\frac{7}{5}, \frac{5}{3}, \frac{9}{7}\)
2. \(\frac{5}{3}, \frac{7}{5}, \frac{9}{7}\)
3. \(\frac{5}{3}, \frac{7}{5}, \frac{7}{5}\)
4. \(\frac{7}{5}, \frac{5}{3}, \frac{7}{5}\)

Answer: 1. \(\frac{7}{5}, \frac{5}{3}, \frac{9}{7}\)

Question 232. 1 g of water, of volume 1 cm³ at 100ºC, is converted into steam at the same temperature under normal atmospheric pressure ≈1 ×10⁵ Pa. The volume of steam formed equals 1671 cm³. If the specific latent heat of vaporization of water is 2256 J/g, the change in internal energy is:

1. 2423 J
2. 2089 J
3. 167 J
4. 2256 J

Answer: 2. 2089 J

Question 233. The efficiency of a Carnot engine depends upon

1. The temperature of the sink only
2. The temperatures of the source and sink
3. The volume of the cylinder of the engine
4. The temperature of the source only

Answer: 4. The temperature of the source only

Question 234. The P-V diagram for an ideal gas in a piston-cylinder assembly undergoing a thermodynamic process is shown in the figure. The process is

1. Adiabatic
2. Isochoric
3. Isobaric
4. Isothermal

Answer: 4. Isothermal

Question 235. The quantities of heat required to raise the temperature of two solid copper spheres of radii r₁ and r₂ (r₁ = 1.5 r₂) through 1K are in the ratio

1. \(\frac{5}{3}\)
2. \(\frac{27}{8}\)
3. \(\frac{9}{4}\)
4. \(\frac{3}{2}\)

Answer: 3. \(\frac{9}{4}\)

Question 236. Two cylinders A and B of equal capacity are connected via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is

1. Isobaric
2. Isothermal
3. Adiabatic
4. Isochoric

Answer: 4. Isochoric

Question 237. The mean free path for a gas molecule depends upon the diameter, d of the molecule as

1. \(\ell \propto \frac{1}{\mathrm{~d}^2}\)
2. \(\ell \propto d\)
3. \(\ell \propto \mathrm{d}^2\)
4. \(\ell \propto \frac{1}{d}\)

Answer: 1. \(\ell \propto \frac{1}{\mathrm{~d}^2}\)

Question 238. The average thermal energy for a mono-atomic gas is : (kB is Boltzmann constant and T, absolute temperature)

1. \(\frac{7}{2} k_B T\)
2. \(\frac{1}{2} k_B T\)
3. \(\frac{3}{2} k_B T\)
4. \(\frac{5}{2} k_B T\)

Answer: 3. \(\frac{3}{2} k_B T\)

Question 239. The mean free path for a gas, with molecular diameter d and number density n, can be expressed as

1. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2}\)
2. \(\frac{1}{\sqrt{2} n \pi d}\)
3. \(\frac{1}{\sqrt{2} n \pi d^2}\)
4. \(\frac{1}{\sqrt{2} n^2 \pi d^2}\)

Answer: 3. \(\frac{1}{\sqrt{2} n \pi d^2}\)

Question 240. Match Column-1 and Column-2 and choose the correct match from the given choices.

1. 1–Q, 2–R, 3–S, 4–P
2. 1–Q, 2–P, 3–S, 4–R
3. 1–R, 2–Q, 3–P, 4–S
4. 1–R, 2–P, 3–S, 4–Q

Answer: 2. 1–Q, 2–P, 3–S, 4–R

Question 241. n moles of a monoatomic gas is carried around the reversible rectangular cycle ABCDA as shown in the diagram. The temperature at A is T₀. The thermodynamic efficiency of the cycle is

1. 15%
2. 50%
3. 20%
4. 25%

Answer: 2. 50%

Question 242. An engine has an efficiency of 1/6. When the temperature of the sink is reduced by 62ºC, its efficiency is doubled. The temperature of the source will be

1. 37ºC
2. 62ºC
3. 99ºC
4. 124ºC

Answer: 3. 99ºC

Question 243. Assertion: The melting point of ice decreases with the increase of pressure. Reason: Ice contracts on melting.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If Assertion is true but the reason is false.
4. If both assertion and reason are false.

Answer: 1. If both assertion and reason are true and reason is the correct explanation of assertion.

