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 I to state 2 - W denotes the corresponding work done on the system- The equation and plots in the table have standard notations as used in thermodynamic processes- Here - is the ratio 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- Y -1 P 2 V 2- P 1 V 1 i IsothermalPQII W 1 - 2- PV 2- PV 1ii IsochoricQRRIII W 1 - 2-0iii IsobaricSSIV W 1 - 2- nRT ln V 2-V1iv AdiabaticWhich of the following options is the only correct representation of a process in which - U - Q - P - V -

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Pressure and Temperature

An ideal gas ...

Question

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 I to state $2 .$ $W$ denotes the corresponding work done on the system. The equation and plots in the table have standard notations as used in thermodynamic processes. Here $γ$ is the ratio 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) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$

(i) Isothermal

(P)

(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$

(ii) Isochoric

(Q)

(III) $W_{1 \to 2} = 0$

(iii) Isobaric
(R)

(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$

(iv) Adiabatic
(S)

Which of the following options is the only correct representation of a process in which $Δ U = Δ Q - P Δ V ?$

(II) (iii) (P)

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(II) (iii) (S)

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(II) (iv) (R)

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(III) (iii) (P)

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Solution

The correct option is A (II) (iii) (P)
Work done in Adiabatic process $= \frac{1}{γ - 1} [P_{2} V_{2} - P_{1} V_{1}]$
Work done in Isobaric process $= - {P V}_{2} + {P V}_{1}$
Work done in Isochoric process $= 0$
Work done in Isothermal process $= - n R T ln (\frac{V_{2}}{V_{1}})$

Hence, option A is correct.

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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 I to state $2 .$ $W$ denotes the corresponding work done on the system. The equation and plots in the table have standard notations as used in thermodynamic processes. Here $γ$ is the ratio 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) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

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 I to state $2 .$ W denotes the corresponding work done on the system. The equation and plots in the table have standard notations as used in thermodynamic processes. Here $γ$ is the ratio 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) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

Which of the following options correctly represents the thermodynamics process that is used as a correction in the determination of the speed of sound ?

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 I to state $2 .$ W denotes the corresponding work done on the system. The equation and plots in the table have standard notations as used in thermodynamic processes. Here $γ$ is the ratio 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) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

Which of the following options correctly represents the thermodynamics process that is used as a correction in the determination of the speed of sound ?

Column 1	Column 2	Column 3
(I) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric
(III) $W_{1 \to 2} = 0$	(iii) Isobaric
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic

Column 1	Column 2	Column 3
(I) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal	(P)
(II) $W_{1 \to 2} = - {P V}_{2} + {P V}_{1}$	(ii) Isochoric	(Q)
(III) $W_{1 \to 2} = 0$	(iii) Isobaric	(R)
(IV) $W_{1 \to 2} = - n R T ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic	(S)

Which of the following options is the only correct representation of a process in which

Δ U = Δ Q - P Δ V ?

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The correct option is A (II) (iii) (P)Work done in Adiabatic process =1γ−1[P2V2−P1V1] Work done in Isobaric process =−PV2+PV1 Work done in Isochoric process =0 Work done in Isothermal process =−nRTln(V2V1) Hence, option A is correct.