A reversible power cycle receives QH from a hot reservoir at TH and rejects Qsurr to the surroundings at T0. The work developed by the power cycle is used to drive a reversible refrigeration cycle that removes QC from a cold reservoir at TC and rejects heat to the same surroundings T0.
a.) Develop an expression for the ratio QC / QH in terms of the temperature ratios TH / T0 and TC / T0.
b.) Plot QC / QH versus TH / T0 for TC / T0 = 0.85, 0.90 and 0.95.
c.) Plot QC / QH versus TC / T0 for TH / T0 = 2, 3 and 4.
2 comments:
Hey Dr. B, I have done tried to do this problem a few times, my problem is the expression I have has Qh/Qc on one side and Th/To and Tc/To on the other side and so with the givens I don't know how to relate Tc to To to Th?
Does this make sense...?
Basically I am unable to numbers on my axis because there are to many unknown variables in my expression.
Can you maybe walk me through how to set up the expression, it seems this should be fairly straightforward.
Thanks.
TG 9:04 PM
Start by writing the equations for the efficiency of the Carnot HE and the COP of the Carnot refrigerator. These eqns ONLY have T's in them.
Both efficiency and COP are = desired / required. So, eff = W/QH and COP = QH/W. So if you multiply eff by COP you get QC/QH which is what you were looking for.
Now, use the Carnot eff and COP in terms of T's. Do a bit of algebra to group terms so that you only have (Tc/To) and (TH/To) on the right hand side...no stray T's. This should not be too difficult.
Once you have accomplished this, use Excel to help make your plots.
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