A Carnot heat engine operates between reservoirs at 182℃ and 0℃. If the engine extracts 25 J of energy from the hot reservoir per cycle, how many cycles will it take to lift a 10 kg mass a height of 10 m?

Video transcript

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A Carne engine works between a high temperature reservoir at 700 Kelvin and a low temperature reservoir at 300 Kelvin. If the engine is 100% efficient, and it extracts 50 joules of energy from the hot reservoir per cycle, determine the number of cycles needed to displace a kg mass by 12 m. So that's their end goal. So we're given some multiple choice answers. Let's read them off to see what our final answer might be. A is 28. B is 57 C is 82 and D is 50. So first off, we must recall and use the equation for the efficiency of a Carno engine. And that's represented by Ada to the A A subscript C where C represents carnot is equal to one minus the temperature of the cold reservoir divided by the temperature of the hot reservoir. So we need to plug in our known variables to solve for a So let's do that. So one minus the temperature of the cold reservoir, which was 300 Kelvin divided by the temperature of the hot reservoir, which was 700 Kelvin. So when we plug that into a calculator, we should get 0. we also need to recall that Ada C. So the EC is equal to the work out divided by the heat transfer of the pot reservoir. Thus, we can write that the work out is equal to NC multiplied by qh which when we plug in or known variables, it's 0. multiplied by 50 jewels which when we plug into a calculator is 28. jewels. Note that this is the work done in one cycle. So the work done by moving a 20 kg mass by 12 m is written as the work is equal to the force multiplied by the distance. So when we plug in our values that we know, we know that and force is equal to F so F is equal to ma mass times acceleration. So it would be the mass is 20 kg and the acceleration is gravity. So 9.81 meters per second squared multiplied by the distance which is 12 m. So when we plug that into a calculator, we should get walls. So 2352 jewels. So for 2352 Jews of mechanical work. The number of cycles required will have to be 2352 jewels divided by our work out, which was 28 point 28 points, 57 drools. So we plug into a calculator. We should get 82 point 32 and rounding up the number of cycles that we should get is which is our final answer. We did it. So that means looking at our multiple choice answers, the correct answer is C 82. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.