# Heat Englines Efficiency

1. Apr 3, 2008

### FriedrichLuo

1. The problem statement, all variables and given/known data
An engine using 1.00 mol of an ideal gas initially at a volume of 24.6 L and a temperature of 400 K performs a cycle consisting of four steps: (1) an isothermal expansion at a temperature of 400 K to twice its initial volume, (2) cooling at constant volume to a temperature of 300 K, (3) an isothermal compression to its original volume, and (4) heating at constant volume to its original temperature of 400 K. Assume that Cv = 21.0 J/K. Sketch the cycle on a PV diagram and find its efficiency.

2. Relevant equations

efficiency = W/Qh = (Qh-Qc)/Qh = 1 - Qc/Qh

3. The attempt at a solution

I have efficiency = 1 - (T2-T1)/(T4-T3) = 1 - (400-300)/(400-300). The result is zero, very absurd. I think I must misunderstand the concept of Qc and Qh. But my understanding also seems right on account of one example in the book. Please help me with this question. Thank you in advance!