First law of thermodynamics
Energy conservation for systems that exchange heat and work: ΔU = Q − W. Energy is never created or destroyed, only transferred or stored.
Definition
The first law of thermodynamics is the principle of energy conservation extended to thermal systems. It states that the change in a system's internal energy equals the heat added to it minus the work it does on its surroundings: ΔU = Q − W (physics sign convention, with Q positive flowing in and W positive done by the system). Heat and work are simply the two channels through which energy crosses a boundary; once across, it is banked indistinguishably as internal energy.
The law forbids perpetual motion of the first kind — a machine that produces work from nothing. Over a complete cycle the working substance returns to its initial state, so ΔU = 0 and the net work can never exceed the net heat absorbed: W_net = Q_net. There is no surplus to harvest, and every proposed self-powering engine must fail on this accounting alone.
It was discovered three times in a single decade by men working independently: Julius von Mayer reasoned it from physiology (1842), James Joule pinned it down by experiment (1843), and Hermann von Helmholtz proved it as a universal mathematical principle (1847). Their convergence marked energy conservation as one of the deepest unifying laws in physics.