Your friend claims they have a design for a reversible heat engine that can operate between the freezing and boiling temperatures of water that has an efficiency of 30%. Is this possible?

Hey, guys. Got another practice problem. Hope you got a chance to figure this out. So your friend has a very bold claim. They claim they have a design for a reversible heat engine. Remember, that just means a Carnot heat engine, between the freezing and boiling temperatures of water. And they claim that their new design here has an efficiency of 30%. And we wanna figure out is that possible. So how do we figure this out? Remember, a reversible just means a Carnot heat engine, and they're talking about the efficiency. So basically we're gonna have to use the E. E. Carnot equation. And basically what's going on here is that this efficiency equation, remember, tells us the maximum theoretical efficiency, and it relates it to the two temperatures involved. We have this equation over here. So what happens is if we calculate E Carnot between these two temperatures, it can either be less than or greater than or equal to 30%. If we calculate eCarnot and it's less than 30 percent, so if eCarnot is less than 30%, then it's impossible. Because remember, you can't get anything higher than the maximum theoretical efficiency. Right? If e Carnot is, whoops, is greater than or equal to 30%, then it is possible, and your friend actually could have a plausible design here. So really, we're just testing out. We're gonna calculate this E Carnot here and compare it to 30%. Okay? So here's my equation here. I've got that E Carnot is equal to 1 minus Tc over T H, the temperatures of the reservoirs. If you just do a quick little sketch here, what's going on is we have the hot reservoir, which is gonna be the boiling point of water. So this boiling temperature of water here is a 100 degrees Celsius, which is 373. So this t h here is 373 Kelvin. So this makes up the hot reservoir, and the cold reservoir here is gonna be the freezing point of water. The freezing point of water is gonna be 0 Celsius, which is gonna be 270 3 Kelvin. Right? So that's 0 degrees Celsius, which is 2 70 3 Kelvin, and we've seen that number before. So really, these are just the two numbers that we're gonna plug into our equation. So this E Carnot here equals 1 minus 273 divided by 373. Remember, you can't plug them in in Celsius. You have to plug them in in Kelvin. And if you work this out, what you're gonna get is 0.268. So this is equal to 26.8%. So again, this is the maximum theoretical possible efficiency. If you could build a perfect engine without any friction losses, anything like that, the best you could possibly hope for is 26.8 degrees, point 8 percent. So because eCarno is less than 30%, then this design that your friend supposedly claims is impossible. So, in other words, the answer is gonna be no. That is the answer. Alright? So you tell your friend that they're a liar. They can't create one that's better than 30%. Okay? So that's it for this one. Let me know if you have any questions.

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Your friend claims they have a design for a reversible heat engine that can operate between the freezing and boiling temperatures of water that has an efficiency of 30%. Is this possible?

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