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

A reversible composite heat engine operates between three reservoirs at temperatures of 400K, 300K and 200K. One engine operates between the 400K and 300K reservoirs and a second engine operates between the 300K and 200K reservoirs and is synchronised with the first. In one cycle 1200 J of heat is extracted from the 400K reservoir and 100 J of heat is rejected to the 200K reservoir. Calculate the heat exchanged per cycle with the 300K reservoir and the net work done by the engine. Find the total entropy change.

2. Relevant equations

[tex]S_\mathrm{in}=\frac{Q_H}{T_H}=\frac{Q_C}{T_C}=S_\mathrm{out}[/tex]

[tex]W=Q_H-Q_C[/tex]

where [itex]Q_H>Q_C[/itex], [itex]T_H>T_C[/itex]

3. The attempt at a solution

I've attatched my attempt at a solution as a scanned image onto this post which is mostly the same as what i've put below but with what i think makes an acceptable diagram (in fact i didn't use a ruler it's more of a quick sketch =P ). I've had a few attempts at this solution and although i think this is better than the others i made i still think it's wrong so if somebody could show me where i've went wrong i'd appreciate it very much.

Thanks in advance for any help =)

[tex]S_\mathrm{in}=\frac{1200 J}{400K}=\frac{Q_2}{300K}=S_\mathrm{out}[/tex]

[tex]Q_2=900 J[/tex]

[tex]W_1=1200 J - 900 J = 300 J[/tex]

[tex]S_\mathrm{in2}=\frac{Q_3}{300K}=\frac{100J}{200K}=S_\mathrm{out2}[/tex]

[tex]Q_3=150 J[/tex]

[tex]W_2=150 J - 100 J = 50 J[/tex]

Net work done by the system [itex]W_T=W_1+W_2=300 J + 50 J = 350 J[/itex]

The total change in entropy is:

[tex]S_\mathrm{in} - S_\mathrm{out2} = 3 J/K - 0.5 J/K = 2.5 J/K[/tex]

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# Homework Help: Reversible Composite Heat Engine 3 Reservoirs

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