Solving Heat Engine & Refrigerator Problems

[Ki-nana18]

Homework Statement

A Carnot heat engine operates between temperatures T₁= 400K and T₂= 300K. In each cycle the engine receives Q_in=1200 J from the high temperature reservoir.
a) Calculate the heat Q_out delivered to the low temperature reservoir.
b) Suppose the engine is operated in reverse as a refrigerator. Now the engine receives Q_in= 1200 J from the low temperature reservoir. Determine the heat delivered to the high temperature reservoir.
c) Calculate the work done by the engine in part a, and the work done on the refrigerator in part b. Note that both answers should be positive.
d) Find the efficiency of the engine in part a, and the performance coefficient of the refrigerator in part b.

Homework Equations

Q_H+Q_C+W=0
$\frac{Q_H} {T_H}$+$\frac{Q_C} {T_C}$=0
e=W/Q_H
performance coefficient=$\frac{|Q_c|} {W}$

The Attempt at a Solution

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My confusion arises when I get negative values for part c. Mathematically they should be negative, I suspect that I am not grasping a concept somewhere.

 

[Matterwave]

Let's take the case for the engine first. Look at the diagram you drew at the top. Heat flows from the hot reservoir and a part of it is converted into work done by the engine, while the rest is dumped into the cold reservoir. This statement, translated into mathematical language says $Q_h=W+Q_c$ where $Q_h,~Q_c,~W$ are defined analogously from the above sentence with positive values corresponding to the bolded words. Does this equation make sense to you in terms of the language that it is translated to? Does the sign convention make sense to you?

Now look at the equation you provided in your "relevant equations". You have the quite different equation $Q_h+Q_c+W=0$, so again, looking at the picture you drew, what English sentence do you think this equation gets translated to?

 

[Andrew Mason]

Your value for COP, .3333, is not correct. Since it is a Carnot cycle, COP = |Qc/W| = |Qc/(Qh-Qc)| = |Tc/(Th-Tc)|

AM