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:
“It is time that we start thinking about foundational issues: about our attitudes toward fair trials... Who are the People in a multicultural society?... The victims of discrimination are now organized. Blacks, Jews, gays, women—they will no longer tolerate second-class status. They seek vindication for past grievances in the trials that take place today, the new political trial.”
—George P. Fletcher, U.S. law educator. With Justice for Some, p. 6, Addison-Wesley (1995)
“Concord is just as idiotic as ever in relation to the spirits and their knockings. Most people here believe in a spiritual world ... in spirits which the very bullfrogs in our meadows would blackball. Their evil genius is seeing how low it can degrade them. The hooting of owls, the croaking of frogs, is celestial wisdom in comparison.”
—Henry David Thoreau (1817–1862)