Thermodynamics - Cycle efficiency

[Jalo]

Homework Statement

Consider the following reversible cycle:

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

η= 1 - 2*T₆ / (T₁+T₃)

Homework Equations

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!

 

[TSny]

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

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

 

[Jalo]

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

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!