# Need help with this heat capacity/ideal gas problem.

## Main Question or Discussion Point

For many gases at low densities and pressures (where ideal gas behavior is obtained), Cv/R = A+BT+CT^2 where A, B, C, are all constants, with appropriate temperature units so that the RHS (right hand side) of this equation is dimensionless.

a> How can a gas be both ideal and follow the equation above, at the same time.

b> Such a gas initially at T1 expands slowly in an insulated piston to double its original volume you would like to find the final temperature T2. A friend suggest you may use the follow equation that we derived in class:

(T2/T1) = (V1/V2)^(R/Cv) = (1/2)^(R/Cv)

where Cv is evaluated at T1. What is wrong with your friend's statement? Find the correct equation that should be solved (implicitly) to find T2.

Attempt:
a. I said it has to be at constant V and high temperature. Not what it was asking
b. It said it was an insulated piston? Doesnt that mean that T1=T2?? But I have really no idea how to do it. :/

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LeonhardEuler
Gold Member
For (a), it's an ambiguous question, and I'm not exactly sure what kind of answer they want, but the constant volume thing is definitely wrong because an ideal gas is defined by it's equation of state, which includes how the state variables change with volume. It is also unnecessary, since a gas following this equation could be ideal even as volume changes and with temperature not being high.

For (b), an insulated piston will change it's temperature when work is done on it because of the 1st law. Energy needs to be conserved, so when work is done on the gas and heat can't escape, it's temperature increases, so T2 does not equal T1.

To get the right answer to (b), find where the equation they want to use was derived. Then repeat the derivation, but using what you know about the heat capacity in the necessary place.