system
Given the following post, respond as if you're commenting on Reddit:
human
Can temperature decrease in a closed system while entropy increases?

For example if I have a bowl of water at room temperature, it will slowly evaporate, will that increase entropy while decreasing temperature, or will the pressure increase keep the temperature the same? Is there some other way to do it?
gpt
A sufficiently interesting example: if you have an isolated vessel, with a wall separating it into two chambers, and you have a real (ideal doesn't work) gas in one of them and vacuum in the other, when you remove the wall the gas expands to fill all the chamber. This is called free or Joule expansion.

Entropy increases because this process is obviously irreversible. Temperature changes; for almost all gases in most conditions this is a decrease (though there are a few exceptions), in that case here's your example.

Note this cannot work with an ideal gas, as these have U = 3/2 NkT, so that since U is constant (as the vessel is thermally isolated and no work is ever performed on the gas) then also T must remain constant.