Introduction to Mathematical Physics/Continuous approximation/Energy conservation and first principle of thermodynamics

Statement of first principle

Energy conservation law corresponds to the first principle of thermodynamics ([#References|references]). \index{first principle of thermodynamics}

Template:IMP/prin Template:IMP/eq This implies: Template:IMP/thm Template:IMP/thm Template:IMP/rem

Consequences of first principle

The fact that $U$ is a state function implies that:

• Variation of $U$ does not depend on the followed path, that is variation of $U$ depends only on the initial and final states.
• $dU$ is a total differential that that Schwarz theorem can be applied. If $U$ is a function of two variables $x$ and $y$ then:

Template:IMP/eq Let us precise the relation between dynamics and first principle of thermodynamics. From the kinetic energy theorem: Template:IMP/eq so that energy conservation can also be written: Template:IMP/label Template:IMP/eq System modelization consists in evaluating $E_c$, $P_e$ and $P_i$. Power $P_i$ by relation eint is associated to the $U$ modelization.