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Question
Assertion :CP−CV=R for an ideal gas. Reason: [∂U∂V]T=0 for an ideal gas
Assertion :CP−CV=R for an ideal gas. Reason: [∂U∂V]T=0 for an ideal gas
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Solution
The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
R=Cp−Cv
This is so because U depends on temperature only, and dU is the same for any dT , regardless of what caused the change. For an adiabatic process, Q = 0 , so dU = -W = -p dV = Cv dT . From the ideal gas law, pV = RT (n= 1), p dV + V dp = R dT and we have that R = Cp−Cv .
R=Cp−Cv
This is so because U depends on temperature only, and dU is the same for any dT , regardless of what caused the change. For an adiabatic process, Q = 0 , so dU = -W = -p dV = Cv dT . From the ideal gas law, pV = RT (n= 1), p dV + V dp = R dT and we have that R = Cp−Cv .Suggest Corrections
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