Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

A. Reversible Isothermal Expansion

For a reversible isothermal process:

$$|W| = nRT \ln\left(\frac{V_2}{V_1}\right)$$

• $$n = 2 \text{ mol}$$, $$R \approx 8.314 \text{ J/mol}\cdot\text{K}$$, $$T = 300 \text{ K}$$
• $$V_1 = 2 \text{ dm}^3$$, $$V_2 = 20 \text{ dm}^3 \Rightarrow \frac{V_2}{V_1} = 10$$
• $$|W| = 2 \times 8.314 \times 300 \times \ln(10) \approx 4988.4 \times 2.303 \approx 11,488 \text{ J} \approx \mathbf{11.5 \text{ kJ}}$$
• A matches with II.

B. Irreversible Isothermal Expansion

For expansion against a constant external pressure:

$$|W| = P_{ext}(V_2 - V_1)$$

• $$P_{ext} = 3 \text{ kPa} = 3000 \text{ Pa}$$
• $$V_1 = 1 \text{ m}^3$$, $$V_2 = 3 \text{ m}^3 \Rightarrow \Delta V = 2 \text{ m}^3$$
• $$|W| = 3000 \text{ Pa} \times 2 \text{ m}^3 = 6000 \text{ J} = \mathbf{6 \text{ kJ}}$$
• B matches with III.

C. Adiabatic Expansion (Internal Energy Change)

The change in internal energy ($$\Delta U$$) is calculated as:

$$\Delta U = n C_v \Delta T$$

• $$n = 1 \text{ mol}$$, $$C_v = \frac{3}{2}R$$, $$\Delta T = 320 \text{ K}$$
• $$|\Delta U| = 1 \times \frac{3}{2} \times 8.314 \times 320 = 1.5 \times 8.314 \times 320 \approx 3990 \text{ J} \approx \mathbf{4 \text{ kJ}}$$
• C matches with I.

D. Enthalpy Change at Constant Pressure

The change in enthalpy ($$\Delta H$$) is calculated as:

$$\Delta H = n C_p \Delta T$$

• $$n = 1 \text{ mol}$$, $$C_p = \frac{5}{2}R$$, $$\Delta T = 337 \text{ K}$$
• $$|\Delta H| = 1 \times \frac{5}{2} \times 8.314 \times 337 = 2.5 \times 8.314 \times 337 \approx 7004 \text{ J} \approx \mathbf{7 \text{ kJ}}$$
• D matches with IV.