A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320 K and 270 K. (a) If in each cycle the refrigerator receives 415 J of heat energy from the reservoir at 270 K, how many joules of heat energy does it deliver to the reservoir at 320 K?

Video transcript

Hey everyone, welcome back in this problem. We have an experiment conducted in the lab at 25°C and a student measured a carnal refrigerator withdraws 500 jewels of heat from the refrigerated space and the refrigerated space is maintained at negative five degrees Celsius. We are asked how many jewels of heat are delivered to the lab. Okay. Okay so here we have temperatures and some quantity of heat. Okay so let's recall that we can relate the quantity of heat and the temperature. When we're talking about carnal refrigeration through the following QC divided by Q. H. Is equal to negative T. C. Divided by th Okay now T. C. And th are the temperature of the cold and hot reservoirs respectively? Okay. Q. C. Is going to be the amount of heat that's coming out of the cold reservoir and Q. H. Is going to be the amount of heat delivered to the hot reservoir. Okay. Alright. So let's go ahead and write out what we have. So Q. H. That's how much heat is being delivered to the hot reservoir in this case the hot reservoir is the lab. Okay, so we don't know this but this is what we want to find. Okay. Qc. On the other hand, how much heat Is leaving or coming out of the Cold Reservoir which in this case is a refrigerator and we're told that this is 500 jewels. Also you have 500 rules. All right now we have our temperatures in case we have the temperature c. of the cold reservoir which is the refrigerator -5°C. In converting this into absolute temperature Calvin. We get 268.15 Kelvin. Okay we added 273.15 Calvin. And our temperature for the hot reservoir we're told is 25 degrees Celsius K. The lab is our hot reservoir 25 degrees Celsius which again add 273.15 to get 298.15 Calvin. Okay great. So now we have an equation with 44 variables. Okay we know three of the four so we can plug in and solve for the one we're looking for. So we're going to get 500 jewels divided by Q. H. Is equal to negative T. C. So negative. 268.15 Calvin divided by T. H. 298.15 Calvin. Okay and again we're looking for Q. H. The unit of Calvin will cancel. Okay we divide and multiply and we're gonna get that Q. H. Is equal to negative .94 jewels. Okay, our unit is jules. Once we divide and cancel these calvins and so that's going to correspond with answer C. Negative 556 jewels. That's going to be the heat delivered to the lab. Thanks everyone for watching. I hope this video helped see you in the next one