Baby Collar, Dong people. China, Yunnan province, 20th century 38 x 19 cm. From the collection of Tan Tim Qing, Kunming. Photograph by D Dunlop. |

Newtonian particles are dense and heavy. And we regularly assume that they are in dynamic equilibrium with their surroundings. Then as discussed earlier, their enthalpy $H$, is related to their mass $m$, by the approximation

$\left| \, H \, \right| \simeq mc^{2}$

But the mechanical energy $E$ of any material particle is approximately $E \simeq \gamma m c^{2}$ where $\gamma$ is the Lorentz factor. Then

$E \simeq \gamma \, \left| \, H \, \right|$

For particles in slow motion, $\gamma \simeq 1$ so that $E \simeq \, \left| \, H \, \right|$. But the absolute-value signs can usually be ignored because ordinary particles are composed from electrons, neutrons and protons which all have positive enthalpy. So if we exclude anti-particles and processes like annihilation, then we usually have

$H \simeq E \simeq m c^{2}$

Thus the mechanical energy and the enthalpy are almost interchangeable for slow Newtonian particles made of ordinary matter. But enthalpy is conserved for *all* particles and conditions. So the energy and mass must also be approximately conserved for slow Newtonian particles too. This idea is honoured as an energy conservation *law* because it is so important in classical mechanics. Moreover, a conservation law for mass is a basic principle in benchtop chemistry. These excellent approximations are used everyday. Together with the routine assumption of dynamic equilibrium they typify Newtonian particles.

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Conservation of Energy |