# Air condition and net heat [closed]

I have attempted to solve a problem, but my answer is not quite the same as in the book. Thus, I would really appreciate it if someone could confirm/disconfirm whether or not my solution is correct.

PROBLEM

A window air conditioner has an average coefficient of performance of $2.0$. In a futile attempt to cool a bedroom, this unit has been placed on the floor by the bed. During this attempt, $8.2 \cdot 10^4 J$ of heat is removed from the air in the front of the unit. Determine the net heat added to the room by operating the air conditioner in this manner.

SOLUTION

Ok, so we know that:

$$\frac{|Q_C|}{|W|} = \frac{|8.2 \cdot 10^4|}{|W|} = 2$$

Furhter, we have, due to conservation of energy:

$$|Q_H| = |W| + |Q_C|$$

The first equation can be rearranged so that:

$$|W| = \frac{|8.2 \cdot 10^4|}{2}$$

Thus:

$$|Q_H| = \frac{|8.2 \cdot 10^4|}{2} + |8.2 \cdot 10^4|$$

So the net heat added is $\frac{|8.2 \cdot 10^4|}{2} = 41000 J$.

According to my book, the correct answer should be $38000 J$. So am I doing something wrong here? Or is the book wrong?

Any help will be greatly appreciated!

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I'm sorry, but Physics.SE is not a homework help site. We'd be very happy to help you work through any misunderstanding of the physics that you may be having, but "check my work for me" is not part of what we do here: it is roughly equivalent to "do my work for me" and is forbidden by the FAQ. – dmckee Sep 28 '12 at 20:56
OK. I wasn't aware of this, and will keep this in mind from now on. Thanks for notifying me. – user12277 Sep 28 '12 at 21:17
No fret. The thing is that if you can formulate this question in a more general and conceptual way they can be helpful to the next personal along, and we can answer them. Have a look at How do I ask homework questions on Physics Stack Exchange?. – dmckee Sep 28 '12 at 22:18

## closed as too localized by dmckee♦Sep 28 '12 at 20:54

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