Hey everybody. So let's check out our example problem. We have a Carnot heat engine that's taking in some heat from a hot reservoir, expelling it to a cold, and we want to calculate the total change in entropy of the universe. Now we already know this is going to be an entropy problem that involves multiple objects, because the hot and the cold reservoirs are both exchanging heats at different temperatures. So let's go ahead and draw our quick little diagram here. That's my hot. That's my engine, that's my cold. We've got the temperature of the hot is 500. The temperature of the cold is 350. All the stuff is in Kelvin. And so we have the heat that's taken in from the hot reservoir is 2,000 Joules. So that's my QH. Right? That's QH = 2,000 Joules. So then what happens is, it expels some heat to the cold reservoir, but we actually don't know what that Qc is. So the next thing we want to do is just set up our delta S total equation. The total change in entropy for the universe is going to be adding up the two entropy changes for the hot and cold reservoirs. So in other words, delta SH + delta SC.
So what happens here is that this delta SH, because we can assume that this happens at constant temperature, is going to be Qh over Th. But remember, we have to add a negative sign because the hot reservoir loses some heat to the engine, whereas this delta SC here is going to be plus QC over TC. And that's because this cold reservoir is absorbing heat from the engine. Right? So one's positive, one's negative. Okay? So, basically, let's go ahead and figure this out. Right? So we've got delta S, or sorry, negative QH, which is going to be negative 2,000 divided by the 500. Now we have the TC here. We have this 350. But we don't actually have what the QC is. So we're going to have to go figure that out. Now, the way that we did this in another problem was that we actually had the work done. And so if we use the work equation, right, this W equation, we calculate QC. But we actually don't have that here. So in order to figure out what this QC here is, I'm going to need another equation. So let's go ahead and do that. So which equation can we use for the Carnot cycle? We actually have a couple of them. If we knew the efficiency we would use this equation, but we don't have the efficiency. We can't use this equation here. So the only one that I can use that's sort of special to a Carnot engine is going to be this one over here.
This the ratio of the heats is equal to the ratio of the temperatures. Remember, we can only use this for a Carnot cycle. So let's set this up here. So we've got QC over QH equal to TC over TH. Alright. So if you look at this, I have 3 of 4 variables. Right? I've got all the heats and the temperatures. So I can calculate this real quick here. This QC is really just going to be well, TC over TH is 350 over 500. So we're going to multiply that times the QH, which was 2,000. If you go ahead and work this out, what you're going to get here is you're going to get, let's see, I get 1400. So this is 1400 Joules. That's what we plug into this equation now. Alright? So basically, this just becomes, negative 2,000 over 500 plus 1400 over 350. Now when you work this out, what you're going to get is that this delta S total here is actually equal to 0. So essentially what happens is these two things will cancel each other out. So what's going on here is that because Carnot heat engines are ideal and they are perfectly reversible, then essentially what that means is that the change in entropy for a Carnot cycle is always equal to 0. So in other words, Carnot engines are perfect and perfectly reversible, then basically what happens is that the best outcome happens. You have no total change in entropy of the universe.
Alright, guys. So that's it for this one.
