Temperature

Temperature is a measure of the average thermal energy per microscopic degree of freedom in a body — an intensity, not an amount. It is defined operationally by thermal equilibrium: temperature is the single quantity that two bodies come to share when placed in contact, and the existence of a consistent numerical temperature is guaranteed by the zeroth law of thermodynamics. Two systems are at the same temperature precisely when no net heat flows between them.

Crucially, temperature is distinct from heat. Heat is energy in transit, measured in joules; temperature is the intensity that sets the direction of that flow — always from higher temperature to lower. A spark may be far hotter than a bathtub yet carry far less thermal energy. Temperature tells you which way heat will move on contact; it says nothing on its own about how much.

Only the absolute (Kelvin) scale makes temperature a true ratio quantity, because its zero is the physical floor of thermal motion. Statistical mechanics later identifies the precise microscopic meaning of temperature through the relation 1/T = ∂S/∂U — the reciprocal of temperature is how a system's entropy responds to added energy.

The concept matured only once instruments existed to make it quantitative: Galileo's thermoscope (1592), Fahrenheit's sealed mercury thermometer (1714), Celsius's centigrade scale (1742), and Kelvin's absolute scale (1848). The microscopic interpretation as mean molecular energy came with the kinetic theory of the nineteenth century.