Question

Match List-I with List-II.

Choose the correct answer.

• A. A-II, B-III, C-I, D-IV
• B. A-II, B-I, C-IV, D-III
• C. A-II, B-I, C-III, D-IV
• D. A-I, B-II, C-III, D-IV

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to match specific thermodynamic processes with their defining mathematical expressions.
Step 2: Key Formula or Approach:
- First Law: \(\Delta U = q + w\). For isothermal ideal gas, \(\Delta U = 0 \Rightarrow q = -w\).
- Work: Reversible \(w = -nRT \ln(V_2/V_1)\); Irreversible \(w = -P_{ext}(V_{final} - V_{initial})\).
Step 3: Detailed Explanation:
A. Reversible expansion: For isothermal rev. expansion, \(q = -w = nRT \ln(V_2/V_1)\). Match: II.
B. Free expansion: \(P_{ext} = 0 \Rightarrow w = 0\). For isothermal, \(\Delta U = 0\), so \(q = 0\). Match: I.
C. Irreversible Compression: Work done is \(-P_{ext}(V_2 - V_1) = -P_{ext}(V_{final} - V_{initial})\). In compression, \(V_2<V_1\), so expression can be written as \(-P_{ext}(V_1 - V_2)\) to show positive work. Match: III.
D. Cyclic reversible: For any reversible cycle, the net change in state functions is zero. \(\oint \frac{dq_{rev}}{T} = \Delta S = 0\). Match: IV.
Step 4: Final Answer:
The matching is A-II, B-I, C-III, D-IV.