Question

Give an expression for work done in an isothermal process.

Answer 1

The work done by the gas, W = ${\displaystyle {\int }_{{\text{V}}_{\text{i}}}^{{\text{V}}_{\text{f}}}\text{P}.\text{dV}}$

Writing pressure in terms of volume and temperature,

P = ${\displaystyle \frac{\mu \text{RT}}{\text{V}}}$

Substituting this value we get

W = ${\displaystyle {\int }_{{\text{V}}_{\text{i}}}^{{\text{V}}_{\text{f}}}\frac{\mu \text{RT}}{\text{V}}\text{dV}=\mu \text{RT}{\int }_{{\text{V}}_{\text{i}}}^{{\text{V}}_{\text{f}}}\frac{\text{dV}}{\text{V}}}$

By performing the integration in equation, we get

W = ${\displaystyle \mu \text{RT}\ln \left(\frac{{\text{V}}_{\text{f}}}{{\text{V}}_{\text{i}}}\right)}$