How Does Temperature Distinguish Thermal States in Equilibrium?

[pitbull]

Homework Statement

Prove that there is a parameter that distinguishes different thermal states if thermal equilibrium between thermodynamic systems is an equivalence relation.

Homework Equations

Equivalence relation>>>> reflexive, symmetric and transitive

The Attempt at a Solution

The parameter should be temperature. First I could say that thermal equilibrium is reflexive (every thermal equilibrium of a system is in equilibrium with itself), and symmetric (if A is in equilibrium with B, then B is in equilibrium with A). If thermal equilibrium is an equivalence relation, then it must also be transitive (you can compare thermal equilibrium without thermal contact, aka 0th law of Thermodynamics). So you need a parameter to compare, and that parameter must be the temperature. Is this all I must answer?

PS> Sorry for my English

 

[DEvens]

The part you are missing is what happens when there are different thermal states? You described what it means to be in equilibrium. But you did not connect that to systems that are not in thermal equilibrium.

 

[pitbull]

The part you are missing is what happens when there are different thermal states? You described what it means to be in equilibrium. But you did not connect that to systems that are not in thermal equilibrium.

Thanks, man!