Zeroth Law of Thermodynamics & Temperature Explained

 

Zeroth Law of Thermodynamics states that if two thermodynamic systems A & B are in thermal equilibrium (i.e. they are of the same temperature) with a third thermodynamic system C, then the two thermodynamic systems A & B are also in thermal equilibrium with each other.

 

Conversely, the law can be stated as follows:-

If three or more thermodynamic systems are in thermal contact with each other by diathermic walls and are in thermal equilibrium with each other, then any two systems taken from them will be in thermal equilibrium with each other.

It basically says that if two objects are in thermal equilibrium with an object, then they will be in thermal equilibrium with each other.

(Systems A and B are in thermal equilibrium with C. Then they will be in equilibrium with each other also.)

Zeroth’s Law of Thermodynamics was framed after the first and second laws of thermodynamics has been pronounced.

Significance

This law helped us to define the term ‘temperature’ because temperature is a quantity that remains constant when there’s a thermal equilibrium.

Zeroth Law – An Equality Relation

A thermodynamic system is by meaning in the state of its internal thermodynamic equilibrium, that is to say, there is no change in its observable state over time and no flows occur in it.

One of the detailed statements of the Zeroth law is that the relation of thermal equilibrium is an equality relation on couples of thermodynamic systems.

Mathematical Explanation

Consider 3 systems A, B & C.

Let Pa & Va represents the pressure and value of the system A, Pb & Vb be the pressure & volume of the system B and Pc & Vc be the pressure of C.

If A & B are in thermal equilibrium then,

Ø1(Pa,Va)=ø2(Pb,Vb)

Or

F1[Pa,Vb,Pb,Vb]=0

So we can write above as,

Pb=f1(Pa,Va,Vb)   – (1)

Similarly,

For B & C

Ø2 (Pb,Vb)= Ø3(Pc,Vc)

Or, F2[Pb,Vb,Pc,Vc]=0

Also, Pb=f2[Vb,Pc,Vc]      – (2)

From 1 & 2,

f1(Pa,Va,Vb)= f2[Vb,Pc,Vc]      

The above equation shows that when two or more system are in thermal equilibrium, for each system there exist a single value function of state variable P and V which has a common value for all of them.

The common of this function is called empirical temperature

Ø(P,V)=m  (thermal equilibrium between systems)

The above equation can be written as

Ø(P,V,m)=0

This equation is called an equation of state.