Thermodynamic Temperature Scale

A temperature scale, which does not depend on the thermodynamic property of the substance can be established by making use of the fact that the efficiency of a reversible heat engine does not depend on the nature of the nature of the working fluid but depends only upon the temperature of the reservoirs between which it operates. The establishment of thermodynamic temperature scale is also a consequence of the second law of thermodynamics. Refer to Figure 20.1.

Figure 20.1

Let, and be the isotherms. Let the two reversible adiabatics intersect the three isotherms. Let the reversible engine 1 absorb energy as heat, from the reservoir at and reject energy as heat, to the reservoir at . Let the reversible engine 2 absorb energy as heat, from the reservoir and reject heat, to the reservoir at . Let and represent the work done by engines 1 and 2, respectively. Let a third Carnot engine absorb energy as heat from the reservoir at and reject energy as heat to the reservoir at . The work done by the engine is given by

(20.1)

Also,

(20.2)

or,

(20.3)

or,

(20.4)

Now,

(20.5)

or,

(20.6)

or,

(20.7)