# Homework Help: Thermodynamics - Cycle efficiency

1. Nov 23, 2012

### Jalo

1. The problem statement, all variables and given/known data
Consider the following reversible cycle:

Where S2=S3=(S1+S4)/2 .
Prove that the efficiency η is:

η= 1 - 2*T6 / (T1+T3)

2. Relevant equations

3. The attempt at a solution

I know that in a T-S diagram the heat received by the system is equal to the area delimited by the upper boundaries of the diagram and the line T=0. I also know that the heat dispensed by the system is equal to the area under the diagram (I got the same results calculating both heats analitically). Therefore I get:

η = 1 - (S4-S1)T6 / [ (S2-S1)T1+(S4-S2)T3 ] =
= 1 - 2*S2T6 / [ (S2-S1)T1+(S4-S2)T3 ]

I don't know how to get rid of the entropies tho... If anyone could point me in the right direction I'd appreciate.

Thanks!

2. Nov 23, 2012

### TSny

Check the blue highlighted region. I don't believe it's correct. Note that S4-S1 ≠ 2S2

Also, think about the relation between S2-S1 and S4-S2

3. Nov 23, 2012

### Jalo

Oh, for some reason I tought S2 was equal to (S4-S1)/2 instead of (S1+S4)/2 ....

I can solve it from here.
Thanks!