By Vera, Juan H.; Wilczek-Vera, Grazyna

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**Example text**

In order to decide whether the differentials of the functions are exact, we verify whether the functions preceding the differentials of the variables x and y meet Maxwell’s conditions. For clarity, we consider the following general form: ∂F ∂F dF = dx + dy ∂x y ∂y x An exact differential should meet Maxwell’s relation of the form ∂ ∂y ∂F ∂ ∂F = ∂ x x ∂y x ∂ y x y For the function f, ∂ ∂ 9 x 2y 2 − 2y + 7 = 18 x 2y − 2 and 6 x 3y − 2x = 18 x 2y − 2 x y ∂y ∂x Thus, df is an exact differential.

17a) T where A is the integration constant. This semiempirical correlation for the vapor pressure of pure compounds is known as the Riedel equation. A simple empirical equation for the vapor pressure applicable over a limited temperature range, closely related to the Riedel equation, is the Antoine equation. 17b) where the temperature t is in degrees Celsius and the constants A A, BA, CA are also empirically evaluated. 18) The fact that this exact equation is verified using experimental data can be considered among the best evidence of the usefulness of the definition of entropy.

10 63 The Chemical Potential and the Gibbs–Helmholtz Equation in this form here. 8, the Gibbs–Duhem equation, written in terms of the chemical potentials. 8) This equation is one of the stepping-stones for the calculation of chemical potentials. At constant pressure and temperature, it may seem to indicate that the chemical potential of a compound i in a mixture is constant and independent of composition. On the other hand, we know that like any partial property, chemical potential is a function of the composition of the mixture.