It is likewise possible to shift the dependence of the energy from the extensive variable of entropy,, to the ( often more convenient ) intensive variable, resulting in the free energies.
12.
The above expression of the first law in terms of entropy change defines the entropic potential energies; their gradients are called thermodynamic forces as they cause flows of the corresponding extensive variables as expressed in the following equations.
13.
Alongside the internal energy, the other cardinal function of state of a thermodynamic system is its entropy, as a function,, of the same list of extensive variables of state, except that the entropy,, is replaced in the list by the internal energy,.
14.
It makes good sense, for example, to say of the extensive variable, or of the extensive variable, that it has a density per unit volume, or a quantity per unit mass of the system, but it makes no sense to speak of density of temperature per unit volume or quantity of temperature per unit mass of the system.
15.
It makes good sense, for example, to say of the extensive variable, or of the extensive variable, that it has a density per unit volume, or a quantity per unit mass of the system, but it makes no sense to speak of density of temperature per unit volume or quantity of temperature per unit mass of the system.
16.
For the thermodynamic operation of adding two systems with internal energies and, to produce a new system with internal energy, one may write " U " 1 + " U " 2 } }; the reference states for, and should be specified accordingly, maintaining also that the internal energy of a system be proportional to its mass, so that the internal energies are extensive variables.
17.
In particular, when the body is described by stating its internal energy, an extensive variable, as a function of its entropy, also an extensive variable, and other state variables, with " U " ( " S ", " V ", " N " } } ), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy:
18.
In particular, when the body is described by stating its internal energy, an extensive variable, as a function of its entropy, also an extensive variable, and other state variables, with " U " ( " S ", " V ", " N " } } ), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy:
19.
Where for every system with degree of freedom " r " one may choose r variables, e . g . \ big ( X _ 1, \ dots, X _ i, Y _ { i + 1 }, \ dots Y _ r \ big ) \,, to define a coordinate system, where " X " and " Y " are extensive and intensive variables, respectively, and where at least one extensive variable must be within this set in order to define the size of the system.
