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 process. 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) $W_{1 \rightarrow 2}=\frac{1}{\gamma-1}$ $\left(P_2 V_2-P_1 V_1\right)$ (i) Isothermal (P)
(II) $W_{1 \rightarrow 2}=$ $-P V_2+P V_1$ (ii) Isochoric (Q)
(III) $W_{1 \rightarrow 2}=0$ (iii) Isobaric (R)
(IV) $W_{1 \rightarrow 2}=$ $-n R T \ln \left(\frac{V_2}{V_1}\right)$ (iv) Adiabatic (S)
Which of the following options is the only correct representation of the process $∆ U = ∆ Q - P ∆ V$ ?

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 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 process. 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) $W_{1 \rightarrow 2}=\frac{1}{\gamma-1}$ $\left(P_2 V_2-P_1 V_1\right)$	(i) Isothermal	(P)
(II) $W_{1 \rightarrow 2}=$ $-P V_2+P V_1$	(ii) Isochoric	(Q)
(III) $W_{1 \rightarrow 2}=0$	(iii) Isobaric	(R)
(IV) $W_{1 \rightarrow 2}=$ $-n R T \ln \left(\frac{V_2}{V_1}\right)$	(iv) Adiabatic	(S)

Which of the following options is the only correct representation of the process

∆ U = ∆ Q - P ∆ V

?

Accepted Answer

(D) (I) (iv) (Q)

Answer

(A) (I) (ii) (Q)

Answer

(B) (IV) (ii) (R)

Answer

(C) (III) (iv) (R)

Answer & Solution

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