Equation of Energy Conservation

The fundamental heat equation is given as,

where s is entropy per unit mass, and simply states that the rate of increase of heat is due to L, the net effect of all sources and sinks of energy. By using the first law of thermodynamics it can be shown that Eqn. 18 can be rewritten in a concise form,

where p is pressure and γ is the ratio of specific heats (polytropic index). For a thermally isolated plasma such that no heat is exchanged (L=0), Eqn. 19 reduces to,

which may be expressed as,