Calorimetry — Notes

• Heat: energy flowing from hot to cold; unit J (1 cal ≈ 4.2 J). Temperature: degree of hotness; unit K (°C in practice; a change of 1 °C = 1 K).
• Heat capacity $C$: heat to raise the temperature of a body by 1 K; unit J K⁻¹; depends on mass and material.
• Specific heat capacity $c$: heat to raise 1 kg by 1 K; unit J kg⁻¹ K⁻¹; depends only on material. Water 4200, ice 2100, aluminium 900, copper 400.
• $C = mc$; $Q = mc\,\Delta T$.

Principle: when hot and cold bodies are mixed and no heat is lost to the surroundings, heat lost by the hot body = heat gained by the cold body.

$m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2)$ (+ $m_{cal} c_{cal} (T - T_2)$ for the calorimeter).

A calorimeter is a thin polished copper vessel (low heat capacity, good conductor, polished to reduce radiation) in an insulating jacket, with stirrer and thermometer.

Water warms and cools slowly. Consequences and uses:

• Sea breeze by day (land hotter), land breeze at night (sea warmer).
• Coastal climates are moderate; inland deserts have extreme days and nights.
• Coolant in car radiators, power stations; hot-water bottles.
• Farmers flood fields on frosty nights; water gives out heat as it cools.
• Body temperature stays steady (body is mostly water).

A pure substance changes state at a fixed temperature (ice melts at 0 °C at normal pressure). Heat absorbed during melting separates the molecules and does not raise the temperature.

Specific latent heat of fusion $L$: heat to change 1 kg of solid at its melting point into liquid at the same temperature. Ice: $L = 336\,000\ \text{J kg}^{-1}$ (336 J g⁻¹). $Q = mL$.

Heating curve (ice → steam): sloping parts $Q = mc\Delta T$; flat parts at 0 °C (melting) and 100 °C (boiling) are latent heat.

• Ice at 0 °C cools better than water at 0 °C: each kilogram absorbs 336 000 J to melt before warming.
• Snow on mountains melts slowly, so rivers keep flowing in summer.
• Ponds and lakes freeze slowly: a lot of heat must be removed first.
• Frozen food and ice-cream stay cold longer.
• Freezing water gives out heat: trays of water in a cellar protect stored vegetables from frost.