ABSTRACT
We can do the same for system 2. Thus, according to the zeroth law, the two systems 1 and 2 are at equilibrium along each of the isotherms. The property which is common to these systems is called temperature. For fixed values of a certain value of the force corresponds to a value of the displacement Therefore, a relation exists between the four variables
33 , xX
1X .1x
( ) 0,, 331113 =xXxXF which expresses the equilibrium between systems 1 and 3. A similar relation holds for systems 2 and 3 as ( ) 0,, 332223 =xXxXF so that, solving for the two equations, we obtain 3X ( ) ( )322233311133 ,,,,, xxXfXxxXfX == (7.1)
Hence, we have ( ) ( )3222331113 ,,,, xxXfxxXf = (7.2) and this yields ( )32211231 ,,, xxXxfX = (7.3) The equilibrium condition for systems 1 and 2, following from the zeroth law, can be written as ( ) 0,, 221112 =xXxXF and it follows that ( )221121 ,, xXxfX = (7.4) This allows us to eliminate from Eq.(7.3). In a similar manner we can eliminate from Eq.(7.2), which becomes
( ) ( )222111 ,, xXfxXf = Thus, for systems at equilibrium, there exists a function which takes the same value in all systems. Denoting it by ( ) θ=xXf , (7.5) this equation is called the equation of state, and θ is known as empirical temperature.
