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 1Column 2Column 3I W1 - 2-1-1P2V2-P1V1i Isothermal-PII W1 - 2-PV2-PV1ii Isochoric-QIII W1 - 2-0iii IsobaricRIV W1 - 2-nRTlnV2-V1iv AdiabaticSWhich of the following options is the only correct representation of a process in which -U-Q-P-V -

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Heat Capacity

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)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(II) (iii) (S)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(II) (iv) (R)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(III) (iii) (P)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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.

Suggest Corrections

Similar questions

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 ?

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 ?

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 ?

Join BYJU'S Learning Program

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.