Determination of Isochoric Steps in a Gas Cycle

An isochoric process is a thermodynamic process in which the volume ($V$) of a closed system remains constant ($\Delta V = 0$).

In a $P\text{--}V$ (Pressure vs. Volume) diagram:

• A process represented by a horizontal line (parallel to the Volume axis) occurs at constant pressure, which corresponds to an isobaric process.
• A process represented by a vertical line (parallel to the Pressure axis) occurs at constant volume, which corresponds to an isochoric process.

Analyzing each transformation in the given cyclic path $K \to L \to M \to N \to K$:

1. Process $K \to L$: The path is a horizontal line, so pressure $P$ remains constant. Hence, it is an isobaric process.
2. Process $L \to M$: The path is a vertical line, so volume $V$ remains constant ($V_L = V_M$). Hence, it is an isochoric process.
3. Process $M \to N$: The path is a horizontal line, so pressure $P$ remains constant. Hence, it is an isobaric process.
4. Process $N \to K$: The path is a vertical line, so volume $V$ remains constant ($V_N = V_K$). Hence, it is an isochoric process.

Therefore, the pair of transformations representing isochoric processes is $L \to M$ and $N \to K$.

Correct Answer: (B)