Thermodynamic Temperature
In the derivation of the second law we have introduced thermodynamic temperature T as the factor of proportionality between the heat transfer rate Q˙ and the entropy flux Ψ˙ .
In previous sections we have seen that this definition of thermodynamic temperature stands in agreement with the direction of heat transfer: heat flows from hot (high T ) to cold (low T ) by itself. The heat flow aims at equilibrating the temperature within any isolated system that is left to itself, so that two systems in thermal equilibrium have the same thermodynamic temperature. Moreover, the discussion of internal friction showed that thermodynamic temperature must be positive.
The discussion of energy conversion processes between two reservoirs adds another requirement for thermodynamic temperature: For any reversible engine operating between two reservoirs, it must fulfill the relation
This relation follows from (5.1)2 for the case of a fully reversible engine, S˙gen = 0, independent of the realization of the reversible engine, or the working substance employed.
It is therefore possible, at least in principle, to measure temperature ra- tios through measurement of the heat exchange in fully reversible engines. Accordingly, to define the thermodynamic temperature scale, only a single reference temperature is required.
The Kelvin temperature scale, named after William Thomson, Lord Kelvin (1824 – 1907), uses the triple point of water (611 kPa, 0.01 ◦C) as reference. The triple point is the state at which a substance can coexist in all three phases, solid, liquid and vapor, see Sec. 6.3. The Kelvin scales assigns the value of TTr = 273.16 K to this unique point, which can be reproduced easily in laboratories.
Since thermodynamic temperature cannot be negative, the smallest possible thermodynamic temperature is 0 K, known as absolute zero.
The ideal gas temperature scale, introduced in Sec. 2.13, coincides with the Kelvin scale. This will be seen later, in Sec. 8.2, when we explicitly compute the thermal efficiency of a Carnot cycle operating with an ideal gas.