An ideal gas at pressure $P$ and volume $V$ is expanded to volume $2V$. Column $I$ represents the thermodynamic processes used during expansion. Column $II$ represents the work done during these processes in random order:
Column $I$ Column $II$ $(p)$ isobaric $(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$ $(q)$ isothermal $(y)$ $PV$ $(r)$ adiabatic $(z)$ $PV \ln 2$
The correct matching of column $I$ and column $II$ is given by:
| Column $I$ | Column $II$ |
| $(p)$ isobaric | $(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$ |
| $(q)$ isothermal | $(y)$ $PV$ |
| $(r)$ adiabatic | $(z)$ $PV \ln 2$ |
The correct matching of column $I$ and column $II$ is given by:
- A$p-y, q-z, r-x$
- B$p-y, q-x, r-z$
- C$p-x, q-y, r-z$
- D$p-z, q-y, r-x$
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One mole of a monatomic ideal gas is taken along two cyclic processes $E \rightarrow F \rightarrow G \rightarrow E$ and $E \rightarrow F \rightarrow H \rightarrow E$ as shown in the $PV$ diagram. The processes involved are purely isochoric,isobaric,isothermal,or adiabatic. Match the paths in List-$I$ with the magnitudes of the work done in List-$II$ and select the correct answer using the codes given below the lists.
List-$I$ List-$II$ $P. \quad G \rightarrow E$ $1. \quad 160 P_0 V_0 \ln 2$ $Q. \quad G \rightarrow H$ $2. \quad 36 P_0 V_0$ $R. \quad F \rightarrow H$ $3. \quad 24 P_0 V_0$ $S. \quad F \rightarrow G$ $4. \quad 31 P_0 V_0$
Codes: $P \quad Q \quad R \quad S$
| List-$I$ | List-$II$ |
| $P. \quad G \rightarrow E$ | $1. \quad 160 P_0 V_0 \ln 2$ |
| $Q. \quad G \rightarrow H$ | $2. \quad 36 P_0 V_0$ |
| $R. \quad F \rightarrow H$ | $3. \quad 24 P_0 V_0$ |
| $S. \quad F \rightarrow G$ | $4. \quad 31 P_0 V_0$ |
Codes: $P \quad Q \quad R \quad S$
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