Temperature and Thermal Equilibrium

Temperature is not a measure of how much energy something contains — a bath of lukewarm water holds far more energy than a spark from a firework, yet the spark is at the higher temperature. Temperature tells you the average kinetic energy of the random motion of the particles, and it tells you which way energy will flow if two objects are placed in contact.

Thermal equilibrium — two objects are in thermal equilibrium when there is no net flow of thermal energy between them. This happens when, and only when, they are at the same temperature.

Direction of energy flow — thermal energy always flows from the region at higher temperature to the region at lower temperature. It does not flow from the object with more total internal energy to the object with less.

Example: a 1 kg block of metal at 20 °C and a 10 g nail at 300 °C are put in contact. The block holds far more internal energy in total, but energy flows from the nail to the block, because the nail is at the higher temperature.

Absolute zero — the lowest temperature possible, the point at which particles have the minimum kinetic energy they can have. It is not possible to cool anything below it, because there is no energy left to remove.

The thermodynamic (kelvin) scale — a temperature scale whose zero is absolute zero. One kelvin is the same size as one degree Celsius, so converting between them is only a shift:

T / K = θ / °C + 273.15

Why kelvin, not Celsius, in equations — every gas equation and every expression for mean kinetic energy uses absolute temperature. Doubling the temperature on the Celsius scale does not double the mean kinetic energy; doubling it on the kelvin scale does. Using Celsius in pV = nRT gives nonsense, including negative pressures.

Example: 27 °C is 27 + 273.15 = 300.15 K, usually written as 300 K to 3 significant figures. Note that 0 °C is 273 K, not zero — a common and expensive slip.