Calorimetry

A system is isolated when it exchanges no heat with its surroundings. When bodies at different temperatures are placed in contact inside such a system, heat flows from the hot ones to the cold ones until they share one temperature.

Principle of calorimetry: in an isolated system, heat lost by the hot bodies = heat gained by the cold bodies.

A calorimeter is the device for measuring heat. It is a metal vessel with a stirrer of the same metal, usually copper or aluminium, placed inside a wooden jacket with glass wool between them to keep heat from escaping.

A thermometer passes through the lid into the liquid. The metal vessel itself takes part in the heat exchange, so its heat must be counted as well as the liquid's.

Heat changes are found from Q = m s ΔT for each body. For mixtures the unknown is usually a specific heat or the final temperature.

Worked example: an aluminium sphere of 0.047 kg at 100 °C is dropped into a copper calorimeter of 0.14 kg holding 0.25 kg of water at 20 °C; the final temperature is 23 °C.

Heat gained by water and calorimeter = (0.25 × 4.18 × 10³ + 0.14 × 0.386 × 10³) × 3 = 3297.1 J. Heat lost by the sphere = 0.047 × s_Al × 77. Equating gives s_Al ≈ 911 J kg⁻¹ K⁻¹ = 0.911 kJ kg⁻¹ K⁻¹.

Losses to the surroundings make a real measurement less exact, which is why the insulation, lid and quick readings matter.