I will reply to every one with one message instead of individually.
First u/bystander, I do not like to say that thermal contact means thermal contact. This means thermal contact can mean anything which is not true, or that meaning of the word thermal contact is irrelevant which is also false. Two systems are said to be in thermal contact if they can exchange energy with each other through the process of heat. Now this does not necessarily mean that the two systems must have physical contact. For example, a cake is not in physical contact with the heating element of an oven but it is in thermal contact because the energy of the heating element is transferred into the cake by a process called heat via the medium of the air contained in the oven. I stated I am taking thermal contact here to mean physical contact because it was the method I chose to establish thermal contact in my example. Physical contact is, indeed, a meathod by which one system can exchange energy with another by the process of heat. If you don't believe me I propose an experiment. Turn on your stove and leave it for 5 minutes after 5 minutes establish physical contact with the stove with your hand. Then see if any energy is exchanged. :)
u/JeremyG Yes, I know that in time themal equilibrium will be reached. Probably as governed by Fourier's law. That is not what the law as my professor says. The quotation I posted is precicely what is in his script and precicely what he said in lecture. As I said before I chose physical contact as a method in which thermal contact could be established.
u/BvU I did ask him that. I said, "when you say system I and system II are in thermal contact with system III should they not also be in thermal equilibrium with system III?" His reply was to laugh and throw his hands up in the air and said, " this is not a precise definition, we haven't defined system, thermal contact or thermal equilibrium." My belief is that you can use words and words mean things and depending on how you string those words together it is a true statement, a false statement or a (sorta) true statement. The implication of saying that when two systems are in thermal contact (separately) with another system then they are in thermal equilibrium means that thermal contact and thermal equilibrium are two distinct ideas. I guess, what he means is similar to what you have said which is that they are in some sort of contact and some time has passed and all systems have equal energy so energy transfer by heat no longer occurs. However, when I asked weather that was true he did not answer but instead scoffed at me. What I assume that means is I am missing something or it is stupid to believe that the clarification of equilibrium being reached is necessary for the statement to be true. I am wondering if my interpretation of the two statements:"0th law of thermodynamics: If two subsystems I,II are separately in thermal contact with a third system, III, then they are in thermal equilibrium with each other."
Reference
https://www.physicsforums.com/threads/zeroth-law-of-thermodynamics.848448/#post-5319998
and
0th law of thermodynamics: If two subsystems I, II are separately in thermal equilibrium with a third system, III, then they are in thermal equilibrium with each other."
are, in fact, equivilent statements or not. If they are equivilant does that then mean thermal contact implies that there is some time associated with it? IE the time that it takes to achieve thermal equilibrium?
Edit: In the interest of completeness this is the script (p 83): http://home.uni-leipzig.de/tet/wp-content/uploads/2015/02/datei.pdf From what I can tell of the mathematical description of what follows it appears that thermal contact and thermal equilibrium are used interchangeably.