Question

Given below are two statements
Statement - I: For isothermal irreversible change of an ideal gas, \[ q = -w = P_{\text{ext}}(V_{\text{final}} - V_{\text{initial}}) \] Statement - II: For adiabatic change, \[ \Delta U = W_{\text{adiabatic}} \] The correct answer is:

• A. Both Statement-I and Statement-II are correct
• B. Both Statement-I and Statement-II are not correct
• C. Statement-I is correct but Statement-II is not correct
• D. Statement-I is not correct but Statement-II is correct

Hint:

In thermodynamics, isothermal processes have zero change in internal energy, and work done is equal to heat absorbed. In adiabatic processes, the change in internal energy is equal to the work done as there is no heat exchange.

Answer 1

The Correct Option is A

Step 1: For isothermal processes, the change in internal energy of an ideal gas is zero. The first law of thermodynamics gives the relationship \( q = -w \). The work done during an isothermal irreversible process can be calculated as \( P_{\text{ext}} (V_{\text{final}} - V_{\text{initial}}) \), which matches Statement-I. Therefore, Statement-I is correct.

 Step 2: For an adiabatic process, there is no heat exchange (\( q = 0 \)), and the change in internal energy is equal to the work done, \( \Delta U = W_{\text{adiabatic}} \), which matches Statement-II. Therefore, Statement-II is also correct. Thus, both Statement-I and Statement-II are correct.