What are (a) the heat extracted from the cold reservoir and (b) the coefficient of performance for the refrigerator shown in FIGURE EX21.21?

Video transcript

Hey, everyone. So this problem is dealing with heat pumps. Let's see what it's asking us. We have a heat pump that extracts heat from a cold outdoor environment and releases it into a warm interior space. We're asked what the heat extracted from the cold outdoor environment is and the coefficient performance of the heat pump. Our multiple choice answers here are a Q sub C of 67 jewels and a coefficient of performance of 1.26 B jewels and 2.61 C 53 Jews and 1.26 or D jewels and 2.61. So the first thing that they are asking for is our heat extracted. So we can recall that the equation for heat exhausted, Q sub H is equal to our work in plus Q sub C or heat extracted. And so Q sub C is what we are solving for in this problem. So we can rearrange this equation and it is Q sub C is equal to Q sub H minus work in. Now from the graph, our Q sub H is Jews. So we can see here in this step, after the 80 bad expansion, we have an iso choric process where the heat is exhausted into the environment where our pressure is going down volume staying in the same. And so we have 120 jewels going out. And then our work in we can recall is equal to negative WS. So work N is equal to negative WS and so we have two instances WS for both our adiabatic expansion. So that's negative. So that's um negative. And then works of for our 80 ban expansion is a positive 95 jules. And then for our adiabatic compression, we have a negative 148 jules. So actually, we can write that as negative 95 jewels plus 148 Jews as we distribute that negative sign throughout both terms. And that comes out to a work in of jewels. So now we can solve for our some seeds are extracted heat. It's going to be jewels minus 53 Jews which equals 67 Jews. And that is the answer to part one. And so if you look at our multiple choice answers, we can eliminate answer choices B and C. So now for part two, we have to find our coefficient of performance, we can recall that our coefficient of performance K is equal to Q sub C divided by work N. And so we've already solved for both of those values. Q sub C is 67 Jews. Our work in is 53 Jews. We plug that into our calculator and we get a value of 1.26. So looking at our multiple choice answers, that means that answer choice A is the correct answer for this problem. That's all we have for this one. We'll see you in the next video.