Cp vs Cv

[clarissa_ram 2L]

Hi! I was wondering, what is the relationship between Cp and CV? I understand that Cp is the heat capacity at constant pressure (in which there needs to be a change in volume to maintain that constant pressure) and Cv is it at constant volume (so pressure changes since the volume is set in place?).

That said, is there a correlation between the two and if so is there a way to calculate the Cp from the Cv and vice versa?

[Stella Huang 2C]

Hi Clarissa! Hmm I don't remember this being covered in lecture, but what Dr. Lavelle did mention was that qp = nCp∆T, and qv = nCv∆T. What was mentioned in lecture was that for polyatomic gases, Cp is always greater than Cv, and as temperature decreases their values converse and both decrease to zero. Cp is greater than Cv because when heat is added at constant pressure, the substance expands and work is done to overcome the pressure. I also read that (source linked below) together, Cv and Cp form the heat capacity ratio y = Cp/Cv, so they are inversely proportional to each other, so if given y and Cp, you can calculate Cv and vice versa :-)

https://www.linkedin.com/pulse/cp-cv-ideal-gases-relations-nikhilesh-mukherjee#:~:text=These%20two%20values%20are%20usually,the%20substance%20expands%20and%20works.

[Marina Nimnual]

I don't think this was gone over in class either, but when I searched it up, Cp=Cv+R, in which R is the ideal gas constant.

[Jasmine Patel 1B]

Knowing that Cp is the molar heat capacity of a gas at constant pressure and Cv is molar heat capacity of a gas at a constant volume, using the equation PV=NRT should allow for conversions between the two expressions (similarly to how we could convert to concentration and partial pressures in chem equilibrium) using the equation stated in a previous response.

[SanthoshNandakumar3L]

Hey I had a follow up question...so for number 19 on the achieve homework there is a table with the different Cv values for gases. I was curious as to what are some examples of what "linear" and "nonlinear" gases are. I know atoms are examples such as Xe, C, S, etc. But what are examples of linear and nonlinear gases?

[Graciela Ayala 2I]

There is a way to go between the two! The explanations on achieve for the homework really help to explain, but basically Cv= Cp-R, and vice versa Cp=Cv-R.

You can see in some of the homework problems it will say things like in this example the Cp is equal to 4R or something like that. So in that case you could put Cv=4R-R which gives you 3R. Then you just look up the constant value for R, multiply it by 3 and that's your Cv value.