Showing mathematical relations for coefficient of performance of refrigeratror
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This page shows efficiency of a carnot engine.
http://www.oberlin.edu/physics/dstyer/P111/Carnot.pdf
The refrigerator uses the same process only it run backwards. By using the same recipe as in the link above I want a mathematical derivation of the coefficient of performance of a refrigerator. A little additional information is in the attachment for my question. I am only interested in a mathematical explanation as that is what would work for me. Thank you! I also need the answer to be written in a computer document.
See the attached file.
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The solution shows the mathematical relations for coefficient of performance of a refrigerator.
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A reverse Carnot engine works as following:
From point 1 to point 2 an isotherm expansion at temperature
From point 2 to point 3 an adiabatic compression.
From point 3 to point 4 an isotherm compression at temperature
From point 4 to point 1 an adiabatic expansion back to the original cycle.
Process 1 to 2: isotherm.
Since the temperature ...
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