Internal Energy of Multi-component Systems
In addition to including the entropy S and volume V terms in the internal energy, a system is often described also in terms of the number of particles or chemical species it contains:
where the terms Nj are the numbers of constituents of type j in the system. The internal energy is an extensive function of the extensive variables variables S, V, and the set of components, the internal energy may be written as a linear homogeneous function of first degree:
where α is a factor describing the growth of the system. The differential internal energy may be written as
where the coefficients are the chemical potentials for the components of type i in the system. The chemical potentials are defined as the partial derivatives of the energy with respect to the variations in composition:
As conjugate variables to the composition, the chemical potentials are intensive properties, intrinsically characteristic of the system, and not dependent on its extent. Because of the extensive nature of U and its variables, the differential dU may be integrated and yields an expression for the internal energy:
- .
The sum over the composition of the system is the Gibbs energy:
that arises from changing the composition of the system at constant temperature and pressure. For a single component system, the chemical potential equals the Gibbs energy per amount of substance, i.e. particles or moles according to the original definition of the unit for .
Read more about this topic: Internal Energy
Famous quotes containing the words internal, energy and/or systems:
“I maintain that I have been a Negro three times—a Negro baby, a Negro girl and a Negro woman. Still, if you have received no clear cut impression of what the Negro in America is like, then you are in the same place with me. There is no The Negro here. Our lives are so diversified, internal attitudes so varied, appearances and capabilities so different, that there is no possible classification so catholic that it will cover us all, except My people! My people!”
—Zora Neale Hurston (1891–1960)
“Just as we are learning to value and conserve the air we breathe, the water we drink, the energy we use, we must learn to value and conserve our capacity for nurture. Otherwise, in the name of human potential we will slowly but surely erode the source of our humanity.”
—Elaine Heffner (20th century)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)