Question

Match the LIST-I with LIST-II. 

Choose the correct answer from the options given below:

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

Hint:

Use appropriate thermodynamic equations for each process: logarithmic form for reversible work, \( P\Delta V \) for irreversible work, and \( nC\Delta T \) for energy changes.

Answer 1

The Correct Option is B

Step 1: Process A (Reversible isothermal work).
\[ W = nRT \ln\left(\frac{V_2}{V_1}\right) \Rightarrow W = 2 \times 8.314 \times 300 \ln(10) \approx 11.5\,\text{kJ}. \] Thus, A \(\rightarrow\) II.
Step 2: Process B (Irreversible isothermal work).
\[ W = P_{\text{ext}}(V_2 - V_1) = 3 \times (3 - 1) = 6\,\text{kJ}. \] Thus, B \(\rightarrow\) I.
Step 3: Process C (Change in internal energy).
\[ \Delta U = n C_V \Delta T = 1 \times \frac{3}{2}R \times 320 \approx 6\,\text{kJ}. \] Thus, C \(\rightarrow\) III.
Step 4: Process D (Change in enthalpy).
\[ \Delta H = n C_P \Delta T = 1 \times \frac{5}{2}R \times 337 \approx 7\,\text{kJ}. \] Thus, D \(\rightarrow\) IV.
Step 5: Final matching.
\[ \boxed{\text{A-II,\; B-I,\; C-III,\; D-IV}} \] Final Answer: \[ \boxed{\text{Option (B)}} \]