By the end of this chapter, you will be able to:
Mastering these skills will help you understand how energy works in real-world systems, making you confident in applying physics principles in your trade.
Heat energy is energy that flows from a hotter body to a colder one because of the temperature difference between them. It is measured in joules (J), the same unit as all other forms of energy. When heat is added to a substance, it either raises the temperature (the particles move faster) or changes the state (the particles are pulled apart without a rise in temperature). In an analytical laboratory these ideas explain how water baths, ovens, muffle furnaces, distillation units and freeze dryers work, and how much energy each one uses. Example: the quality control laboratory of a sugar factory in Katito works out how much steam heat its juice heaters need from the specific heat capacity of cane juice.
Two kinds of heat are distinguished:
The heat capacity (C) of a body is the quantity of heat needed to raise the temperature of the whole body by one kelvin (or one degree Celsius, since a change of 1 K equals a change of 1 °C). It depends on both the material and the amount of material, so a large copper calorimeter has a bigger heat capacity than a small one.
Formula: C = Q ÷ Δθ
Unit: joule per kelvin (J/K)
Worked example: an aluminium block absorbs 4,500 J and its temperature rises by 20 K. Find its heat capacity.
C = Q ÷ Δθ
C = 4,500 ÷ 20
C = 225 J/K
Heat capacity matters when a calorimeter, beaker or heating block takes up part of the heat in an experiment: its heat capacity must be added to that of the sample, or the result will be too low.
The specific heat capacity (c) of a substance is the quantity of heat needed to raise the temperature of 1 kg of the substance by 1 K. It is a property of the material only, so it can be used to identify materials and to size heating and cooling equipment.
Formula: Q = mcΔθ, so c = Q ÷ (mΔθ), and heat capacity C = mc
Unit: joule per kilogram per kelvin (J/kg K)
| Substance | Specific heat capacity (J/kg K) |
|---|---|
| Water | 4,200 |
| Ice | 2,100 |
| Ethanol | 2,400 |
| Aluminium | 900 |
| Glass | 670 |
| Iron | 450 |
| Copper | 390 |
| Mercury | 140 |
Worked example: how much heat is needed to raise 0.5 kg of water from 20 °C to 80 °C?
Q = mcΔθ
Q = 0.5 × 4,200 × (80 − 20)
Q = 0.5 × 4,200 × 60
Q = 126,000 J = 126 kJ
The high specific heat capacity of water is why it is used in water baths, cooling jackets and car radiators: it absorbs a lot of heat for a small temperature rise.
Latent heat is the heat absorbed or released when a substance changes state at constant temperature. The word latent means hidden: the heat goes into breaking (or forming) the bonds between particles, not into making them move faster, so a thermometer shows no rise during melting or boiling. The specific latent heat (L) is the heat needed to change the state of 1 kg of the substance without a change in temperature.
Formula: Q = mL
Unit: joule per kilogram (J/kg)
The specific latent heat of fusion (Lf) is the heat needed to change 1 kg of a solid at its melting point into liquid at the same temperature. For ice, Lf = 3.34 × 10⁵ J/kg. The same amount of heat is released when 1 kg of the liquid freezes.
Worked example: find the heat needed to melt 0.2 kg of ice at 0 °C.
Q = mLf
Q = 0.2 × 3.34 × 10⁵
Q = 66,800 J = 66.8 kJ
Ice packs and ice baths in sample transport keep samples at about 0 °C because the ice absorbs heat while it melts, without its temperature rising.
The specific latent heat of vaporization (Lv) is the heat needed to change 1 kg of a liquid at its boiling point into vapour at the same temperature. For water at 100 °C, Lv = 2.26 × 10⁶ J/kg, nearly seven times its latent heat of fusion, because the particles must be separated completely.
Worked example: find the heat needed to boil away 0.05 kg of water already at 100 °C.
Q = mLv
Q = 0.05 × 2.26 × 10⁶
Q = 113,000 J = 113 kJ
Latent heat of vaporization is used in distillation and rotary evaporation (heat supplied at the flask is removed again at the condenser), in steam sterilisation in autoclaves, and in evaporative cooling.
Sublimation is the direct change from solid to vapour without passing through the liquid state. The specific latent heat of sublimation (Ls) is the heat needed to change 1 kg of a solid directly into vapour at the same temperature. For a substance at the same temperature, Ls = Lf + Lv, because sublimation does the work of melting and boiling in one step. For ice near 0 °C, Ls ≈ 3.34 × 10⁵ + 2.50 × 10⁶ ≈ 2.83 × 10⁶ J/kg.
Worked example: dry ice (solid carbon dioxide) has Ls ≈ 5.71 × 10⁵ J/kg at −78.5 °C. Find the heat absorbed when 0.1 kg sublimes.
Q = mLs
Q = 0.1 × 5.71 × 10⁵
Q = 57,100 J = 57.1 kJ
Sublimation is used in freeze drying (lyophilisation) of biological and food samples, in purifying iodine, naphthalene and camphor, and in dry ice for shipping frozen samples.
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