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:
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:
Show Hint
- Both Statement-I and Statement-II are correct
- Both Statement-I and Statement-II are not correct
- Statement-I is correct but Statement-II is not correct
- Statement-I is not correct but Statement-II is correct
The Correct Option is A
Solution and Explanation
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.
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