Question

Match List-I (Isothermal Process) with List-II (work done)

• A. $4, 3, 2, 1$
• B. $2, 1, 3, 4$
• C. $1, 2, 3, 4$
• D. $3, 4, 1, 2$

Hint:

Work done by the system is negative. Work during irreversible processes depends on external pressure $P_{\text{ext}}$, while reversible work depends on internal pressure (via integration).

Answer 1

The Correct Option is B

To solve this problem, we need to match the types of isothermal processes from List-I with the corresponding expressions for work done from List-II.

1. Reversible expansion:
   • In a reversible isothermal expansion, the work done is given by the formula: \(w = -nRT \ln \frac{V_f}{V_i}\), where \(n\) is the number of moles, \(R\) is the gas constant, \(T\) is the temperature, and \(V_f\) and \(V_i\) are the final and initial volumes, respectively.
   • Therefore, the match is with option 2: \(w = -nRT \ln \frac{V_f}{V_i}\).
2. Free expansion:
   • In a free expansion, no work is done because the process occurs without any external pressure change.
   • The work done, \(w\), is zero. So, it matches with option 1: \(w = 0\).
3. Irreversible expansion:
   • In an irreversible expansion against a constant external pressure, the work done is given by \(w = -P_{\text{ext}} (V_f - V_i)\).
   • Thus, it matches with option 4: \(w = -P_{\text{ext}} (V_f - V_i)\).
4. Irreversible compression:
   • Similar to irreversible expansion, but since it's compression, the volume change \((V_i - V_f)\) is considered as positive work done by the surroundings.
   • So, it matches with option 3: \(w = -P_{\text{ext}} (V_i - V_f)\).

Therefore, the correct matching order is 2, 1, 3, 4, corresponding to the option 2, 1, 3, 4.