## The Effect of Temperature and Pressure on AG

The Gibbs energy is a function of temperature and pressure, and the effects of T and P on AG are shown in the following derivation based on Eq. (3.56). For a reversible process, 5Q and TdS in Eq. (3.56) cancel because of the Second Law relationship. If the system is restricted to doing only expansion work, then 8W and PdV cancel:

For an ideal gas, if T is constant, the Gibbs energy at one pressure can be determined with respect to its value at a reference pressure. The ideal gas equation of state begins the derivation for an expression that shows the pressure dependency of the Gibbs function:

In the ideal gas equation, n is the number of moles, R is the molar gas constant, and T is the absolute temperature.

For an isothermal process, Eq. (3.60) becomes:

The ideal gas equation is substituted for V, dG = nRTp and the differential is integrated.

The Gibbs energy change for a change in pressure at constant temperature is

If state 1 is replaced by a standard reference state, G°, and a reference pressure, P°, the change in Gibbs energy is

Eq. (3.61) can be rewritten in a molar quantity (lowercase) (kJ/mol) and denoted by the overhead bar, g2 = f + RTln (P)

The standard Gibbs energy at the reference state is a function only of temperature, and the pressure term allows the Gibbs to be calculated for different pressures. In thermodynamics texts, the standard Gibbs function is tabulated in terms of temperatures at a fixed reference pressure (P° = 1 atm).

This equation resembles Eq. (3.54), which was used in Section 3.3.2 (Example 2) to determine the entropy of the components in a gas mixture.

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