Question 244. 1 mole of H₂ gas is contained in a box of volume V = 1.00 m³ 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. Same as the pressure initially
2. 2 times the pressure initially
3. 10 times the pressure initially
4. 20 times the pressure initially

Answer: 4. 20 times the pressure initially

Question 245. Assume the gas to be ideal the work done on the gas in taking it from A to B is :

1. 200 R
2. 300 R
3. 400 R
4. 500 R

Answer: 3. 400 R

Question 246. The work done on the gas in taking it from D to A is

1. –414 R
2. + 414 R
3. – 690 R
4. + 690 R

Answer: 2. + 414 R

Question 247. The net work done on the gas in the cycle ABCDA is:

1. Zero
2. 276 R
3. 1076 R
4. 1904 R

Answer: 2. 276 R

Question 248. One kg of a diatomic gas is at a pressure of 8 × 104 N/m². The density of the gas is 4 kg/m³. What is the energy of the gas due to its thermal motion?

1. 5 × 10⁴J
2. 6 × 10⁴J
3. 7 × 10⁴J
4. 3 × 10⁴J

Answer: 1. 5 × 10⁴J

Question 249. A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V, the efficiency of the engine is:

1. 0.5
2. 0.75
3. 0.99
4. 0.25

Answer: 2. 0.75

Question 250. A Carnot engine operating between temperatures T₁ and T₂ has effeiciency \(\frac{1}{6}\). When T₂ is lowered by 62 K, its efficiency increases to \(\frac{1}{3}\). Then T₁ and T₂ are, respectively:

1. 372 K and 310 K
2. 372 K and 330 K
3. 330 K and 268 K
4. 310 K and 248 K

Answer: 1. 372 K and 310 K

Question 251. Three perfect gases at absolute temperatures T₁, T_2, and T₃ are mixed. The masses of molecules are m₁, m_2, and m₃ and the number of molecules is n₁,n_2, and n₃ respectively. Assuming no loss of energy, the final temperature of the mixture is:

1. \(\frac{\left(\mathrm{T}_1+\mathrm{T}_2+\mathrm{T}_3\right)}{3}\)
2. \(\frac{\mathrm{n}_1 \mathrm{~T}_1+\mathrm{n}_2 \mathrm{~T}_2+\mathrm{n}_3 \mathrm{~T}_3}{\mathrm{n}_1+\mathrm{n}_2+\mathrm{n}_3}\)
3. \(\frac{n_1 T_1^2+n_2 T_2^2+n_3 T_3^2}{n_1 T_1+n_2 T_2+n_3 T_3}\)
4. \(\frac{n_1^2 T_1^2+n_2^2 T_2^2+n_3^2 T_3^2}{n_1 T_1+n_2 T_2+n_3 T_3}\)

Answer: 2. \(\frac{\mathrm{n}_1 \mathrm{~T}_1+\mathrm{n}_2 \mathrm{~T}_2+\mathrm{n}_3 \mathrm{~T}_3}{\mathrm{n}_1+\mathrm{n}_2+\mathrm{n}_3}\)

Question 252. A thermally insulated vessel contains an ideal gas of molecular mass M and a ratio of specific heat γ. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

1. \(\frac{(\gamma-1)}{2(\gamma+1) R} M v^2 K\)
2. \(\frac{(\gamma-1)}{2 \gamma R} M^2 K\)
3. \(\frac{\gamma M v^2}{2 R} K\)
4. \(\frac{(\gamma-1)}{2 R} M^2 K\)

Answer: 4. \(\frac{(\gamma-1)}{2 R} M^2 K\)

Question 253. A container with insulating walls is divided into equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure P and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be:

1. \(\frac{P}{2}, \frac{T}{2}\)
2. P, T
3. \(P, \frac{T}{2}\)
4. \(\frac{P}{2}, T\)

Answer: 4. \(\frac{P}{2}, T\)

Question 254. Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in the figure. The efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

1. 15.4%
2. 9.1%
3. 10.5%
4. 12.5%

Answer: 1. 15.4%

Question 255. A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency of 60%. Then, the intake temperature for the same exhaust (sink) temperature must be:

1. The efficiency of the Carnot engine cannot be made larger than 50%
2. 1200 K
3. 750 K
4. 600 K

Answer: 3. 750 K

Question 256. The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is:

1. \(\mathrm{P}_0 \mathrm{v}_0\)
2. \(\left(\frac{13}{2}\right) p_0 \mathrm{v}_0\)
3. \(\left(\frac{11}{2}\right) \mathrm{P}_0 \mathrm{v}_0\)
4. \(4 p_0 v_0\)

