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Question

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, then γ (specific heat) satisfies the equation
  1. 12γ1=(1γ)ln2
  2. 121γ=(γ1)ln2
  3. 2γ1=ln2
  4. 121γ=γln2


Solution

The correct option is B 121γ=(γ1)ln2
Work done =nRT2ln(V2V1) for isothermal process.
Work done =nR(T2T1γ1) for Adiabatic process.
from question, 
nRT2ln(V2V1)=nR(T2T1γ1)
T2T1=(V2V1)y1
ln2(γ1)=(1T1T2)
ln2(γ1)=112γ1
ln2(γ1)=121γ

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