ABSTRACT
Sometimes called The First Law of Thermodynamics, the balance of energy principle is stated as follows: the rate of change of total energy in a body, including internal energy and kinetic energy, is equal to the corresponding rate of work done by external forces on the body together with the rate of heat added to the body. In rate form
_Kþ _ ¼ _W þ _Q (6:1)
in which is the internal energy with density j
_ ¼ ð r _j dV (6:2a)
_W is the rate of mechanical work, satisfying
_W ¼ ð _uT t dS (6:2b)
_Q is the rate of heat input, with heat production h and heat flux q, satisfying
_Q ¼ ð rh dV
ð nTq dS (6:2c)
and _K is the rate of increase in the kinetic energy,
_K ¼ ð r _uT
d _u
dt dV (6:2d)
It has been tacitly assumed that all work of external forces is done on the boundary S, and that no work is done by body forces.
