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Physics Question on Kinetic molecular theory of gases

Which of the following is true in the case of an adiabatic process, where γ=Cp/Cv\gamma = C_{p} / C_{v} ?

A

p1−γT1−yp^{1 -\gamma} T^{1 - y} = constant

B

pγT1−γp^{\gamma} T^{1 - \gamma} = constant

C

pTyp T^{ y} = constant

D

pγTp^{\gamma} T = constant

Answer

p1−γT1−yp^{1 -\gamma} T^{1 - y} = constant

Explanation

Solution

For adiabatic change equation of state is
pVγpV^{\gamma} = constant
It can also be re-written as
TVγ−1TV^{\gamma - 1} = constant as p=nRTVp = \frac{ n RT}{V}
and p1−γTyp^{1- \gamma} T^{y} = constant as V=nRTpV = \frac{nRT}{p}