Ideal Gas
This is a derivation to obtain an expression for for an ideal gas.
An ideal gas has the equation of state:
where
- P = pressure
- V = volume
- n = number of moles
- R = universal gas constant
- T = temperature
The ideal gas equation of state can be arranged to give:
- or
The following partial derivatives are obtained from the above equation of state:
The following simple expressions are obtained for thermal expansion coefficient :
and for isothermal compressibility :
One can now calculate for ideal gases from the previously-obtained general formula:
Substituting from the ideal gas equation gives finally:
where n = number of moles of gas in the thermodynamic system under consideration and R = universal gas constant. On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows:
This result would be consistent if the specific difference were derived directly from the general expression for .
Read more about this topic: Relations Between Heat Capacities
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