This note covers how solids, liquids and gases expand when heated, how much energy it takes to raise a temperature (specific heat capacity), and how much energy it takes to change state (specific latent heat). These ideas explain why kettles take time to boil, why ice keeps drinks cold and why bridges have gaps.
Key ideas
Thermal expansion. When a substance is heated, its particles vibrate or move faster and push slightly further apart. The substance expands. The particles do not get bigger. When an object is cooled, the particles move closer together and it contracts.
- Gases expand the most, liquids expand less, and solids expand the least for the same temperature rise.
- Uses and problems: gaps in railway tracks and bridges allow room for expansion; liquid-in-glass thermometers rely on a liquid expanding up a narrow tube; power cables are hung loosely in summer so they do not snap when they contract in winter.
Thermal energy and temperature. Temperature tells you how hot something is. Thermal energy depends on temperature and also on the mass and the material. A bath of warm water holds far more thermal energy than a cup of boiling water.
Specific heat capacity. Different materials need different amounts of energy for the same temperature rise. The specific heat capacity, c, of a material is the energy needed to raise the temperature of 1 kg of it by 1 °C (or by 1 K). Water has a very high value (4200 J/(kg °C)), so it warms and cools slowly. Metals such as aluminium have lower values, so they heat up quickly.
The energy transferred when a temperature changes is:
energy = mass × specific heat capacity × temperature change, or Q = mcΔT
ΔT is the final temperature minus the starting temperature. A change of 1 °C is the same size as a change of 1 K.
Measuring specific heat capacity. Place an electric heater and a thermometer in a block of metal (or in water in an insulated container). Record the starting temperature, the mass, the power of the heater and the time it is switched on. Energy supplied = power × time. Then c = E ÷ (mΔT). Wrapping the block in insulation reduces energy lost to the air, which would otherwise make the measured value of c too high.
Changes of state and latent heat. During melting or boiling, the temperature stays constant even though energy is still being supplied. The energy is used to break the bonds between particles, not to speed them up. This energy is called latent heat. When the substance changes state the other way (freezing or condensing) the same energy is released.
(Extended) Specific latent heat is defined as follows.
- Specific latent heat of fusion: energy to melt 1 kg of a solid at its melting point, without any change in temperature.
- Specific latent heat of vaporisation: energy to boil 1 kg of a liquid at its boiling point, without any change in temperature.
(Extended) The energy needed to change state is:
energy = mass × specific latent heat, or Q = mL
Vaporisation needs far more energy than melting, because the particles must be separated completely.
Heating and cooling curves. A graph of temperature against time for heating ice shows sloping sections, where the temperature is rising, and flat sections, where the substance is changing state. The flat section at 0 °C is melting. The flat section at 100 °C (for water) is boiling.
Evaporation and boiling. Evaporation happens at the surface of a liquid at any temperature. The fastest particles near the surface escape, so the liquid left behind becomes cooler. Evaporation is faster when the liquid is warmer, when its surface area is larger and when there is a draught of air. Boiling happens throughout the liquid at one fixed temperature, with bubbles of vapour forming inside it.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Thermal expansion | Increase in size of a substance when its temperature rises, because its particles move further apart. |
| Specific heat capacity, c | Energy needed to raise the temperature of 1 kg of a substance by 1 °C. Unit: J/(kg °C). |
| Q = mcΔT | Energy transferred when the temperature of a mass changes and there is no change of state. |
| Specific latent heat, L (Extended) | Energy needed to change the state of 1 kg of a substance without a change in temperature. Unit: J/kg. |
| Q = mL (Extended) | Energy transferred during melting, freezing, boiling or condensing. |
| E = Pt | Energy supplied by a heater of power P (watts) in time t (seconds). |
Worked examples
Example 1 An electric kettle contains 0.80 kg of water at 20 °C. The specific heat capacity of water is 4200 J/(kg °C). (a) Find the energy needed to heat the water to 100 °C. (b) The kettle has a power of 2000 W. Find the time needed, assuming no energy is lost.
(a) ΔT = 100 − 20 = 80 °C.
Q = mcΔT = 0.80 × 4200 × 80 = 268 800 J.
(b) E = Pt, so t = E ÷ P = 268 800 ÷ 2000 = 134.4 s.
Answer: (a) 2.69 × 105 J; (b) 134 s
Example 2 A heater of power 60 W is placed in a 0.50 kg metal block and switched on for 300 s. The temperature of the block rises by 40 °C. Assume no energy is lost. Find the specific heat capacity of the metal.
Energy supplied: E = Pt = 60 × 300 = 18 000 J.
Rearrange Q = mcΔT to give c = Q ÷ (mΔT).
c = 18 000 ÷ (0.50 × 40) = 18 000 ÷ 20 = 900.
Answer: 900 J/(kg °C)
Example 3 (Extended) The specific latent heat of fusion of ice is 3.34 × 105 J/kg and the specific latent heat of vaporisation of water is 2.26 × 106 J/kg. Find (a) the energy needed to melt 0.25 kg of ice at 0 °C and (b) the energy needed to turn 0.50 kg of water at 100 °C into steam at 100 °C.
(a) Q = mL = 0.25 × 3.34 × 105 = 83 500 J.
(b) Q = mL = 0.50 × 2.26 × 106 = 1 130 000 J.
Neither stage involves a temperature change, so only Q = mL is used.
Answer: (a) 8.35 × 104 J; (b) 1.13 × 106 J
Common errors
- Common error: using Q = mcΔT for a change of state. While a substance melts or boils its temperature does not change, so ΔT = 0 and Q = mL must be used instead.
- Common error: using the final temperature instead of the temperature change. Always subtract the starting temperature from the final temperature.
- Common error: saying the energy during melting or boiling "is lost". It is stored as potential energy as the bonds between particles are broken, and it is released again when the substance freezes or condenses.
- Common error: confusing evaporation with boiling. Evaporation happens only at the surface and at any temperature. Boiling happens throughout the liquid at the boiling point.
- Common error: writing that particles expand when heated. The particles move further apart, but each one stays the same size.
Exam tip: Decide first whether the temperature is changing or the state is changing. Write Q = mcΔT for the sloping parts of a heating curve and Q = mL for the flat parts, and add the energies if there are several stages.
Check yourself
- Why do gaps get left between sections of a steel bridge?
Answer
On hot days the steel expands. The gaps give it room to expand without buckling or pushing on other parts of the structure. - How much energy is needed to warm 2.0 kg of aluminium (c = 900 J/(kg °C)) from 15 °C to 65 °C?
Answer
ΔT = 50 °C. Q = 2.0 × 900 × 50 = 90 000 J = 9.0 × 104 J. - (Extended) A freezer removes 6.7 × 104 J from water at 0 °C and freezes it completely. Use L = 3.34 × 105 J/kg to find the mass of water that freezes.
Answer
m = Q ÷ L = 6.7 × 104 ÷ 3.34 × 105 = 0.201 kg (about 0.20 kg). - Why does a person feel cooler when sweat evaporates from the skin?
Answer
The fastest, most energetic particles escape from the surface of the sweat. The average energy of the particles left behind falls, so the sweat and the skin are cooled.