Question

Column-I (Isothermal process)

• A. P-(ii); Q-(iv); R-(iii); S-(i)
• B. P-(iii); Q-(ii); R-(iv); S-(i)
• C. P-(iv); Q-(i); R-(ii); S-(iii)
• D. P-(i); Q-(iii); R-(ii); S-(iv)

Hint:

Remember: In isothermal processes, temperature remains constant. Free expansion has zero work and heat, while reversible processes follow exact thermodynamic relations.

Answer 1

The Correct Option is A

Step 1: Understanding each process.
Reversible expansion (P): In an isothermal reversible expansion, heat absorbed is given by:
\[ q = nRT \ln\left(\frac{V_2}{V_1}\right) \]
Hence, it matches with option (ii).
Reversible cyclic process (Q): For any cyclic process, change in internal energy is zero, so:
\[ \Delta U = 0 \Rightarrow q = W \]
Also, for a reversible cyclic process:
\[ \oint \frac{dq_{rev}}{T} = 0 \]
Hence, it matches with option (iv).
Irreversible compression (R): Work done in irreversible process is:
\[ W = -P_{ext}(V_2 - V_1) \]
Hence, it matches with option (iii).
Free expansion (S): In free expansion, no work is done and no heat is exchanged:
\[ q = 0 \]
Hence, it matches with option (i).

Step 2: Final matching.
P-(ii); Q-(iv); R-(iii); S-(i)
Final Answer: (A) P-(ii); Q-(iv); R-(iii); S-(i)