Enthalpy - Other Expressions

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 C_p 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 C_p 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 μ_i is the chemical potential per particle for an i-type particle, and N_i is the number of such particles. The last term can also be written as μ_idn_i (with dn_i the number of moles of component i added to the system and, in this case, μ_i the molar chemical potential) or as μ_idm_i (with dm_i the mass of component i added to the system and, in this case, μ_i the specific chemical potential).