Other Expressions
The expression of dH in terms of entropy and pressure may be unfamiliar to many readers. However, there are expressions in terms of more familiar variables such as temperature and pressure
Here Cp is the heat capacity at constant pressure and α is the coefficient of (cubic) thermal expansion
With this expression one can, in principle, determine the enthalpy if Cp and V are known as functions of p and T.
In a more general form, the first law describes the internal energy with additional terms involving the chemical potential and the number of particles of various types. The differential statement for dH then becomes:
where μi is the chemical potential per particle for an i-type particle, and Ni is the number of such particles. The last term can also be written as μidni (with dni the number of moles of component i added to the system and, in this case, μi the molar chemical potential) or as μidmi (with dmi the mass of component i added to the system and, in this case, μi the specific chemical potential).
Read more about this topic: Enthalpy
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