The average internal kinetic energy of an object refers to its temperature. If the kinetic energy increases, the temperature of the object increases and vice versa. If that's right, then falling water should heat up? When water falls from a height, its molecules, of course, have some amount of kinetic energy already. So when it starts to fall and its potential energy gets converted to kinetic energy, shouldn't the molecules' kinetic energy also increase? If it does, then its temperature should go up, right? But it doesn't seem like that happens. Can someone explain this please?


2 Answers 2


It's mean kinetic energy of a body's particles in the frame of reference of the body's centre of mass that is correlated with its temperature. This is the frame in which the body's centre of mass is at rest, so random motion of particles will increase the total energy in this frame, since the total energy is the scalar sum of the particles' energy. This is consistent with the particles' 'thermal' motion being random. The kinetic energy of a falling body is increasing in our frame of reference (at rest with respect to the Earth) but not in the body's (centre of mass) frame.

  • $\begingroup$ ... and this is, I think, what is meant by the key word "internal" in the first sentence of the question. $\endgroup$
    – kricheli
    May 11 at 7:12
  • $\begingroup$ I do get your point that it should be measured with reference to the centre of mass of the water, but it would be great if you could check the link in Farcher's answer as well and let me know if it is right or wrong as I'm quite confused right now. $\endgroup$ May 11 at 8:07
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    $\begingroup$ @Ishaan Manish Farcher is (as usual) correct. Whereas I was 'talking' about the water while it was falling, Farcher is referring to the water after it has hit rocks (or whatever) at the bottom of its fall. During the impact almost all the kinetic energy of unidirectional motion acquired by the water during the fall is transferred to random energy of particles. [And because the water is no longer falling, the Earth's frame of reference, in which Joule measured the water's 'final' temperature is pretty much the same as the centre of mass frame.] $\endgroup$ May 11 at 14:26

It is said that the Physicist James Joule during his honeymoon in the Alps in 1849 attempted to verify that the temperature of water at the bottom of a waterfall was higher than at the top.
There is an increase in temperature but it is very small and note that the motion of the water has to be randomised by it hitting something at the bottom of its fall.

Falling lead shot is used in demonstrations to illustrate the effect.

If you research this topic you will most probably come across the term mechanical equivalent of heat which heralds a time when the connection between work done and energy (heat) was a matter of debate.

  • $\begingroup$ Thanks for the experiment pdf, quite some good info! So, I guess it would be correct to say that with water, it won't heat up as much but substance of lower specific heat capacity could show some significant increase in heat if allowed to drop by several hundred meters? $\endgroup$ May 11 at 7:54
  • $\begingroup$ You can easily estimate and know that no plausible material can have a specific heat capacity low enough for that to matter. Say, you drop a big block of steel from the top of a tall building and it hits the floor. Even if you assume all the energy converts to heat inside the block and not shared to the ground, the temperature rise is ridiculously tiny. $\endgroup$ May 11 at 8:35
  • $\begingroup$ @Ishaan "note that the motion of the water has to be randomised by it hitting something at the bottom of its fall." $\endgroup$
    – PM 2Ring
    May 11 at 9:18
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    $\begingroup$ The nice anecdote of Joule contains a distraction in regard to the original question. You have to be aware that there can be other mechanisms at play, like heat exchange with the surrounding air. If the air is cold enough, falling water drops can freeze on their way down. $\endgroup$
    – kricheli
    May 11 at 9:19

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