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. (b) How much mechanical work is performed by the engine during each cycle?

Accepted Answer

Everyone. Welcome back in this problem. We have an engine operating on the basis of a cardinal cycle. Okay. It's used for a particular function. It's going to run between two thermal sources with temperatures 600 Calvin and 400 Calvin. And each cycle, 2500 jules is going to be transferred from the higher temperature source. Okay. And we are asked to find the amount of work w that can be obtained from the engine per cycle. Okay, so let's think about this. We're trying to find work. Okay, We recall that work can be written as the difference of the absolute values of the quantities of heat. Okay, So we get Q. H minus the absolute value of QC. Okay, now Q. H. Is going to be the quantity of heat transferred from the high temperature source and QC is a quantity of heat transferred to the cold reservoir. Okay. Alright. So, let's see from this problem. We're given that 2500 jules is transferred from the high temperature source. Okay, So we know that Q. H. There's going to be 2500 jewels but we aren't told any information about QC. Okay, so in order to find the work w that we need we have to find this value of QC. All right, well, we're also giving information about temperature. Okay, So we are told that the temperatures are 600 Calvin and 400 Calvin. Okay, so T. H. The temperature of the hot reservoir. The high temperature reservoir is 600 Calvin And TC. The low temperature is going to be 400 Kelvin or the temperature of the cold reservoir. Okay so let's recall that we have a relationship between the ratio of these quantities of heat and the ratio of the temperature we can write that Q. C. The absolute value divided by the absolute value of Q. H. Is equal to the absolute value of T. C. Divided by the absolute value of th. Okay so the ratio of the quantity of heat is the same as a ratio of the temperatures. This is going to give us Q. C. Okay we multiply by Q. H. And we get 2500 jewels Times 400 Kelvin Divided by Calvin in the unit of Calvin cancel we're going to be left with the absolute value of Q. C. is equal to 6.67 jewels. So this is our value of Q. C. That we needed to find in order to find the work. W. Okay so let's give ourselves a little bit more room and then we can go ahead and find that work that we were looking for. So W. Is equal to the absolute value of Q. H minus the absolute value of QC. Which is equal to 2500 jewels -1666.67 jewels. Which gives us a work of 833.33 jewels. Okay that is the work we were looking for. Let's go back up to our answer choices and we are going to find That this corresponds to answer. Be okay. The amount of work that can be obtained from the engine per cycle is jewels. Thanks everyone for watching. I hope this video helped see you in the next one.

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