Finding specific heat capacity of a non-monatomic (ideal gas)

1. Nov 12, 2013

BOAS

1. The problem statement, all variables and given/known data

Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant
pressure of 1.40x104 Pa while changing its volume from 3.00x104 to 8.00x104 m3.
The gas is not monatomic, so the relation CP = 5/2R does not apply. (a) Determine the
change in the internal energy of the gas. (b) Calculate its molar specic heat capacity
CP .

2. Relevant equations

3. The attempt at a solution

I have completed part a) using the knowledge that it is an isobaric process, but i'm a bit unsure of my answer for b)

My text book says that for a diatomic ideal gas, Cp is given by 7/2 R, but the question only says the gas is not monatomic.

Is there a piece of info i'm missing?

Thanks!

2. Nov 12, 2013

CAF123

Because U is a state variable, you can define a path between the initial and final states of the gas where V is a constant. This will allow you to find cv, from which you can extract cp.

3. Nov 12, 2013

Staff: Mentor

Just apply the constant pressure version of the first law: ΔU=Q-PΔV. Also, since ΔH=ΔU+Δ(PV), which for this constant pressure process becomes ΔH=ΔU+PΔV. So, for this process ΔH=Q. For an ideal gas, ΔH=CpΔT and ΔU=CvΔT. So,
ΔH/ΔU=Cp/Cv=(Q-PΔV)/Q. You also know that Cp-Cv for an ideal gas is equal to R. This should give you enough information to determine Cp.