# How is 0th law of thermodynamics possible?

If a body of gas A (say at $$25\ ^\circ \rm C$$) is brought in contact with another body of gas B (say at $$10\ ^\circ \rm C$$), then B absorbs heat from A until they both reach $$17.5\ ^\circ \rm C$$ and are in thermodynamical equilibrium.

When a body of gas C (say at $$15\ ^\circ \rm C$$) is brought in contact with A, C absorbs heat from A until they both reach $$20\ ^\circ \rm C$$. So now if B is brought in contact with C, heat should flow from C to B right?

• @Triatticus Please do not answer questions in the comments. If you have an answer, write it up! Thanks! – tpg2114 Sep 3 '19 at 23:27
• It's not an answer at all really, because any answer will need to address why this does/doesn't concern the zeroth law. I should have asked why they think that this is a problem for that specific law – Triatticus Sep 3 '19 at 23:29
• Related answer – Aaron Stevens Sep 4 '19 at 2:40

I have tried to follow your sequence. It was not clear to me from the description if at the end you were bringing B together with C before or after they each were each in contact with A. But it turned out not to matter as either way heat will flow from C to B. If I followed you correctly, the sequences are as shown in the diagram below. The equilibrium temperatures you assigned to B and C after initial contact with A assumes they have the same mass and specific heat as A.

The thing is I don't see that your description has anything to do with the Zeroth Law of thermodynamics, which states:

If two thermodynamic systems are in thermal equilibrium with a third one, then they are in thermal equilibrium with each other.

At the end of your sequence B and C are in thermal equilibrium with each other, but neither is in thermal equilibrium with the third, A, either the original A, or the A after contact with each of B and C. Perhaps you could elaborate further at to how this applies to the title of your post.

For a detailed discussion of the Zeroth Law see

https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics

Thanks for the answer! What I meant to ask was: after the first two steps, B and C were in thermal equilibrium with A but they were not in equilibrium with each other. Isn't this against the 0th law?

But there is no reason why they should be. Neither B nor C were initially in thermal equilibrium with A.

To apply the law to your bodies, it would say that if B is in thermal equilibrium with (the same temperature as) A and C is in thermal equilibrium with (the same temperature as) A, then B is in thermal equilibrium with (the same temperature as) C. But that's not what you have.

Hope this helps.

• Thanks for the answer! What I meant to ask was: after the first two steps, B and C were in thermal equilibrium with A but they were not in equilibrium with each other. Isn't this against the 0th law? – Karthikeya Kaza Sep 4 '19 at 1:58
• @KarthikeyaKaza I have updated my post to answer your follow up comment. – Bob D Sep 4 '19 at 2:14
• Thanks Bob. My textbook says this about the 0th law : Imagine two systems A and B, separated by an adiabatic wall, while each is in contact with a third system C, via a conducting wall [Fig. 12.2(a)]. The states of the systems (i.e., their macroscopic variables) will change until both A and B come to thermal equilibrium with C. After this is achieved, suppose that the adiabatic wall between A and B is replaced by a conducting wall and C is insulated from A and B by an adiabatic wall. It is found that the states of A and B change no further i.e. they are found to be in thermal equilibrium. – Karthikeya Kaza Sep 4 '19 at 2:20
• @KarthikeyaKaza That's certainly true. After the two systems A and B are in contact with C via a conducting wall, then both A and B will eventually be in thermal equilibrium with C, which means temperature A is the same as C and temperature B is the same as C. Now if the adiabatic wall between A and B is removed, this allows for the possibility of heat transfer between A and B. But since the temperatures of A and B are the same, no further change to either occurs because heat will not flow if thermal equilibrium exists. Heat is defined as energy transfer SOLELY due to temperature difference. – Bob D Sep 4 '19 at 2:32
• So when A and B are in contact with C, the heat energy of the three systems combined gets distributed such that all three are in thermal equilibrium? If so, thanks for clearing that up! – Karthikeya Kaza Sep 4 '19 at 2:56