First Law of Thermodynamics

The First Law of Thermodynamics is that the increase in internal energy of a closed system equals the amount of heat energy added minus the work performed by the system.

Mathematically, this is described as follows:

$\mathrm {d} U=\delta Q-\delta W\,$

where $\mathrm {d} U$ is the infinitesimal increase in the internal energy, $\delta Q$ is the infinitesimal amount of heat added, and $\delta W$ is the infinitesimal amount of work performed.

A ramification of this is the Principle of conservation of energy; the amount of energy in the closed system of the universe remains constant. This can be combined with the principle of Mass-Energy Equivalence to demonstrate that the amount of mass in the universe is constant.

Note that if no energy is added, then the maximum amount of work that can be performed by the system is equal to its initial energy. This prevents the existence of a type of perpetual motion machine.