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Q.

One mole of an ideal gas (Cp /Cv = γ) at absolute temperature T1 is diabatically compressed from an initial pressure P1 to a final pressure P2. The resulting temperature T2 of the gas is given by

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a

T2=T1P2/P1γ/(γ−1)

b

T2=T1P2/P1(γ−1)/γ

c

T2=T1P2/P1γ

d

T2=T1P2/P1γ−1

answer is B.

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Detailed Solution

For adiabatic process, PVγ= constant For an ideal gas PV = RT   or V = (RT/ P)∴ P(RT/P)γ= constant or    Tγ/Pγ−1= constant      (∵R= constant )∴ T2γP2γ−1=T1γP1γ−1or    T2=T1P2/P1(γ−1)/γ
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One mole of an ideal gas (Cp /Cv = γ) at absolute temperature T1 is diabatically compressed from an initial pressure P1 to a final pressure P2. The resulting temperature T2 of the gas is given by