# About Zeroth Law of thermodynamics vs. Geology

In Zeroth law of thermodynamics, it clearly says that the systems connected together are in thermal equilibrium.

My question is:

In Earth Science, scientists say that Earth's core temperature is 6000 °C, but the Earth's crust temperature is only 200 °C — 392 °C, why the temperature in Earth's crust, mantle, core aren't the same? It is stated in the law of thermodynamics that any system will have a thermal equilibrium when they are in contact, like thermometers if they get contact with us, we and them will have the same temperature, right?

But why earth's layers don't have thermal equilibrium? If scientists of geology were right, then thermodynamics is? If thermodynamics is right, then geology is? What is right? Law of Thermodynamics or geology? Because, if earth's layer will have a thermal equilibrium earth's core must not be at 6000 °C, or if earth's core is 6000 °C then earth's crust must be at 6000 °C also, right?

In Zeroth law of thermodynamics, it clearly says that the systems connected together are in thermal equilibrium.

It does not say this at all. It takes time for any systems that are in contact to come to equilibrium. Therefore before this point in time they are not in equilibrium (and this doesn't even consider other processes at play that can even drive systems further from equilibrium). The rest of your question pretty much becomes invalid at this point since it was built on a faulty understanding.

The Zeroth law is more of a mathematical requirement so that thermal equilibrium can be a well defined equality. It just says if $$x$$ is in equilibrium with $$y$$, and if $$y$$ is in equilibrium with $$z$$, then $$x$$ is in equilibrium with $$z$$. This might seem obvious, but this is because we are so used to this holding for equality that we don't realize it needs to be a condition rather than a result. A somewhat silly relationship that does not have this property is that of being a son. If Alan is Bob's son, and if Bob is Cody's son, then is Alan Cody's son? Of course not. Therefore "being a son" is not a sense of "equality" (however you could argue that the relation "being in the same family" does serve as an equivalence relation).

As a quick note, you also need reflexivity ($$x$$ is in thermal equilibrium with itself) and symmetry (if $$x$$ is in equilibrium with $$y$$, then $$y$$ is in equilibrium with $$x$$) to establish that thermal equilibrium is an equivalence relation. I guess these other two points are more obvious than the transitive property, so we don't give them their own law? Just like we did above, you can think of relations where these properties do not hold, and so they can't be considered equivalence relations.

• So it doesn't work on all things? And it takes time? But it is like million years ago when Earth is formed, or I missed understand it? – James Jul 20 '19 at 14:44
• @James The Zeroth law defines a property of thermal equilibrium. It doesn't matter what the system is. It doesn't say anything about how, when, etc. thermal equilibrium is achieved. And it also doesn't say any system in contact is in thermal equilibrium. When you walk outside on a cold day does your entire body instantly become cold? No. Can you think of times where your hands were cold and your body was warm? Obviously systems in contact do not have to be in thermal equilibrium. – BioPhysicist Jul 20 '19 at 14:55

And after 4.5 billion years, the interior still has not come to equilibrium because there are sources of heat:

1. Radioactive decay of unstable nuclei
2. Heavier stuff gravitating to the center