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# Heat capacity for real gas with ideal gas (zero pressure) equation2

## Heat capacity for real gas with ideal gas (zero pressure) equation

(OP)
I'm looking at this problem and I'm stuck.
I usually question everything but this problem is confusing me.
I don't know how they've made the jump from reduced properties (from generalized Cp charts(?)) to Cp-Cp°=1.70 cal/molK

Usually Cp-Cv=R
I've searched online and it seems Cp-Cv=ZR
This is not the same as Cp-Cp°=ZR, which would mean they've made Cp°=Cv (zero pressure so this is true?)
Has the author got the compressibility factor from the generalised compressibility chart for the Pr and Tr (Z=0.92)
I'm confused how they've made something straight forward look confusing.

Below is the problem plus the authors solution:

### RE: Heat capacity for real gas with ideal gas (zero pressure) equation

CPo means that the gas has and ideal behavior it is call specific heat at zero pressure or ideal gas... It doesn't mean that is not pressure.

Which is the source for the calculation ??? They correct the CP value for pressure but in the text has to be the source of the 1,7 value. It is done using an isothermal calculation.

Horacio

### RE: Heat capacity for real gas with ideal gas (zero pressure) equation

While not clearly stated, it looks like the solution presumes you are going to use the specific heat of the ideal gas (from some source like NASA Glenn) plus the Nelson-Obert generalized compressibility chart to obtain an estimate of the real gas specific heat at some given conditions. There aren't any "generalized" Cp charts, though there are generalized "residual" enthalpy and entropy charts, which represent the difference between real and ideal gas behavior. Cp-Cpo doesn't equal ZR because Z=1 corresponds to ideal gas behavior, so if anything Cp-Cpo=(Z-1)R. The equation for residual enthalpy is attached. I refer you to Chapter 10 of Fundamentals of Classical Thermodynamics by van Wylen and Sonntag, which is the text I learned and taught from. Their eqn. (10.24) is dh=CpdT+[v-T(∂v/∂T)p]dP

### RE: Heat capacity for real gas with ideal gas (zero pressure) equation

2
Hi,
To answer to your query you should consider this link where you can find way to calculate Cp using Thermodynamic (EOS) and Excel.
Note : a spreadsheet is available .
https://cheguide.com/specific_heat_ratio.html
Probably people were not responsive because it seemed to be a student problem!.
Don't expect more than what you supply .
My view .
Pierre

### RE: Heat capacity for real gas with ideal gas (zero pressure) equation

(OP)
Thanks!

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