Two samples A and B of the same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume. If the work done by the gas is the same for the two cases, show that γ satisfies the equation 1 – 21– γ = (γ – 1) ln2.

Let P1 = Initial Pressure, V1 = Initial Volume, P2 = Final Pressure, V2 = Final Volume

Here A is expanded isothermally,

I.e. the work done,

Also, B is expanded adiabatically, i.e.

Given WA=WB


In an adiabatic process,

PVγ = const,


Substituting in (1)

We know, PV= nRT by ideal gas equation


, the required relation