Internal energy per unit mass

V is the material velocity. a is the stress tensor. g is the acceleration of gravity. e is the internal energy per unit mass. h is the energy flux. 

Fig ure 6-1. Energy balanoe in ohemioal reaotors, where G = mass flow-rate u = internal energy per unit mass P = pressure p = fluid density m = mass of fluid in the system Q = rate at whioh heat is transferred to the system and = rate at whioh work is done on the surroundings. 

To use Equation 6-12, a relationship is required between either the internal energy per unit mass u or the enthalpy per unit mass h and the state variables such as the temperature T, pressure P, and composition nij. 

Internal energy This is the energy associated with the physical state of the fluid, ie, the energy of the atoms and molecules resulting from their motion and configuration [Smith and Van Ness (1987)]. Internal energy is a function of temperature. The internal energy per unit mass of fluid is denoted by 17. 

This muse equal the changes in kinetic energy and in internal energy per unit mass. 

In these equations pt is the mass density (g. cm.-3) of the fth chemical species, fc is the rate of production of the fth chemical species by chemical reaction (g. cm.-3 sec.-1), and Fi is the external body force per unit mass acting on the ith species. The velocity v is the local mass average velocity (that velocity measured by a Pitot tube), p is the over-all density of the fluid, and U is the local thermodynamic internal energy (per unit mass) of the mixture. The j, are the fluxes of the various chemical species in g. cm.-2 sec.-1 with respect to the local mass average velocity, v. It should be noted that 2j, = 0, 2/c,- = 0, and = p these relations are used in deriving the over-all equation of continuity [Eq. (4)] by adding up the individual equations of continuity given in Eq. (24). 

The internal energy per unit mass e is an intensive (state) function. Enthalpy h, a compound thermodynamic function defined by Equation 1.8, is also an intensive function. 

Dimensionless Dimensionless u Internal energy per unit mass j- g Btu/lbm... 

Let denote the absolute internal energy of species K per unit mass of species K and let u denote the absolute internal energy per unit mass of mixture. Then... 

---