# What is the effect of volume on liquid temperature during evaporative cooling?

Imagine two evaporative cooling experiments: In the first, a beaker contains a known volume of liquid. The liquid starts at ambient temperature. The temperatue of the body of liquid remaining in the beaker is measured as the liquid is allowed to evaporate. The experiment concludes before the liquid in the beaker has completely evaporated.

The second experiment repeats the first exactly except that the volume of liquid used is less.

Over a period of time the liquid shows a drop in temperature, with a rate of cooling that is greatest at the start but the rate of decrease becomes less.

What effect would the reduction in volume have on the measured results?

I've tried to think about this in small incremental time periods. My understanding is that the initial energy loss due to evaporation would be unaffected as same initial temp and surface area (same beaker), however losing this energy would represent a larger proportion of the internal energy of the remaining liquid (less liquid to start with) so the temperature drop during that first delta(t) time period would be greater in the second experiment.

Would this effect continue or would the now colder liquid lose LESS energy in the next delta(t) period? Clearly the liquid is approaching an equilibrium temperature with its surroundings where evaporative heat loss = heat gained from the now warmer ambient, but will the smaller volume get there quicker?

Is it possible with just the information given to assert that the temperature change measured would be bigger, smaller or unaffected?

What could we say about the temperature measured in each experiment at a set time T from the start BEFORE equilibrium was reached?

• Is the beaker in a room, or is it in a chamber containing no air? Can heat be exchanged between the surroundings and the liquid (say, at the liquid surface)? Commented Jun 1, 2016 at 11:22
• Although not stated in the question (which is therefore poorly constructed in my opinion) the assumption would be that the beaker is in a room and that heat exchange could take place. This question is to be asked of 15 year olds and I am rapidly coming to the conclusion that they are not equipped by high-school physics to be able to answer it - but that is not a discussion for these boards. I wanted to try and get the physics straight before taking up that point with the exam board. It turns out that I can't answer it too well either hence my post! Commented Jun 1, 2016 at 22:21