Zeroth Law As Equivalence Relation
A system is said to be in thermal equilibrium when it experiences no net change in thermal energy. If A, B, and C are distinct thermodynamic systems, the zeroth law of thermodynamics can be expressed as:
If A and C are each in thermal equilibrium with B, A is also in equilibrium with C.
This statement asserts that thermal equilibrium is a Euclidean relation between thermodynamic systems. If we also grant that all thermodynamic systems are in thermal equilibrium with themselves, then thermal equilibrium is also a reflexive relation. Relations that are both reflexive and Euclidean are equivalence relations. One consequence of this reasoning is that thermal equilibrium is a transitive relationship: If A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. Another consequence is that the equilibrium relationship is symmetric: If A is in thermal equilibrium with B, then B is in thermal equilibrium with A. Thus we may say that two systems are in thermal equilibrium with each other, or that they are in mutual equilibrium. Implicitly assuming both reflexivity and symmetry, the zeroth law is therefore often expressed as:
If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
Again, implicitly assuming both reflexivity and symmetry, the zeroth law is occasionally expressed as the transitive relationship:
If A is in thermal equilibrium with B and if B is in thermal equilibrium with C, then A is in thermal equilibrium with C.
Read more about this topic: Zeroth Law Of Thermodynamics
Famous quotes containing the words law and/or relation:
“The law is a great thing,because men are poor and weak, and bad. And it is great, because where it exists in its strength, no tyrant can be above it. But between you and me there should be no mention of law as the guide of conduct. Speak to me of honour, and of duty, and of nobility; and tell me what they require of you.”
—Anthony Trollope (18151882)
“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of Gods being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (19091943)