Match the LIST-I with LIST-II

Choose the correct answer from the options given befow:

1. Reversible Expansion (A $$\rightarrow$$ II)

In a reversible process, the expansion happens infinitely slowly such that the external pressure ($$P_{ext}$$) is always nearly equal to the internal pressure ($$P_{int}$$). To find the work, we integrate the pressure over the volume change.

• Formula: $$w = -nRT \ln \frac{V_f}{V_i}$$
• Key Detail: Because the temperature is constant (isothermal), the work is defined by the logarithmic ratio of final to initial volume.

2. Free Expansion (B $$\rightarrow$$ I)

Free expansion occurs when a gas expands into a vacuum. By definition, a vacuum exerts zero external pressure ($$P_{ext} = 0$$).

• Formula: $$w = 0$$
• Key Detail: Since there is no opposing force to push against, the gas does no work, regardless of how much the volume increases.

3. Irreversible Expansion (C $$\rightarrow$$ III)

This occurs when a gas expands against a constant external pressure that is significantly lower than the initial internal pressure (like suddenly removing a weight from a piston).

• Formula: $$w = -P_{ex}(V_f - V_i)$$
• Key Detail: The work is simply the product of the constant external pressure and the change in volume ($$\Delta V$$). Since $$V_f > V_i$$, the work value is negative, indicating energy is leaving the system.

4. Irreversible Compression (D $$\rightarrow$$ IV)

Compression is the opposite of expansion; an external force is used to decrease the volume of the gas.

• Formula: $$w = -P_{ex}(V_i - V_f)$$
• Key Detail: In compression, $$V_f < V_i$$. This formula is mathematically structured to ensure that work done on the system results in a positive value, reflecting an increase in the system's energy.