# Homework Help: Thermo cycles with only T and mol

1. Feb 5, 2012

### bmartz

1. The problem statement, all variables and given/known data
A three-step cycle is undergone by 3.8 mol of an ideal diatomic gas:
(1) the temperature of the gas is increased from 210 K to 550 K at constant volume;
(2) the gas is then isothermally expanded to its original pressure;
(3) the gas is then contracted at constant pressure back to its original volume.
Throughout the cycle, the molecules rotate but do not oscillate. What is the efficiency of the cycle?

2. Relevant equations
Q=nCvΔT
Q=nCpΔT
Cv=5/2 R
Cp=7/2 R
W = nRTln(V2/V1)
ε=Wnet/QH
3. The attempt at a solution
I know I need to find the total work and heat flow in. For step one it is easy enough, W=0 and Q=nCvΔT.
I'm stuck at step 2. I know that since it is isothermal ΔEint is 0, so Q=W. I am trying to calculate by:
W = nRTln(V2/V1)
But without any initial or final pressure or volume values I am lost.

2. Feb 5, 2012

### Spinnor

Assume the problem as stated gives all the required information. Can you just let either the initial pressure or volume equal to an unknown with the hope that it will cancel out in the end? Just a thought.