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.
Initial pressure of the gas = P1
Initial volume of the gas = V1
Final pressure of the gas= P2
Final volume of the gas = V2
Given, V2 = 2 V1, for each case.
In an isothermal expansion process,
Adiabatic work done,
It is given that same work is done in both cases.
In an adiabatic process,
From eq (1),
and nRT1 = P1V1
Or (γ − 1) ln 2 = 1 − 21−γ
HC Verma - II