# Thermodynamics - Ideal gas expansion

1. Apr 13, 2014

### Chase11

1. The problem statement, all variables and given/known data
2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x

2. Relevant equations
ΔU=Q-W
W=$\int$pdV
U=nCvT

3. The attempt at a solution

I'm not sure if I'm even on the right track here.
I have W=$\int$pdV = nRT$\int$dv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.

2. Apr 13, 2014

### Andrew Mason

You are given Q. What is the relationship between Q and W if the process is isothermal?

AM

3. Apr 14, 2014

### Chase11

Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.

4. Apr 14, 2014

### Andrew Mason

Express W in terms of n, T and Vi and Vf (check your equation for W - your integration is not correct). You have values for T, and Vf/Vi. If Q = W, express n in terms of Qm T, Vf/Vi

AM