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**1. The problem statement, all variables and given/known data**

Here is the cycle:

I am to assume cold-air standard applies.

I need to:

a)Draw a T-s diagram

b)Find where heat is transferred and work is done

c)Calculate the coefficient of performance

**2. Relevant equations**

COP = 1 / (T

_{H}/T

_{L}- 1)

**3. The attempt at a solution**

For the T-s diagram, as you can see on the image above, I just labeled what happens to entropy on each process (except I forgot to label the turbine, which like the compressor would be constant s ideally). I'm not really sure if this is an ideal case or not, so I guess s=const could be wrong.

Each compressor does work on the fluid, the fluid does work on the turbine, heat is transferred from the fluid to the surroundings in the intercoolers between the compressors, and heat is transferred from the surroundings to the fluid between 6 and 1. So that settles the second part of the hw.

Assuming that the fluid reaches equilibrium with the environment in the intercooling stage and the evaporation stage, T

_{H}would be 293K and T

_{L}would be 293. So COP would be infinity. Which obviously is impossible, but I think that could be the intention of this problem since we are starting to learn about irreversibility (and also because it seems to say that the turbine is driving the compressors, which would be a perpetual motion machine). But is it possible I'm neglecting something? Even if T

_{H}was higher, what would be the point of the second compressor? Like say T

_{3}=T

_{5}=T

_{H}=303. Then COP would calculate the same whether there was one compressor or two. Perhaps if there were only 1 compressor, T

_{6}would be higher?