Question

derive a relation for reversible work done.

Answer 1

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