# Fraction of heat energy used to do expansion work of a gas?

1. Oct 12, 2011

### JustinLiang

1. The problem statement, all variables and given/known data
Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?

2. Relevant equations
ΔU = Q - W
Q = nC_pΔT
W = PΔV
C_p = C_v + R => C_p = 3R/2 + R => C_p = 5R/2

3. The attempt at a solution
So we sub in the Q and W in the internal energy formula and we get:
ΔU = nC_pΔT - PΔV
ΔU = (5/2)(nRΔT) - PΔV
ΔU = (5/2)(PΔV) - PΔV
ΔU = (3/2)(PΔV)

Therefore we can take ΔU/Q to find the fraction:
(3/2)(PΔV)/(5/2)(PΔV)

Which gives me 3/5. However the answer is 2/5. What am I doing wrong?
Personally, I think the answer key is wrong.

Thanks.

Last edited: Oct 13, 2011
2. Nov 16, 2014

### Hatmatbbat10

I know this is an old question, but I thought I'd reply for future students that need help with this question.

All of the work shown is right, except for the very end. The question wants the ratio of W/Q, while the original poster found the ratio of ΔU/Q.

W/Q =
PΔV / (5/2)(PΔV) = 2/5

3. Feb 15, 2015

### BabyPhys

Could someone please explain to me how (nRΔT) = PΔV in the third step of this derivation?

4. Feb 15, 2015

### Staff: Mentor

Ideal gas law. PV=nRT. If P is constant, then PΔV=nRΔT

Chet