Details

10 kg of liquid water are cooled from an initial temperature of 40 °C. An energy balance is used to determine the final temperature :

,

where is the liquid heat capacity (kJ/[kg °C]), is the heat of vaporization at 20 °C (average of initial temperature and 0 °C) in kJ/kg and is in °C.

The amount of liquid is 10 kg minus the amount of water vaporized (both in kg):

.

Integrating between the initial conditions (, ) and the final conditions yields:

,

.

Thus the final temperature for a given amount of water vaporized is:

, where .

When 0.66 kg of water vaporizes, the liquid temperature is 0 °C and additional vaporization freezes some of the remaining liquid. An energy balance at 0 °C determines the amount of liquid that forms solid ice:

.

Here is the mass of ice formed (kg), is the heat of fusion (kJ/kg) and is the heat of vaporization at 0 °C (kJ/kg).

The screencast video at [1] explains how to use this Demonstration.

Reference

[1] Evaporative Cooling of Water [Video]. (Sep 3, 2019) http://www.learncheme.com/simulations/thermodynamics/thermo-1/evaporative-cooling-of-water.