Question

Match the LIST-I with LIST-II for an isothermal process of an ideal gas system.
\begin{center} \begin{tabular}{|c|l||c|l|} \hline List-I & & List-II & Work done ($V_f>V_i$)
\hline A. & Reversible expansion & I. & $w = 0$
B. & Free expansion & II. & $w = -nRT\ln\!\left(\dfrac{V_f}{V_i}\right)$
C. & Irreversible expansion & III. & $w = -P_{\text{ex}}(V_f - V_i)$
D. & Irreversible compression & IV. & $w = -P_{\text{ex}}(V_i - V_f)$
\hline \end{tabular} \end{center} Choose the correct answer from the options given below:

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

Always remember: free expansion does no work, and only reversible isothermal processes involve logarithmic work expressions.

Answer 1

The Correct Option is A

Step 1: Reversible isothermal expansion.
For a reversible isothermal expansion of an ideal gas, work done is given by:
\[ w = -nRT\ln\!\left(\frac{V_f}{V_i}\right) \] Hence, A $\rightarrow$ II.
Step 2: Free expansion.
In free expansion, external pressure is zero, so no work is done:
\[ w = 0 \] Hence, B $\rightarrow$ I.
Step 3: Irreversible expansion.
For irreversible expansion against constant external pressure:
\[ w = -P_{\text{ex}}(V_f - V_i) \] Hence, C $\rightarrow$ III.
Step 4: Irreversible compression.
For irreversible compression:
\[ w = -P_{\text{ex}}(V_i - V_f) \] Hence, D $\rightarrow$ IV.
Step 5: Final conclusion.
The correct matching is A-II, B-I, C-III, D-IV, corresponding to option (1).