Answer: 2. \(\left(\frac{13}{2}\right) p_0 \mathrm{v}_0\)

Question 257. One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in the figure. The process BC is adiabatic. The temperatures at A, B, and C are 400K, 800K, and 600 K respectively. Choose the correct statement:

1. The change in internal energy in the whole cyclic process is 250 R.
2. The change in internal energy in the process CA is 700 R
3. The change in internal energy in the process AB is – 350 R
4. The change in internal energy in the process BC is – 500 R

Answer: 4. The change in internal energy in the process BC is – 500 R

Question 258. An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by an additional 46 cm. What will be the length of the air column above the mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)

1. 16 cm
2. 22 cm
3. 38 cm
4. 6 cm

Answer: 1. 16 cm

Question 259. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = \(\frac{U}{V} \propto T^4\) and pressure P = \(\frac{1}{3}\left(\frac{U}{V}\right)\). If the shell now undergoes an adiabatic expansion the relation between T and R is

1. \(\mathrm{T} \propto \mathrm{e}^{-\mathrm{R}}\)
2. \(T \propto e^{-3 R}\)
3. \(T \propto \frac{1}{R}\)
4. \(\mathrm{T} \propto \frac{1}{\mathrm{R}^3}\)

Answer: 3. \(T \propto \frac{1}{R}\)

Question 260. A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways:

1. Sequentially keeping in contact with 2 reservoirs so that each reservoir supplies the same amount of heat.
2. Sequentially keeping in contact with 8 reservoirs, each reservoir supplies the same amount of heat.
3. In both cases, the body is brought from the initial temperature of 100°C to the final temperature of 200°C. Entropy changes of the body in the two cases respectively is

1. ln 2, 4ln2
2. ln 2, ln 2
3. ln 2, 2 ln 2
4. 2 ln 2, 8 ln 2

Answer: 2. ln 2, ln 2

Question 261. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as Vq, where V is the volume of the gas. The value of q is \(\left(\gamma=\frac{C_P}{C_V}\right)\)

1. \(\frac{3 \gamma+5}{6}\)
2. \(\frac{3 \gamma-5}{6}\)
3. \(\frac{\gamma+1}{2}\)
4. \(\frac{\gamma-1}{2}\)

Answer: 3. \(\frac{\gamma+1}{2}\)

Question 262. ‘n’ moles of an ideal gas undergoes a process A▢B as shown in the figure. The maximum temperature of the gas during the process will be:

1. \(\frac{3 P_0 V_0}{2 n R}\)
2. \(\frac{9 P_0 V_0}{2 n R}\)
3. \(\frac{9 P_0 V_0}{n R}\)
4. \(\frac{9 P_0 V_0}{4 n R}\)

Answer: 4. \(\frac{9 P_0 V_0}{4 n R}\)

Question 263. Cp and Cv are specific heats at constant pressure and constant volume respectively. It is observed that

Cp – Cv = a for hydrogen gas

Cp – Cv = b for nitrogen gas

The correct relation between a and b is:

1. a = 28 b
2. \(a=\frac{1}{14} b\)
3. a = b
4. a = 14 b

Answer: 4. a = 14 b

Question 264. The temperature of an open room of volume 30 m³ increased from 17ºC to 27ºC due to the sunshine. The atmospheric pressure in the room remains 1 × 10⁵ Pa. If ni and nf are the number of molecules in the room before and after heating, then nf – ni will be:

1. – 2.5 × 10²⁵
2. – 1.61 × 10²³
3. 1.38 × 10²³
4. 2.5 × 10²⁵

Answer: 1. – 2.5 × 10²⁵

Question 265. Two moles of an ideal monoatomic gas occupy a volume V at 27°C. The gas expands adiabatically to a volume of 2V. Calculate

1. The final temperature of the gas and
2. Change in its internal energy.

1. (1) 189 K (2) –2.7 kJ
2. (1) 195 K (2) 2.7 kJ
3. (1) 189 K (2) 2.7 kJ
4. (1) 195 K (2) –2.7 kj

Answer: 1. (1) 189 K (2) –2.7 kJ

Question 266. A mixture of 2 moles of helium gas (atomic mass = 4u) and 1 mole of argon gas (atomic mass = 40u) is kept at 300 K in a container, the ratio of their rms speeds \(\left[\frac{\mathrm{v}_{\mathrm{rms}}(\text { helium })}{\mathrm{V}_{\mathrm{rms}}(\text { argon })}\right]\), is close to:

