106C = Cv + R/2
=> ΔQ = nCΔT = nCvΔT + nRΔT/2
=> ΔQ = ΔU + nRΔT/2
=> W = nRΔT/2
Consider pVn=c
W = ∫c/VndV
= cV-n+1/(-n+1) lV1V2
W= nRΔT/(1-n)
Comparing both of these
1-n = 2
=> n=-1
So P/V = const
For a certain process ,the molar heat capacity of an ideal gas is CV+ R/2.
Then identify the process
a)PV=constant
b)P/V=constant
c)V2/P=constant
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3 Answers
106
66@asish, what was the reason to believe that we should have pVn = C?
You should have proceeded as follows:
since
δW = nR2 dT
we get p dV = nR2 dT
i.e. dVdT = nR2p = nRV2nRT (from the ideal gas equation pV = nRT)
i.e. dVdT = V2T
i.e 2 dVV - dTT = 0
Integrating we get
ln V2 - ln T = constant
i.e. V2T = constant
which is same as Vp = constant