(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A working substance goes through a cycle within which the absolute temperature varies n-fold, and the shape of the cycle is

,

where T is the absolute temperature, and S the entropy. Find the efficiency cycle.

2. Relevant equations

[tex]\frac{\delta Q_R}{T}=dS[/tex], [tex]\eta=1-\frac{|Q_{out}|}{Q_{in}}[/tex]

3. The attempt at a solution

The total heat is [tex]Q=\int T dS[/tex], that is the area of the surface in the picture. I could just say: it's a triangle so I'll use the formula for the triangle surface:

[tex]P=\frac{1}{2}ab[/tex].

The [tex]Q_{in}[/tex] is easy to calculate:[tex]Q_{in}=T_0\int_{S_0}^{S_1}dS=T_0(S_1-S_0)[/tex].

But how do I get the [tex]Q_{out}[/tex]? The temperature changes. I have found in solution (without explanation) that the answer is:

[tex]Q_{out}=\frac{1}{2}(T_0+T_1)(S_1-S_0)[/tex], but why [tex]T_0+T_1[/tex]? and where does that 1/2 comes from? The triangle area formula? :\

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# Homework Help: Efficiency of a cycle in TS diagram

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