MCQ
Work done per mol in an isothermal change is
- A$R T \log _{10} \frac{V_2}{V_1}$
- B$R T \log _{10} \frac{V_1}{V_2}$
- ✓$R T \log _e \frac{V_2}{V_1}$
- D$R T \log _e \frac{V_1}{V_2}$
✓
Answer
Correct option: C.
$R T \log _e \frac{V_2}{V_1}$
For isothermal process $P V=R T \Rightarrow P=\frac{R T}{V}$
$\therefore W=PdV=\int_{V_1}^{V_2} \frac{R T}{V} d V=R T \log _e \frac{V_2}{V_1}$
$\therefore W=PdV=\int_{V_1}^{V_2} \frac{R T}{V} d V=R T \log _e \frac{V_2}{V_1}$
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