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If I had a 10km vertical tube of water, would the water at the bottom be quite hot?

The reasoning I have is that, as $p=\rho gh$ then as the depth increases, then so should the pressure. However, pressure in a fluid is caused by nothing other than the collision of water molecules against other things. If the pressure is very high, I would imagine the force of impact is very high, meaning that the water molecules have a high velocity and thus a high temperature.

Is this true? I have a feeling it's not but the argument I present seems ok.

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  • $\begingroup$ See en.wikipedia.org/wiki/Mariana_Trench $\endgroup$ – PM 2Ring Jul 16 '20 at 8:14
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    $\begingroup$ It would help if the question was more specific. Even for a real gas, if the pressure is slowly increased and heat transfer with the environment takes place, the increase in temperature is very small. Is your container insulated? Does the pressure increase happen quickly (i.e., adiabatically)? Is the water dropped into an empty tube when filling it? The details matter. $\endgroup$ – David White Jul 16 '20 at 19:30
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The problem with the argument comes in the line "However, pressure in a fluid is caused by nothing other than the collision of water molecules against other things." Pressure in an ideal gas is caused by nothing other than the collision of gas molecules. Pressure in condensed matter comes from interatomic repulsion.

It's true that when you pressurize a material (thus doing work on it), then it heats up; however, it then comes to thermal equilibrium with what's around it. After a while, the bottom of a 10 km vertical tube of water, while under tremendous pressure, would be at room temperature.

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