# Efficiency of a cycle from a diagram

1. Apr 24, 2012

### fluidistic

1. The problem statement, all variables and given/known data
Calculate the efficiency of the heat machine that is shown in the figure. Draw the corresponding Carnot cycle diagram in the S-T plane.

2. Relevant equations
$\varepsilon = \frac{ \Delta W}{\Delta Q}$.
$\Delta Q = T \Delta S$

3. The attempt at a solution
My problem lies in evaluating $\Delta Q$ for the process 1 (or from A to B).
For the process 2, $\Delta Q=T_2(S_2-S_1)$.
For the process 3, $\Delta Q=0$ because there's no change in entropy.
But I'm stuck at process 1. My attempt was $\Delta Q=\Delta T \Delta S=(T_2-T_1)(S_2-S_1)$ but I know this doesn't make any sense.
Using that non sensical result I find $\varepsilon = \frac{1}{T_2-\frac{T_2^2}{T_1}}$ which makes no sense because if $T_1=T_2$ I get an infinite efficiency while I should get 0. A friend of mine reached $\varepsilon =\frac{T_1-T_2}{T_1+T_2}$ but I don't know how he did nor if that's right either.
Any help is appreciated.

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2. Apr 24, 2012

### I like Serena

Did you consider that $dQ=TdS$, and that if T changes with S that then $ΔQ=∫TdS$?

3. Apr 24, 2012

### fluidistic

Actually not! haha.
Now I reach the same answer as my friend. Thank you very much for that.
Hmm I'll think about the Carnot cycle. If I need help I'll post here.