Mechanical equivalent of heat
The fixed conversion factor between mechanical work and heat — 4.186 joules per calorie — that proved heat is a form of energy.
Definition
The mechanical equivalent of heat is the constant ratio between an amount of mechanical work and the heat it produces: 1 calorie = 4.186 joules. Its constancy — the same number however the energy is delivered, by friction, stirring, or electric current — is what establishes heat and work as two forms of a single conserved quantity, energy.
James Joule measured it most precisely with his paddle-wheel apparatus (1843–45), in which a falling weight of known mass and drop turned a paddle in insulated water; the work m g h reappeared exactly as a measured temperature rise. Earlier and contemporary estimates came from Rumford's cannon data and from Julius Robert von Mayer's reasoning about gases.
The mechanical equivalent is the quantitative seed of the first law of thermodynamics. Once heat and work share a common unit and a fixed exchange rate, energy can be tracked as a conserved currency across thermal and mechanical processes.