Hello, I need some precision to make sure I understand your request.

- By "vacuum", are you referring to pressure?

- Are you talking about "direct contact evaporator" where cooling is ensured by mean of evaporation, like in a cooling tower?

Evaporation means that you have a mass transfer from liquid to gas. The phase change is located at liquid/gas interface.

Evaporation (and therefore cooling) is proportional to the difference between the saturated pressure of the gas phase at the vicinity of the interface and the partial pressure a little further in the gas phase.

Therefore, in vacuum, evaporation increases because the partial pressure in the gas phase is lowered.

Actually, we'll the term vaccum, when, there's the pressure less than the vaccum pressure (VP). Lets' take a milk container. When we heat the container, the pressure between the molecules of the milk container is reduced due to molecular expansion. When the pressure in the container goes less than the VP (through heating), the milk within the container boils and evaporation occurs. To be simple, when the compact molecules expanded due to less pressure (vaccum), the heat (evaporation) occurs. I'm not sure, it's just from my perspective.

Let's talk in general form; if you want to evaporate liquid you have two options; the first one is to heat it up and the second option is to have low surrounding pressure (I mean by low, vacuum pressure) so the evaporation will take place and the vapor of the liquid will reach the saturation pressure of it at the current temperature.

No matter what you do, you'll have to provide the heat of evaporation. If you lower the pressure over a liquid, you cause evaporation, and the liquid cools down and will eventually freeze--unless you provide heat. For your qurstion, probably the main point is the saturation temperature Tsat(p). The lower the pressure, the lower the saturation temperature. Hence, at lower pressure, evaporation will take place at lower temperatures. This might be good, because you can use low temperature heat (which is thermodynamically less valuable)+work for the vacuum pump.