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  4. An ideal gas system undergoes an isothermal process, then the work done during the process is

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Q. An ideal gas system undergoes an isothermal process, then the work done during the process is

Thermodynamics

Solution:

Let an ideal gas goes isothermally from its initial state $ (P_1V_1) $ to the final state $ (P_2V_2) $ , then work done
$ W = \int\limits_{V_1}^{V_{2}} P dV $
Taking $ PV= nRT $ or $ P = \frac{nRT}{V} $
Then, $ W= \int\limits_{V_1}^{V_{2}} \frac{nRT}{V} dV $
$ = nRT \int\limits_{V_1}^{V_{2}} \frac{dV}{V} = nRT\, ln\, \frac{V_{2}}{V_{1}} $