Question

Is molar specific heat for two different processes are addable?

Answer 1

We define specific heat as

C=ΔQΔT

In case of isothermal process, if the heat supplied is compensated by P-V work done, then the temperature of the gas will not increase. So, ΔT=0. Then, C=∞.

In case of adiabatic process, however, ΔQ=0, as you cannot supply heat from outside. Therefore, C=0.

However, when we want to calculate the amount of work done, in adiabatic process, we write W=CvΔT (for ideal gas). But Cv should be 0. But that does not make any sense.

How to solve this dialemma?

thermodynamics ideal-gas

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edited Mar 3 '17 at 17:00

asked Feb 28 '17 at 16:33

Shoubhik Raj Maiti

105114

1

The C in isothermal process and the C in adiabatic process are different and should not be written out without differentiating them. For W=CvΔT, I doubt it is correct as this is an adiabatic process but not an isochroric process. – user115350 Feb 28 '17 at 17:25

@user115350 For adiabatic process, dU=dq+dw. dq=0. Then, dU=dw. Again, we know that, dU=CvdT. So, dw=CvdT. There is nothing wrong with this equation. – Shoubhik Raj Maiti Mar 3 '17 at 17:03

You first say that Cadiabatic=0 and then say "Cv should be zero". – lucas Mar 3 '17 at 17:22

Yes, you are right: W=CvδT. It is also correct that Cv≠0 . In your second sentence, you said, for an adiabatic process C=0 which doesn't mean Cv=0. – user115350 Mar 3 '17 at 17:30

@user115350 For adiabetic process C=0, since we are applying Cv for adiabetic process, Cv should also be zero.