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:
“Personal change, growth, development, identity formation—these tasks that once were thought to belong to childhood and adolescence alone now are recognized as part of adult life as well. Gone is the belief that adulthood is, or ought to be, a time of internal peace and comfort, that growing pains belong only to the young; gone the belief that these are marker events—a job, a mate, a child—through which we will pass into a life of relative ease.”
—Lillian Breslow Rubin (20th century)
“The flattering, if arbitrary, label, First Lady of the Theatre, takes its toll. The demands are great, not only in energy but eventually in dramatic focus. It is difficult, if not impossible, for a star to occupy an inch of space without bursting seams, cramping everyone else’s style and unbalancing a play. No matter how self-effacing a famous player may be, he makes an entrance as a casual neighbor and the audience interest shifts to the house next door.”
—Helen Hayes (1900–1993)
“No civilization ... would ever have been possible without a framework of stability, to provide the wherein for the flux of change. Foremost among the stabilizing factors, more enduring than customs, manners and traditions, are the legal systems that regulate our life in the world and our daily affairs with each other.”
—Hannah Arendt (1906–1975)