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The kinetic energy of atoms (and molecules) in a system (in our case a liquid) follows a normal distribution - this is the bell shaped curve that you maybe familiar with in generating grades. It represents the number of atoms at a certain energy level: the maximum population being in the center.

This distribution is maintained as atoms are constantly trading off energy through collisions. All collisions result in the exact same total energy but the individual energies of the involved particles can vary. One atom can have its velocity elevated while the velocity of the other is depressed.

If then a certain atom has its velocity (energy) elevated into the extreme high end of the distribution tail then it has enough energy to evaporate and does so.

Now the total energy of the liquid/gas system remains the same however the energy of the isolated liquid system has gone down, energy has been removed from it. The liquid then willreadjust the distribution of the energies (velocities) of its individual atoms to reacquire the normal distribution. (NOTE: in statistical thermodynamics we say 'will' not 'must' as the quantum mechanics are allowed to. We can only say what the system as a whole will do not what individual atoms do.)

Redistributing energies to fit the normal distribution then, when there has been a net energy loss, requires the system to depress the value of the population of its maximum value - in other words the whole of the bell-curve shifts to the left - towards lower temperatures.

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