Calorimetry

Heat capacity (C) of a body is the heat needed to raise the temperature of the whole body by 1 K (or 1 degree C). It depends on the material AND the mass, so two unequal lumps of the same metal have different heat capacities. Specific heat capacity (c) strips out the mass: it is the heat needed to raise 1 kg of the substance by 1 K, measured in J/(kg·K). It depends only on the material, not on how much you have. The two are linked by C = m × c. Water has an unusually high specific heat capacity, 4200 J/(kg·K), which is why the sea warms and cools so slowly.

To find how much heat energy enters or leaves a body when its temperature changes, use Q = m × c × (change in temperature). Q is in joules, m in kilograms, c in J/(kg·K) and the temperature change is the rise or fall. The same amount of heat causes a small temperature rise in water (high c) but a large rise in copper (low c). This single equation handles all heating and cooling as long as the substance does not change state.

When a hot body is placed in contact with a cold body in an insulated container, heat flows from hot to cold until both reach the same final temperature. If no heat escapes to the surroundings, the heat lost by the hot body equals the heat gained by the cold body. This is the principle of the method of mixtures, or the principle of calorimetry. Writing 'heat lost = heat gained' as an equation lets you solve for an unknown final temperature, mass, or specific heat. The apparatus used is a calorimeter, a polished metal vessel inside an insulating jacket so that stray heat exchange with the room is minimised.

While a substance changes state, ice melting to water or water boiling to steam, its temperature does not change even though heat keeps flowing in. That hidden heat is the latent heat: it breaks the bonds holding the solid or liquid together rather than raising the temperature. The heat is Q = m × L, where L is the specific latent heat of the substance. For melting ice the specific latent heat of fusion is 336000 J/kg, so a full glass of ice absorbs a large amount of heat from a drink while staying at 0 degrees C, which is exactly why ice is such an effective cooler.