An air conditioner removes 5.0 x 10⁵ J/min of heat from a house and exhausts 8.0 x 10⁵ J/min to the hot outdoors. b. What is the air conditioner's coefficient of performance?

Video transcript

Hey, everyone. So this problem is dealing with refrigeration cycles. Let's see what it's asking us. We have an industrial chiller unit that absorbs 7.5 times to the six joles per minute of heat from a process and it discharges 9.2 times 10 to the six jules per minute of waste heat to the environment. We're asked to calculate the coefficient of performance of this unit. Our multiple choice answers are a 2.14 B 3.14 C 1.44 and D 4.41. So the key to solving this problem is recalling first, the coefficient performance equation where we'll denote coefficient performance with the letter K and that equals Q sub C are absorbed T divided by our work. And so in turn, we can recall that our discharged heat is equal to our warp plus our absorbed heat. So given that we are in the problem, given discharged and absorbed heat, we can use that to solve for our work. And then in turn, solve for our coalition of performance. So I'm going to rearrange our discharged heat equation to isolate work on the left hand side. And so we get work is equal to Q sub H minus Q sub C. And we're going to look at this problem with a timescale of one minute. As long as you're using the same timescale, uh when you're calculating your heat, uh the problem will work out. We're given our um heat rates in terms of jewels per minute. So I'm going to use minute as our time frame. And so our work in is equal to our discharged heat, which is 9.2 times 10 to the six jules minus our absorbed heat 7.5 times 10 to the six jules. And so our work is equal to 1.7 times 10, the six Jews, we were given QC C in the problem. And so now we can plug in to solve our coefficient of performance. So we'll have 7.5 times 10 to the sixth Jools divided by 1.7 times 10 to the sixth tools. And that gives us a coefficient of performance of 4.41. And that aligns with answer choice D. So that's all we have for this one. We'll see you in the next video.