Mix two substances with different masses, specific heats, and starting temperatures.
Calorimetry is the experimental technique for measuring heat flow directly, and the calculation behind it — conservation of energy applied to two substances reaching a shared equilibrium temperature — is one of the more intuitive quantitative topics in AP Chemistry Unit 6.
The core equation, q = mcΔT, relates heat transferred (q) to mass (m), specific heat capacity (c, the amount of energy needed to raise one gram of a substance by one degree Celsius), and temperature change (ΔT). When two substances at different starting temperatures are mixed and allowed to reach thermal equilibrium, conservation of energy requires that heat lost by the hotter substance exactly equals heat gained by the cooler one: m1c1ΔT1 = m2c2ΔT2 (with appropriate sign conventions, since one ΔT is negative).
Solving this relationship for the final equilibrium temperature gives Tf = (m1c1T1 + m2c2T2)/(m1c1 + m2c2) — a weighted average where each substance's contribution is weighted by its heat capacity (mass times specific heat), not just its mass alone. This is why mixing a small amount of very hot metal with a large amount of room-temperature water barely changes the water's temperature: water's specific heat (4.184 J/g°C) is dramatically higher than most metals (aluminum 0.897, iron 0.449, copper 0.385, gold 0.129 J/g°C), so water dominates the weighted average despite the metal starting much hotter.
Water's unusually high specific heat has real environmental and biological significance: large bodies of water moderate coastal climate by absorbing and releasing enormous amounts of heat with relatively small temperature swings, and the same property helps organisms maintain stable internal temperature.
Coffee-cup calorimetry (constant pressure, measuring ΔH directly) and bomb calorimetry (constant volume, sealed and pressurized, measuring ΔE) are the two standard experimental setups, differing in exactly what thermodynamic quantity they measure directly.
This calorimetry lab lets you mix two substances with adjustable mass, specific heat, and starting temperature, and calculates the equilibrium temperature live using real specific heat data for eight common materials.