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.
In an adiabatic process,
PVγ = const,
Substituting in (1)
We know, PV= nRT by ideal gas equation
, the required relation