Enthalpy Changes

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Similar with the internal energy, we choose the enthalpy to be a function of T and p, h=h(T,p), and its total differential is: delta H general 1

We know that the term (∂h/∂p)T  equals to zero when the gas is assumed to be ideal gas. However, if the properties of a gas do not follow the ideal gas law, that is, p∙ν=R∙T+f(p,T,ν), then this term, (∂h/∂p)T  , does not disappear. Therefore, it is necessary for us to find out some kind of relation concerning this term which can be determined by the pressure, temperature or volume.

For a compressible system, we know from the definition of entropy that:

dh=T∙ds + ν∙dp                    (1)

What’s more, the entropy is also a function which depends on temperature T and pressure p. So the total differential of entropy function can be expressed as: delta H general 2

Now we eliminate the ds in equation (1) by using equation (2), we obtain: delta H general 3

So we compare the equation (*) with equation (3), we have then the following relations: delta H general 4

Using now the Maxwell Relation, we get:delta H general 5

Hence the total differential of internal energy h can be expressed as: delta H general 6

It is obvious to notice now that the change in enthalpy of a system can be calculated by pressure, temperature and volume (or specific volume).