Arrange the following isothermal processes in order of the magnitude of the work (p - V) involved between states 1 and 2.

A. Expansion in single stage $$w_A$$
B. Expansion in multi stages $$w_B$$
C. Compression in single stage $$w_C$$
D. Compression in multi stages $$w_D$$

Choose the correct option.

The magnitude of work done is equal to the area under the $$P_{\text{ext}}-V$$ curve.

For isothermal expansion:

• A multistage expansion approaches a reversible process and gives maximum work.
• A single-stage expansion is highly irreversible and gives less work.

Hence,

$$|w_B|>|w_A|$$

For isothermal compression:

• A multistage compression approaches a reversible process and requires minimum work.
• A single-stage compression is highly irreversible and requires maximum work.

Hence,

$$|w_C|>|w_D|$$

For the same initial and final states, the magnitude of reversible work lies between irreversible compression and irreversible expansion:

$$|w_C|>|w_D|>|w_{\text{rev}}|>|w_B|>|w_A|$$

Since process D is closer to reversibility than process B,

$$|w_D|>|w_B|$$

Therefore, the overall order of the magnitude of work done is

$$|w_C|>|w_D|>|w_B|>|w_A|$$

Hence, the correct option is (C).