I have written about the first, second and third laws of thermodynamics; these three laws are numbered in chronological order and, I believe, in logical order. But, in 1932, the English physicist Sir Ralph Fowler (1889-1944) proposed that there should be a further law that logically belonged before the other three. So it is called the Zeroth law of themodynamics.
The zeroth law considers three objects a, b and c. It states that if a and c are in thermal equilibrium (meaning there is no spontaneous flow of heat between them – see post 16.34) and b and c are in thermal equilibrium, then a and b are in thermal equilibrium.
Although the zeroth law appears in textbooks and is widely considered to be fundamental to the concept of temperature, I believe it is logically unnecessary.
We can consider temperature as a property of objects that defines whether heat flows between them spontaneously, as described in post 16.34. If no spontaneous flow of heat occurs between two objects, we say that they have the same temperature. Now the zeroth law becomes if a and c are at the same temperature and b and c are at the same temperature, then a and b are at the same temperature. It now seems that the zeroth law is a consequence of simple logic, as explained in the next paragraph.
If I tell you that a is the same height as c and that b is the same height as c, you can deduce immediately that a and b are the same height. You don’t need a physicist to define a law of measurement to obtain this result – it follows from simple logic. So I don’t believe we need a zeroth law of thermodynamics.
Now is the time for two warnings.
First warning. If you are studying thermodynamics to pass an exam you may need to believe that the zeroth law is important – even though I don’t.
Second warning. If you are not interested in details about logic, you may prefer to stop reading at this point.
The zeroth law is about the concept of equality that concerns a relationship between things. Now let’s consider a general relationship R between objects a, b and c. Suppose R has the property that:
IF aRc AND bRc THEN aRb is TRUE.
In this case, we say that R is a transitive relationship. We can see that equality is a transitive relationship because, if x and y are numbers:
IF x = 3 AND y = 3 THEN x =y is TRUE.
Not all transitive relationships are about arithmetic. Let B represent the relationship “is the brother of”, then
IF dBf AND eBf THEN dBe is TRUE
because if d is the brother of f and e is the brother of f than d and e must be brothers.
Not all relations ships are transitive. Let S represent the relationship “is the son of”, then:
IF gSi AND hSi THEN gSh is FALSE
because g and h are brothers.
So I believe that the concept of temperature is a consequence of the second law of thermodynamics and that the zeroth law is no more than the recognition that equality is a transitive relationship.
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