work isothermal

Question

Work done by n moles ideal gas expanding isothermally from V1 to V2 at temperature T?

RankGuru · Accepted Answer

1. **Work Definition**: $W = \int_{V_1}^{V_2} P \, dV$.
2. **Isothermal Condition**: Over an isothermal process ($T = 	ext{const}$), follow the ideal gas law: $P = \frac{nRT}{V}$.
3. **Integration**:
   - $W = \int_{V_1}^{V_2} \frac{nRT}{V} \, dV = nRT \int_{V_1}^{V_2} \frac{1}{V} \, dV$
   - $W = nRT [\ln V]_{V_1}^{V_2} = nRT (\ln V_2 - \ln V_1)$
4. **Log Law**: $\ln V_2 - \ln V_1 = \ln(\frac{V_2}{V_1})$.
5. **Result**: **$W = nRT \ln\left(\frac{V_2}{V_1}ight)$**.

Rank Guru

work isothermal

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