Which of the following statements/relationships is not correct in thermodynamic changes ?
Show Hint
- \(\Delta U = 0\) (isothermal reversible expansion of a gas)
- \(w = -nRT \ln \frac{V_2}{V_1}\) (isothermal reversible expansion of an ideal gas)
- \(w = nRT \ln \frac{V_2}{V_1}\) (isothermal reversible expansion of an ideal gas)
- For a system of constant volume heat involved directly changes to internal energy.
The Correct Option is C
Solution and Explanation
Reversible isothermal expansion: \(w = -\int_{V_1}^{V_2} P\,dV = -nRT\ln\frac{V_2}{V_1}\) (work done on the system, IUPAC convention). Hence (2) is correct.
Since \(V_2 \gt V_1\), \(w\) must be negative for expansion, so \(w = +nRT\ln\frac{V_2}{V_1}\) in (3) has the wrong sign.
At constant volume \(w = 0\), so \(\Delta U = q_V\): statement (4) is correct.
Therefore the incorrect statement is (3).
Answer: (3) \(w = nRT \ln \frac{V_2}{V_1}\) (isothermal reversible expansion of an ideal gas)
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