Fundamental equation of thermodynamics

One of the fundamental equations of thermodynamics concerns systems at equilibrium and relates the equilibrium constant K to the difference in standard free energy (A6°) between the products and the reactants. 

In treating the fundamental equations of thermodynamics, chemical potentials of species are always used, but in making calculations when T and P are independent variables, chemical potentials are replaced by Gibbs energies of formation AfG . Therefore, we will use equation 3.1-10 in the form... 

The fundamental equation of thermodynamics for G for a dilute aqueous solution containing a weak acid HA, and its basic form A- when these species are at equilibrium at a specified pH is (see 4.3-1)... 

Fundamental Equation of Thermodynamics for a System that Contains a Single Biochemical Reactant... 

R. A. Alberty, Fundamental equation of thermodynamics for protein-ligand binding, Biophys. Chem. 104,543-559 (2003). 

Starting from the fundamental equation of thermodynamics for one component ... 

For a reversible process, where the system is always infinitesmally close to equilibrium, the equality in Eq. (1.3) is satisfied. The resulting equation is known as the fundamental equation of thermodynamics... 

From the fundamental equation of thermodynamics, we can deduce relations between the various properties of the system. To see this, let s consider a function f with independent variables x and y. The differential of f (i.e. the total change in /) can be written as ... 

Similarly, if we define the Gibbs free energy G = U — TS + pV, then the fundamental equation of thermodynamics becomes... 

Not all the chemical potentials (and therefore, the activity coeflicients) in a mixture are independent of each other. They are all related to one another through the Gibbs-Duhem equation. To derive this equation, we start with tlie fundamental equation of thermodynamics for the Gibbs free energy, which can be written as... 

The free energy- that has temperature, volume, and mole numbers as its natural variables is the Helmholtz free energy. Before we stated that once the Gibb s free energy of a system is known as a function of temperature, pressure, and mole numbers G(T,p, N, N2,..all the thermodynamics of the system are known. This is equivalent to the statement that once the Helmholtz free energy is known as a function of temperature, volume, and mole numbers of the system A(T, V, Ni,N2, -all the thermodynamics of the system are known. The fundamental equation of thermodynamics can be written in terms of the Helmholtz free energy as... 

Given and equation of state, we can determine an explicit expression for the Helmholtz free energy from the fundamental equation of thermodynamics. At constant temperature and mole numbers, we have... 

We now regard tlio rafundamental equation of thermodynamics, which includes both the first law and the second. If W is the total energy, S the entropy, T the absolute tenqxu-ature, and F the volume, then, as we know,... 

This combination of the first and second laws of thermodynamics is the fundamental equation of thermodynamics. Using the definitions of the composite functions,... 

These four equations are sometimes called the four fundamental equations of thermodynamics in fact, they are simply four different ways of looking at the one fundamental equation, Eq. (10.19). 

Illustrative Problem. Begin with the energy representation of the fundamental equation of thermodynamics U S, V, all Ni) for a system of r-components and transform this complete thermodynamic information to a new state function in which entropy S and all mole numbers Ni [Pg.792]

Illustrative Problem. Begin with the entropy representation of the fundamental equation of thermodynamics for a multicomponent system, S(U, V, all tV,), and derive the Gibbs-Duhem equation. Does this form differ from equation (29-45) in step 4 above ... 

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