Internal Energy and Enthalpy

Microscopic view of a gas is a collection of particles in random motion. Energy of a particle consists of translational energy, rotational energy, vibrational energy and specific electronic energy. All these energies summed over all the particles of the gas, form the specific internal energy, e , of the gas.

Imagine a gas in thermodynamic equilibrium,i.e., gradients in velocity, pressure, temperature and chemical concentrations do not exist. Then the enthalpy, h , is defined as  , where  is the specific volume.   (38.16)   If the gas is not chemically reacting and the intermolecular forces are neglected, the system can be called as a thermally perfect gas, where internal energy and enthalpy are functions of temperature only. One can write

(38.17) For a calorically perfect gas, (38.18)

Please note that in most of the compressible flow applications, the pressure and temperatures are such that the gas can be considered as calorically perfect. For calorically perfect gases, we assume constant specific heats and write (38.19) The specific heats at constant pressure and constant volume are defined as            (38.20)

Equation (38.19), can be rewritten as (38.21)   Also  . So we can rewrite Eq. (38.21) as (38.22)

In a similar way, from Eq. (38.19) we can write (38.23)