## FANDOM

138 Pages

The idea in this method is to keep track of energy going in $\int_0^t Q\left( t' \right) dt'$ and out $\int_0^t L\left(t' \right) dt'$ of a system to infer the energy change.

$\Delta E = \int_0^t Q\left( t' \right) dt' - \int_0^t L\left(t' \right) dt'$

If the energy is conserved then the left hand side vanishes.

$\int_0^t Q \left( t' \right) t' dt' = \int_0^t H \left( t' \right) t' dt'$
$E_2 = E_1 \left(\frac{V_1}{V_2} \right)^{\gamma -1 } = E_1 \left( \left(\frac{v t_1}{v t_2}\right)^3 \right)^{1/3} = E_1 \frac{t_1}{t_2}$