Question
Derive an expression for work done in isothermal reversible expansion of ideal gas.
Solution
Let us consider n moles of ideal gas enclosed in a cylinder fitted with a weightless and frictionless piston. The work of expansion for a small change of volume dV against the external pressure P is given by
Total work done when the gas expands from initial volume V1 to final volume V2, will be
For an ideal gas, PV = nRT i.e.
Hence,
For isothermal expansion, T = constant so that
But at constant temperature,
P1V1 = P2V2
Total work done when the gas expands from initial volume V1 to final volume V2, will beFor an ideal gas, PV = nRT i.e.
Hence,
For isothermal expansion, T = constant so that
But at constant temperature,
P1V1 = P2V2
