So we are cold. A piece of hot metal, A supposed to be rapidly cooled or quenched to 25 degrees C. And that requires that we take, um um 1000 killer jewels out of the metal. Which means that that energia energy heat must go into the working fluid s. So that would be our heat into the fluid. Um, the cold space that absorbs the the energy could be one of the possible. Okay, so, one, it could be a submerging the metal into a bath of liquid water and ice does melting the ice. Okay, so let's take a look at that. Um, um, we have what we want. We want to help the change of entropy of the cooling media for each of the cases and discuss the results. Well, we have. Let's see here. Um, there's no external work done. Um, by this. So so Oh, well, yeah, well, there actually is. There is external work done, but we can use the anthem p, um, and has to figure figure this out because of the system here. So we have Q one that he transfer is the mass times the specific entropy change and in the first case. What? We have ice to gas. We can look out. Look up. What you see here, we can figure out the entropy going from the solid to a gas, and we know that he transfers. So we know the mass we need way Need three about 3 kg of water of, um, water at zero degrees Celsius. And let's see here we can figure out the change in entropy and again looking for the change from going from zero degrees Celsius to the gashes face phase, um, and multiply that times the mass and we get about changing changing entropy of 3.662 killer jewels per kilogram. Um, so that's the change of entropy in the cooling media. Now, the second case, we look at our 22 it's initially at 20 minus 20 degrees c on, but it absorbs the energy, so that becomes a saturated vapor. So, again, we way. We need to look at the change in anthropology form of fluid to gas as it changes from a fluid to a gas. Um, that at minus 20 degrees C, we can look that up for our 22 and we can figure out the mass needs to be about 4.5 kg of this substance. And we can also look up the change in entropy as we go from a fluid to a gas across the two phase. And in that case, we have a change in entropy in the R 22 as 3.95 killer tools for Calvin. And in the final case we have Let's see here, um, again, this is a let's see here, so offended by vaporizing liquid nitrogen. Okay, so again we're looking at had boiling this so again we can use the entropy. And so we're boiling the liquid nitrogen so we can go from Let's see, the pressure is 100 100 didn't write that down here. 103 101 101.3 Killer Pascal's So we can look up the change in, um, the change in entropy going from the fluid saturated, fluid, toe saturated vapor across the to phase region, you can look that up for 101.3 to the Pascal's and then get the mass. And then now we need a mass of about 5 kg of liquid nitrogen. And in this case, if we look to change the way, look at the changing the entropy and going from the saturated fluid to a saturated, vapor saturated, liquid saturated vapor times by the mass, we get 12.9 killer jewels per Calvin and so we can see that basically, as the change in entropy change, the change in entropy goes up as the change. Um, in one, over the the temperature goes up for a given. He transferred. So in this case, we have a given amount of heat we need to transfer. And so the change in temperature, um, we'll need to be, um, won over the change in temperature so way again go from one phase to the other. But we need thio. Have, um a Let's see, here we need we're going to get mawr entropy, more change and entropy in the fluid. Um, because we have a each of these is that a well, each of these is at a lower temperature. So again, um, what's happening is that the water is that zero degrees C or, you know, to 73 Calvin and then this is at minus 20 degrees C. So minus 2. 53 Calvin. So one over tea is greater for this case than in this case, and in this case, the liquid liquid nitrogen. Um, is that a I didn't look up temperature, but whatever, the liquid nitrogen is at a much lower temperature than then a minus 2020 degrees C. So it's one over. T value is bigger than here. So again the entropy goes up as the temperature which the heat transfer is happening is occurring. Uh, the one over it went over, That temperature goes up.