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Question

# One mole of an ideal gas with CpCv=γ at absolute temperature T1 is adiabatically compressed from an initial pressure P1 to a final pressure P2. The resulting temperature T2 of the gas is given by

A

T2=T1(P2P1)γγ1

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B

T2=T1(P2P1)γ1γ

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C

T2=T1(P2P1)γ

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D

T2=T1(P2P1)γ1

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Solution

## The correct option is B T2=T1(P2P1)γ−1γ For an adiabatic process, PVγ=constant. The ideal gas equation is PV=RT or V=RTP. Therefore, we haveP(RTP)γ=constantor TγPγ−1=constant (∵R is a constant)∴Tγ2Pγ−12=Tγ1Pγ−11or T2=T1(P2P1)γ−1γ

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