thermal equilibrium

Meaning: Heat flows spontaneously from the higher-temperature object to the lower-temperature one. Thermal equilibrium is reached when the objects share one temperature, so net heat flow is zero. Molecules still exchange energy, but equally in both directions. The zeroth law of thermodynamics says that if A and B are each in equilibrium with C, then A and B are in equilibrium with each other. This is why a thermometer works.

Equation: m₁c₁(Tf − T₁) + m₂c₂(Tf − T₂) = 0, where m is mass (kg), c is specific heat (J/(kg·K)), T₁ and T₂ are the initial temperatures, and Tf is the common final temperature (K or °C, since only differences matter). This is heat lost = heat gained for an isolated pair.

On the MCAT: A calorimetry passage drops a hot metal into water in an insulated cup, and you solve for Tf or for c. Tf falls between the two starting temperatures, closer to the one belonging to the object with the larger mc. Graphs show two temperature curves converging to a plateau. If a phase change occurs, add Q = mL.

Common confusion: Equal temperature does not mean equal thermal energy or equal heat exchanged. The object with the larger heat capacity changes temperature less.