Question

Match the LIST-I with LIST-II. 

Choose the correct answer from the options given below:

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

Hint:

Use appropriate thermodynamic equations for each process: logarithmic form for reversible work, \( P\Delta V \) for irreversible work, and \( nC\Delta T \) for energy changes.

Answer 1

The Correct Option is B

To solve the matching problem, we need to calculate the thermodynamic quantities based on the given processes and match them with the given magnitudes.

1. For process A, we have a reversible isothermal expansion of 2 mol of an ideal gas from 2 dm³ to 20 dm³ at 300 K:
   • The work done in reversible isothermal expansion is given by \(W = nRT \ln \left(\frac{V_f}{V_i}\right)\).
   • Substitute: \(n = 2\), \(R = 8.314 \, \text{J/mol K}\), \(T = 300 \, \text{K}\), \(V_i = 2 \, \text{dm}^3\), \(V_f = 20 \, \text{dm}^3\).
   • Calculate: \(W = 2 \times 8.314 \times 300 \times \ln(10) \approx 11.5 \, \text{kJ}\).
2. For process B, we have an irreversible isothermal expansion of 1 mol ideal gas from 1 m³ to 3 m³ at 300 K against a constant pressure of 3 kPa:
   • The work done is given by \(W = P \Delta V\).
   • Substitute: \(P = 3 \, \text{kPa} = 3000 \, \text{J/m}^3\), \(\Delta V = 3 - 1 = 2 \, \text{m}^3\).
   • Calculate: \(W = 3000 \times 2 = 6 \, \text{kJ}\).
3. For process C, we have a change in internal energy for adiabatic expansion with a change in temperature of 320 K and \(C_V = \frac{3}{2} R\):
   • The change in internal energy is given by \(\Delta U = nC_V \Delta T\).
   • Substitute: \(n = 1\), \(C_V = \frac{3}{2} \times 8.314\), \(\Delta T = 320 \, \text{K}\).
   • Calculate: \(\Delta U = 1 \times \frac{3}{2} \times 8.314 \times 320 = 4 \, \text{kJ}\).
4. For process D, we have a change in enthalpy at constant pressure with a change in temperature of 337 K and \(C_p = \frac{5}{2} R\):
   • The change in enthalpy is given by \(\Delta H = nC_p \Delta T\).
   • Substitute: \(n = 1\), \(C_p = \frac{5}{2} \times 8.314\), \(\Delta T = 337 \, \text{K}\).
   • Calculate: \(\Delta H = 1 \times \frac{5}{2} \times 8.314 \times 337 = 7 \, \text{kJ}\).

Thus, the correct matching is: A-II, B-III, C-I, D-IV.