# Does pressure cause things to be hot?

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.

• – PM 2Ring Jul 16 '20 at 8:14
• 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. – David White Jul 16 '20 at 19:30