Chapter 12 : Compressible Flow
Lecture 38


    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)