Measurability of Properties
Some properties are easy to measure, and thus quite intuitive, e.g., pressure p, temperature T and specific volume v. Accordingly, the thermal equation of state, p (T, v) can be measured with relative ease. Other properties cannot be measured directly, for instance internal energy u or enthalpy h, which must be determined by means of applying the first law to a calorimeter, or entropy s, which must be determined from other properties by integration of the Gibbs equation.
The Gibbs equation
gives a differential relation between properties for any simple substance. Its analysis with the tools of multivariable calculus, as presented below, shows that specific internal energy u = U/m, specific enthalpy h = H/m, specific Helmholtz free energy f = u − T s, and specific Gibbs free energy g = h − Ts are potentials when considered as functions of particular variables. The evaluation of the potentials leads to a rich variety of relations between thermo- dynamic properties which will be derived and explored in this chapter. In particular, these relate properties that are more difficult, or even impossible, to measure to those that are more easy to measure, and thus reduce the necessary measurements to determine data for all properties.
Later, in Chapter 17, it will be seen that the thermodynamic potentials play an important role in finding the equilibrium states of a system.