A Carnot engine is operated between two heat reservoirs at temper...

Question

A Carnot engine is operated between two heat reservoirs at temperatures of 520 K and 300 K. (a) If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it discard to the reservoir at 300 K?

Accepted Answer

Hey everyone, welcome back in this problem. We have a carnal engine K. And in each cycle it withdraws 3500 jewels of heat from the high temperature source And that source is at Calvin. And it's going to deliver an amount of heat to a heat sink with a temperature of 320 Calvin and were asked in each cycle how many jewels are delivered to the heat sink? All right. So when we're talking about jewels being delivered to a heat sink we're talking about Q. The quantity of heat. Well let's go ahead and write out what we're giving were given Q. This quantity of heat of 3500 jewels that gets withdrawn from a high temperature source. Okay so this is gonna be Q. H. The amount that gets withdrawn from the high temperature source. Okay and this is going to equal 3500 jewels. Were also given the temperature H. Or sorry th Of that high temperature source which is 450 Calvin. Were given the temperature of the sink as well. So T. C. The temperature of the sink or the colder temperatures um reservoir is 320 Calvin. Okay. And were asked how many jewels are delivered to the heat sink? Well that is going to be Q. C. Okay, the quantity of heat delivered to that cold reservoir and that's what we're looking for. Now let's recall that we have a relationship between between the ratio of cubes and the ratio of temperatures T. So we can write that Q. C. Divided by Q. H. Is equal to negative T. C. Divided by th. Okay so the ratio of the quantity of heat Q. Is equal to the ratio of the temperatures T they were looking for QC. So we can multiply by Q. H. We get Q. C. Is equal to the ratio of the temperatures -320 Calvin divided by 450 Calvin Times. q. h. 3500 jules. Okay. And this is gonna give us Q. C. Is equal to negative 2488. jules. Okay. And that is going to be the number of jewels delivered to the heat sink. So our answer is going to be BQ. is equal to negative. 2489. Thanks everyone for watching. I hope this video helped see you in the next one.

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