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**Relations for Enthalpy, Entropy and Internal Energy**

One may conveniently employ the general energy relations and Maxwell equations to obtain expressions for change in enthalpy and entropy and internal energy for any process, which in turn may be used for computing the associated heat and work interactions.

Let H = H (T, P)

**Then: **

**But: **

**Thus: ** ...(5.16)

**Using: ** ...(5.17)

**From Maxwell relations as in eqn. 5.15: ** ...(5.18)

Thus using eqns. 5.17 and 5.18 in 5.16 we get:

...(5.20)

In the same manner starting from the general function: U = U (T,V ) andS = S (T, P ) and applying appropriate Maxwell relations one may derive the following general expressions for differential changes in internal energy and entropy.

...(5.21)

...(5.22)

**Or, alternately: ** ...(5.23)

Thus, eqns. 5.20 to 5.23 provide convenient general relations for computing enthalpy, internal energy and entropy changes as function of volumetric properties and specific heats. If a fluid is described by a suitable EOS, these equations may be conveniently integrated to obtain analytical expressions for energy and entropy changes.

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