The extensive thermodynamic variables we have discussed so far are the volume V, the mass M, internal energy U, the enthalpy H and the entropy S. There are also the intensive parameters, pressure p, and temperature T. It is best to think of the internal energy as a function of the entropy, volume and mass. Note that each is an extensive variable:

The following form of the First Law actually incorporates the Second Law (for fixed mass):

and it shows explicitly that the internal energy is best characterized by these two variables, S and V. Note that this last expression shows how the internal energy changes in terms of other state variables (S and V). The associated intensive parameters are given by partial derivatives:

The enthalpy can be written:

and the First Law (combined with the Second) is expressed (for fixed mass) as dH = TdS + Vdp I (4.81)

along with the corresponding partial derivative expressions. We can also think of the entropy as the dependent variable:

and and

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