# Thermodynamics- Refrigerator Problem

1. Oct 18, 2009

### jessedevin

1. The problem statement, all variables and given/known data
A refrigerator is operated by a 0.25 hp (1 hp=746 watts) motor. If the interior is to be maintained at 2.00 degrees Celsius and the room temperature of the room is 35 degrees C, what is the maximum heat leak in watts that can be tolerated? Assume that the coefficient of preformance is 50% of the maximum theoretical vale. What happens if the leak is greater than your calculated maximum value.

2. Relevant equations
$$\eta$$= Tcold/(Thot-Tcold)
$$\eta$$=Qcold/w
Qhot=Qcold+W.

3. The attempt at a solution
What I am first doing is finding the coefficient of performance $$\eta$$
$$\eta$$=375K/(408K-375K)=11.36
Then it says that the coefficent of preformance is 50% of the the max theoretical value, so $$\eta$$= 11.36/2=5.68
Then I find the rate of Qcold = w*$$\eta$$
Qcold=(746w/4)(5.68)=1059.66w
Lastly I used Qhot=Qcold+W,
Qhot=1059.66w+ 746w/4=1246.16w

But the answer in my book says its 779 watts, so did I miss a step or do something wrong. And what happens if the leak is greater than your calculated maximum value?

2. Oct 18, 2009

### Andrew Mason

First, check your conversion to Kelvin temperature. It is not correct.

Second, your method is correct except that you do not calculate Qh. You use Qc, since this is the heat that has to be removed.

What do you think happens if the refrigerator is not able to remove the heat as fast as it is entering the refrigerator?

AM