# Find Coefficient of Performance of a refrigerator

1. Apr 9, 2017

### grandpa2390

1. The problem statement, all variables and given/known data
I need to find the coefficient of a refrigerator that uses a monatomic gas and only has two steps.
I know the:
initial pressure of the refrigerant
initial temperature
initial volume
and final pressure

Every formula I know requires 4 steps or a knowledge of the outside and inside temperature. This question is unlike anything I have seen to date. The only other problem I have seen like this was for a real refrigerator. it had four steps, and I was given a table for the saturate refrigerant.

2. Relevant equations
$COP = \frac{Q_C}{W}$
$COP = \frac{Q_C}{Q_H-Q_C}$
$COP = \frac{T_C}{T_H-T_C}$

3. The attempt at a solution

Right now, the only thing I can think of is that I could use the equation $COP = \frac{Q_C}{W}$ by finding Q and W of the process the way I did in earlier chapters. And assume that the change in Q is Q_C .
With this attempt, I could take advantage of the formulas that give me these values based on whether or not the gas is monatomic.

Is this the right direction?

edit: I did the problem this way and got a COP of 1...
I assuming that the change in internal energy is 0. the first process is isothermal, and the second process is linear bringing it back to the same initial point. I get that Q=-W so Q/W is 1

Last edited: Apr 9, 2017
2. Apr 9, 2017

### grandpa2390

edit: I see. I think I see my current mistake. It isn't Q of the entire process. Just the Q_in.

So I got a number for the coefficient and I'm onto the next part. I need to compare it into the result I would get from the carnot cycle at the same temperature difference. What I don't get is what the temperature difference is.
All I am given is the temperature of the gas and that the first step is isothermal.

Last edited: Apr 9, 2017