Does zeroth law of thermodynamics hold?

Question

I mean the formulation that there's some variable, called temperature, that's constant in the whole volume of a system when it's in thermal equilibrium.

Well, of course, we can see it every day and we can construct thermometers to measure temperature because of the laws of thermodynamics.

But think of bigger objects, the atmosphere or a deep water: their temperature varies with how high/deep you go. So they seem not to be in thermal equilibrium although they have been there for ages, right? The dependency of temperature in such systems is caused by hydrostatic pressure. Why not apply it to any other object in any state of matter and say that there can be no thermal equilibrium at all under any circumstances as long as there's gravity?

Note I'm thinking in the thermodynamic limit: I'm not interested in the fact the laws are further locally violated by fluctuations. The same for weather.

Answer 1

I don't know how much I can tell you, because you're clearly smarter than I am (so what I am saying may be wrong). But anyways, the reason why these systems you speak of are not in thermal equilibrium, is not because of gravity, but because of the fact that they are constantly receiving energy from the Sun. I think the Zeroth Law does hold...

Answer 2

If I read your question correctly, you are not asking: "does the 0th law hold?", but "Is the premise ever met?"

And the answer if you want to push it far enough is no, which is why we call the subject thermodynamics instead of thermostatics.

Yet the Boltzmann distribution works well enough to describe the energies of particles in any spot even when the entire system is obviously not in equilibrium, which is why we can make thermometers that seem to work okay.  They just measure temperature in a local area which is "close enough" to equilibrium--just as a curve is "close enough" to a straight line if you look closely enough at it.

I'm not sure I see your point about a gravitational field, though.  You could theoretically have a system in equilibrium in a G-field.  The only thing that happens is that you pick up the potential energy in the Boltzmann distribution.  As others have noted, it's the energy input from the sun and the variable impacts of clouds on it which drives the chaos on earth.

Answer 3

The fact that they have been in a state for ages doesn't mean that they are in thermal equilibrium. The difference in temperature in the atmosphere and oceans is not caused by hydrostatic pressure. It is caused by constant energy input from the Sun. The atmosphere and oceans are wildly out of thermal equilibrium. That is why ocean currents and weather are possible.

Answer 4

The zeroth law still applies, but the temperature gradient is there because the system is open and energy can (and does) enter and leave.  If the rate and pattern of energy transfer is constant, the system being considered can still be in equilibrium despite the temperature gradient.