Question

Derive an expression for the work done during an isothermal process.

Answer 1

Consider the isothermal expansion of an ideal gas. Let its initial volume be V_i and the final volumes be V_f. The work done in an infinitesimally small isothermal expansion is given by

dW = pdV

The total work done in bringing out the expansion from the initial volume V_i to the final volume V_f is given by,

W = `int_{V_i}^{V_f} pdV`

∴ W = `int_{V_i}^{V_f} (nRT)/V`dV .............`("for an ideal gas", p = "nRT"/V)`

∴ W = `nRTint_{V_i}^{V_f}(dV)/V`

∴ W = nRT(In V_f - In V_i)

∴ W = nRT In `V_f/V_i`

 

This is the required expression for the work done during an isothermal process.