Specific latent heat equation: E = m L
Thermal energy for a change of state = mass × specific latent heat, or E = m L. E is the energy in joules (J), m is the mass in kilograms (kg) and L is the specific latent heat in joules per kilogram (J/kg). The specifications call it a select and apply equation, and the sheet in your paper shows it.
Equation
E = m L
| Symbol | Quantity | Unit |
|---|---|---|
E | energy transferred | J |
m | mass | kg |
L | specific latent heat | J/kg |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet | E = m L |
| AQA Combined Science (8464) | Given on the sheet | E = m L |
| Edexcel Physics (1PH0) | Given on the sheet | Q = m L |
| Edexcel Combined Science (1SC0) | Given on the sheet | Q = m L |
| OCR Gateway Physics A (J249) | Given on the sheet | E = m l |
| OCR Twenty First Century Physics B (J259) | Given on the sheet | E = m l |
Calculator: E = m L
Energy that changes state
Heat a pan of ice and the temperature climbs to 0 °C, then stops. It stays there until all the ice has melted. The energy still goes in, but it breaks the bonds between particles instead of making them move faster. That hidden energy is called latent heat.
Specific latent heat, L, is the energy needed to change the state of 1 kg of a substance with no change in temperature. There are two kinds. Latent heat of fusion is for melting or freezing. Latent heat of vaporisation is for boiling or condensing, and for water it is much bigger.
Steam burns are worse than burns from boiling water for this reason. When steam condenses on your skin it gives out its latent heat as well as cooling down.
Board by board
- AQA (8463 and 8464): E = m L.
- Edexcel (1PH0 and 1SC0): Q = m L, with Q for the thermal energy.
- OCR Gateway (J249) and OCR Twenty First Century (J259): E = m l, with a lower-case l.
The letters differ, so read your own board's version. Each of the six specifications puts it in the select and apply group, alongside the heat capacity equation. The OCR Twenty First Century page and the full equation sheet guide show the other equations in that group.
Rearranging and using it with heating graphs
- m = E ÷ L
- L = E ÷ m
A heating curve has sloping parts and flat parts. On a slope the temperature rises, so you use specific heat capacity. On a flat part the state changes, so you use E = m L. A question about ice turning into warm water may need both, added together.
If a heater supplies the energy, you can find E from its power and the time with E = P t.
Worked examples
E
- Melting 250 g of ice: 250 g = 0.25 kg
- E = m L
- E = 0.25 × 334 000
- E = 83 500 J
83 500 J
m
- A kettle boils away some water. 45.2 kJ = 45 200 J
- m = E ÷ L
- m = 45 200 ÷ 2 260 000
- m = 0.02 kg, which is 20 g
0.02 kg
L
- Melting 0.5 kg of candle wax: 100 kJ = 100 000 J
- L = E ÷ m
- L = 100 000 ÷ 0.5
- L = 200 000 J/kg
200 000 J/kg
Common mistakes
- Adding a temperature change. E = m L has no Δθ in it, because the temperature stays the same while the state changes.
- Picking the wrong L. Melting uses the latent heat of fusion and boiling uses the latent heat of vaporisation, which for water is about seven times bigger.
- Leaving the mass in grams, so 250 g of ice goes in as 250 and the energy is 1000 times too large.
- Using only E = m L for ice that melts and then warms up. The warming part needs m c Δθ as well.
Switch between E = m L, m = E ÷ L and L = E ÷ m in the Equation Rearranger.
Questions people ask
Why is it called latent heat?
Latent means hidden. The energy goes in without any rise on the thermometer, so it seems to disappear.
Does freezing give energy out?
Yes. When water freezes, it releases the same energy that melting the ice would take in.