Temperature and its scales

Temperature tells how hot or cold a body is. Heat is energy that flows from one body to another because of a temperature difference, always from the hotter to the colder. Once it has arrived, it is part of the body's internal energy; so 'the heat in a body' is not a correct phrase.

The old unit of heat is the calorie, the heat that warms 1 g of water by 1 °C; 1 cal ≈ 4.18 J. Joule showed that a fixed amount of work always makes the same amount of heat.

A temperature scale is made from two fixed points, such as the melting point of ice and the boiling point of water, with the gap between them divided equally:

Because the scales are related by straight lines, (reading – lower fixed point) ÷ (number of divisions) is the same on every scale. This gives the two conversions you need:

• t_F = (9/5)t_C + 32. A body temperature of 37 °C is (9/5) × 37 + 32 = 98.6 °F. The two scales agree at –40°.
• T = t_C + 273.15. The Kelvin degree is the same size as the Celsius degree, so a temperature change is the same number on both.

The boiling point of water changes with the air pressure, so it is not a perfect fixed point. Modern thermometry uses the triple point of water, where ice, water and vapour exist together at one exact temperature and pressure: 273.16 K (0.01 °C). The other end of the Kelvin scale is absolute zero, 0 K.

A constant-volume gas thermometer uses the fact that, at fixed volume, a gas's pressure is proportional to its absolute temperature: T = 273.16 K × (P/P_triple). Thermometers filled with different gases agree with one another only at very low pressures, where real gases behave like an ideal gas.