Question

Match the LIST-I with LIST-II for an isothermal process of an ideal gas system. 

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

Hint:

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

Answer 1

The Correct Option is A

To solve this matching question for an isothermal process of an ideal gas, we need to analyze each process described in List-I and match it with the corresponding formula for work done from List-II.

1. Reversible Expansion (A):

In a reversible isothermal expansion, the work done is given by the formula: \(w = -nRT \ln\left(\frac{V_f}{V_i}\right)\) This matches with option II.

1. Free Expansion (B):

During a free expansion, the system does no work since there is no external pressure against which the system expands. Hence, the work done, \(w = 0\). This corresponds to option I.

1. Irreversible Expansion (C):

For an irreversible expansion against a constant external pressure, the work done is given by: \(w = -P_{ex}(V_f - V_i)\) This matches with option III.

1. Irreversible Compression (D):

Similarly, for irreversible compression against a constant external pressure, the work done is: \(w = -P_{ex}(V_i - V_f)\) This corresponds to option IV.

Based on the analysis above, the correct matching of List-I with List-II is:

• A-II: Reversible expansion corresponds to formula II.
• B-I: Free expansion corresponds to formula I.
• C-III: Irreversible expansion corresponds to formula III.
• D-IV: Irreversible compression corresponds to formula IV.

Therefore, the correct answer is: A-II, B-I, C-III, D-IV.