Question about Calculating the Entropy of Vaporization

[Nathan Sanchez 1F]

According to the textbook, to find the entropy of transition at another temperature other than the normal boiling point, you have to break down the calculation into three steps. For example, to find the entropy of vaporization of water at 25 degrees Celsius and 1 bar, you need to

1) heat the liquid to its normal boiling point, 100 degrees Celsius.
2) allow it to vaporize
3) then cool the vapor back to 25 degrees Celsius.

I understand why we need to do the first two steps. But I don't understand why we have to cool the vapor back down to 25 degrees. How do we "cool" vapor? Wouldn't it turn back into liquid at that point? I need some explanation for these steps because the textbook does not provide them.

[Chem_Mod]

We can think of the entropy change of water boiling at 25C and 1 bar as sort of a hypothetical construct of what the entropy change would be if we could vaporize water at standard conditions. Obviously this is not something that is practically possible as you've mentioned, but we can still ask ourselves hypothetically what that change in entropy would look like, if it were possible.

Because entropy is a state function, we get to do cool things like hypothetically heat it up to its normal boiling point at 100C, vaporize it, then cool it back down to 25C while still a vapor. We know its still a vapor because we told the math to keep it a vapor. It would only be a liquid when we cooled it back down if we also adding the entropy change of condensing the vapor back into a liquid, but we don't in this case because we want to know the entropy change of vaporization into a gas phase at 25 C. If we are doing good book keeping then we can follow along entropically as we tell this strange and truly hypothetical story. The final number that we get for the entropy change of boiling water at 25 C, (while not technically possible) is still a real value, and its a larger increase in entropy if we were to do it at this temperature than if we waited until it were already 100C. Thats how entropy works! Interesting book problem!