1. 0.32
2. 3.16
3. 2.24
4. 0.45

Answer: 2. 3.16

Question 267. A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60J of heat flows into the system and 30J of work is done by the system. If path ADB is used work done by the system is 10J. The heat flow into the system in path ADB is:

1. 80J
2. 100J
3. 20J
4. 40J

Answer: 4. 40J

Question 268. A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature of 27º C. Amount of heat transferred to the gas so that the rms velocity of molecules is doubled, is about: [Take R = 8.3 J/K mole]

1. 0.9 kJ
2. 6 kJ
3. 14 kJ
4. 10 kJ

Answer: 4. 10 kJ

Question 269. Three Carnot engines operate in series between a heat source at temperature T₁ and a heat sink at temperature T₄ (see figure). There are two other reservoirs at temperatures T₂ and T₃ as shown, with T₁ > T₂ > T₃ > T₄. The three engines are equally efficient if:

1. \(\mathrm{T}_2=\left(\mathrm{T}_1 \mathrm{~T}_4^2\right)^{1 / 3} ; \mathrm{T}_3=\left(\mathrm{T}_1^2 \mathrm{~T}_4\right)^{1 / 3}\)
2. \(T_2=\left(T_1 T_4\right)^{1 / 2} ; T_3=\left(\mathrm{T}_1^2 \mathrm{~T}_4\right)^{1 / 3}\)
3. \(T_2=\left(\mathrm{T}_1^3 \mathrm{~T}_4\right)^{1 / 4} ; \mathrm{T}_3=\left(\mathrm{T}_1 \mathrm{~T}_4^3\right)^{1 / 4}\)
4. \(T_2=\left(T_1^2 T_4\right)^{1 / 3} ; T_3=\left(T_1 T_4^2\right)^{1 / 3}\)

Answer: 4. \(T_2=\left(T_1^2 T_4\right)^{1 / 3} ; T_3=\left(T_1 T_4^2\right)^{1 / 3}\)

Question 230. Two kg of a monoatomic gas is at a pressure of 4 × 10⁴ N/m². The density of the gas is 8 kg/m³. What is the order of energy of the gas due to its thermal motion?

1. 105 J
2. 104 J
3. 106 J
4. 103 J

Answer: 4. 103 J

Question 231. Half a mole of an ideal monoatomic gas is heated at a constant pressure of 1 atom from 20°C to 90°C. Work done by the gas is close to: (Gas constant R = 831 J/mol.K)

1. 581 J
2. 146 J
3. 291 J
4. 73 J

Answer: 3. 291 J

Question 232. When 100g of liquid A at 100°C is added to 50 g of liquid B at a temperature of 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100g of liquid A at 100°C is added to 50 g of liquid B at 50°C, will be:

1. 80°C
2. 60°C
3. 70°C
4. 85°C

Answer: 1. 80°C

Question 233. A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is:

1. \(\frac{2}{5}\)
2. \(\frac{5}{3}\)
3. \(\frac{3}{5}\)
4. \(\frac{2}{3}\)

Answer: 1. \(\frac{2}{5}\)

Question 234. An ideal gas enclosed in a cylinder at a pressure of 2 atm and temperature, of 300 K. The mean time between two successive collisions is 6 × 10–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to:

1. 3 × 10^-6 s
2. 4 × 10^-8 s
3. 2 × 10^-7 s
4. 05 × 10^-8 s

Answer: 2. 4 × 10^-8 s

Question 235. A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is l₁, and that below the piston is l₂, such that l₁ > l₂. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by:

(R is the universal gas constant g is the acceleration due to gravity.)

1. \(\frac{\mathrm{RT}}{\mathrm{g}}\left[\frac{2 \ell_1+\ell_2}{\ell_1 \ell_2}\right]\)
2. \(\frac{\mathrm{RT}}{\mathrm{ng}}\left[\frac{\ell_1-3 \ell_2}{\ell_1 \ell_2}\right]\)
3. \(\frac{\mathrm{nRT}}{\mathrm{g}}\left[\frac{1}{\ell_2}+\frac{1}{\ell_1}\right]\)
4. \(\frac{\mathrm{nRT}}{\mathrm{g}}\left[\frac{\ell_1-\ell_2}{\ell_1 \ell_2}\right]\)

Answer: 4. \(\frac{\mathrm{nRT}}{\mathrm{g}}\left[\frac{\ell_1-\ell_2}{\ell_1 \ell_2}\right]\)