Water's temperature is given by (average K.E. of molecules)$=3/2 \ k_{B}T$, so my intuition is that flowing water molecules will gain additional kinetic energy from flowing, leading to a huge temperature rise because$k_{B}$ is very small ($1.380649 × 10^{-23}$). I am aware that (average K.E. of molecules) for the temperature equation, you only use the kinetic energy from random molecular motion - not from bulk motion. However, I don't understand how this is the case because we can think of flowing molecules as if random molecular motion were biased in one particular direction.
In this question,biased random molecular motion is the key point. So, if wereframe the question, it will go something like this. Let's say that there is a very tiny drop of water on a leaf, and we choose to heat it.With sheer luck, if all the molecules in the drop use theextra kinetic energy from the heating to move in a particular direction(kinetic energy they had before heating gets used in the same way: randomly), the drop will start to move in a particular direction. This moving in a particular direction is the same as flowing. To sum it up, when a water's temperature is raised, water can go in a particular direction. So, if water is moving in a particular direction(flowing), the water's temperature should go up. This is, in a way, a counterargument for the duplicate question's answer.
- 1$\begingroup$This is incorrect. Local fluid temperature is given by the deviation of kinetic energy from the mean kinetic energy over the small volume of concern. In other words, flow rate is (mostly) irrelevant. I strongly suspect this is a duplicate question; I'll be searching, and if I (or someone else) doesn't find one, I'll change my comment into an answer.$\endgroup$David Hammen– David Hammen2025-11-22 14:21:17 +00:00CommentedNov 22 at 14:21
- 1$\begingroup$Possible duplicates:Why am I not burned by a strong wind,Why isn't water running faster hotter,Why isn't temperature frame dependent, and many others. I'm marking this question as a duplicate of one of the others.$\endgroup$David Hammen– David Hammen2025-11-22 14:28:29 +00:00CommentedNov 22 at 14:28
- $\begingroup$@DavidHammen I am saying that the flow of water could be analyzed as random molecular motion, and because of this, the flow of water kinetic energy can be used for temperature. I say that it is a difference in how we interpret the flow. Tell me if I should add this to the question, because I think I kind of wrote this in the question$\endgroup$Owlywolf– Owlywolf2025-11-22 14:52:32 +00:00CommentedNov 22 at 14:52
4 Answers4
When water flows down a constant slope, it keeps a constant average speed. Potential energy turns to kinetic energy and then to heat. This does heat the water.
A typical speed for flowing water is about$1$ m/s. A typical drop in$1$ m might be$1$ cm. The energy is$Q = mgh$. The change in temperature is$\Delta T = Q/mc = gh/c$, where$c = 4181$ J/kg K is the specific heat of water. The large specific heat tells you the temperature change in$1$ sec will be small, in this case$2.3 \cdot 10^{-5}$ degrees C.
To get some idea of why, consider the average speed of a water molecule at$20$ C.
$$v_{rms} = \sqrt{3kT/m} = 64 \space m/s$$
The speed change from dropping water$1$ cm is very small compared to this.
- $\begingroup$I believe the OP meant something different, namely, when the waterflows, why doesn't it heat up? To make the apparent paradox stand out even more, consider a spacecraft going into orbit with the speed of multiple km/s, and the air inside it, which would suddenly become extremely hot if the author's understanding of temperature was correct.$\endgroup$Daigaku no Baku– Daigaku no Baku2025-11-22 14:48:18 +00:00CommentedNov 22 at 14:48
- $\begingroup$It does heat up when it flows. The change in temperature is tiny.$\endgroup$mmesser314– mmesser3142025-11-22 14:51:28 +00:00CommentedNov 22 at 14:51
- $\begingroup$I don't believe it heats up when it flows (if you ignore the friction); otherwise the temperature would be frame-dependent, which it is not. It heats up when it stops: the kinetic energy turns into heat. Again, consider a rocket going into space, if your (and OP's) logic was correct, the air inside it would heat up by hundreds of degrees K.$\endgroup$Daigaku no Baku– Daigaku no Baku2025-11-22 14:55:57 +00:00CommentedNov 22 at 14:55
- 1$\begingroup$I see what you mean. It heats up as it flows down a river. But not if it simply moves with respect to you. A lake doesn't heat up if you run by it.$\endgroup$mmesser314– mmesser3142025-11-22 14:59:17 +00:00CommentedNov 22 at 14:59
- 1$\begingroup$In that case, this question is a duplicate ofWhy isn't water running faster hotter?, as others have pointed out.$\endgroup$mmesser314– mmesser3142025-11-22 15:02:18 +00:00CommentedNov 22 at 15:02
In statistical physics we consider the system in its center-of-mass reference frame, so that the velocities of the molecules that are relevant for temperature are those in this reference frame, and would not change, if the body (liquid, gas tank, etc.) moves as a whole. This is a somwhat fine point, since a) it is not always explained in stat. mech. textbooks and, b) if explained, it is done in the early chapters of the text, alongside the other assumptions - these chapters contain few equations and rarely read ;)
Related:
Why do we only use energy in the micro canonical ensemble?
It's important to remember that water is a good conductor of heat. If a thermometer is fixed statically against a flowing stream, then the impact of water molecules does generate heat that could be measured but most of it is carried away by the flowing water. So there is both heating and cooling of the thermometer due to the flowing water and the net result is a negligible change in measured temperature. At low speeds (rivers).
You can do it either way.
The temperature is not frame-independent.
If you define a frame where a particular fluid portion is at rest, your temperature calculation will exclude the bulk motion and you will get some result.
In a different frame, you will get some other temperature that includes the bulk motion.
Usually, this does not matter, as long as the bulk motion is small compared to the random motion. In other cases, you have to account for e.g. converting some bulk motion into heat.
And now the easy part. If you have some flowing water and it comes to rest by internal friction, its temperature will rise in a frame comoving with water, but will not change in the frame at rest. Conserving the energy, that is.
p.s. the whole thing is pretty much not limited to water or fluids in general.
- 1$\begingroup$There is an apocryphal story that James Joule took a thermometer with him on his honeymoon and measured the temperature at the top and bottom of Niagara falls.$\endgroup$mmesser314– mmesser3142025-11-22 14:18:30 +00:00CommentedNov 22 at 14:18
- 2$\begingroup$Temperatureis frame independent. See, for example,Why isn't temperature frame dependent?$\endgroup$David Hammen– David Hammen2025-11-22 14:30:08 +00:00CommentedNov 22 at 14:30
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