Is it possible to... ?

Suppose you take a glass of water, compress it to a few atmospheres with a manual pump mechanism; then dissipate the excess heat, open a valve and let the water vaporize very finely (with a nano-something filter, perhaps).

Is it possible that the resulting glass of water is colder?

It could be a great way to cool drinks on-demand, without using any electricity!

I still haven't done the math (or physics!) but here is some related info:
- Why does pressure increase when volume decreases? [source]
- The combined gas law [source]
- Compressed Water Properties: Specific volume, enthalpy and entropy of compressed water [source]

The main question is: 1 glass of water is possibly 10-20 cl, how much pressure should
one apply to cool it from 20 degrees to 5?
And what is that in terms of force to apply to the mechanical pump that should compress the water?