Specific heat capacity vs specific latent heat: which equation to use
By Engr. Mehmood Kakar · Updated
Quick answer
Use ΔE = mcΔθ when the temperature changes. Use E = mL when the state changes. Specific heat capacity is the energy to raise 1 kg by 1 °C. Specific latent heat is the energy to melt or boil 1 kg with no change in temperature. If a question involves both, such as melting ice and then warming the water, do each step separately and add the energies.
The difference in one table
| Specific heat capacity | Specific latent heat | |
|---|---|---|
| Equation | ΔE = m c Δθ | E = m L |
| Use when | The temperature changes | The state changes |
| Temperature during the process | Rises or falls | Stays constant |
| Unit | J/kg °C | J/kg |
| Water (values often given) | 4200 J/kg °C | 334,000 J/kg (fusion), 2,260,000 J/kg (vaporisation) |
Reading a heating curve
Heat a block of ice steadily from below 0 °C and plot temperature against time. The graph goes up, flattens, goes up, flattens again, then goes up. The sloped parts are where the temperature rises, so ΔE = mcΔθ applies. The two flat parts are melting at 0 °C and boiling at 100 °C, where E = mL applies.
The flat parts are where students lose marks. Energy is still being transferred, but it is changing the state, not the temperature. So asking "how much did the temperature change?" gives zero, and ΔE = mcΔθ would wrongly give zero energy.
When the temperature changes
Calculate the energy needed to warm 0.50 kg of water from 20 °C to 100 °C. c = 4200 J/kg °C.
- Δθ = 100 − 20 = 80 °C
- ΔE = m c Δθ = 0.50 × 4200 × 80
- ΔE = 168,000 J
When the state changes
Calculate the energy needed to turn 0.50 kg of water at 100 °C into steam. L = 2,260,000 J/kg.
- E = m L = 0.50 × 2,260,000
- E = 1,130,000 J
Compare the two answers. Boiling the water away takes nearly seven times as much energy as heating it from 20 °C all the way to boiling point. That is why a kettle takes a while to boil dry.
Questions that need both
Longer questions often chain the two. Split the process into stages, calculate each, and add them.
Calculate the energy needed to turn 0.20 kg of ice at 0 °C into water at 20 °C. Specific latent heat of fusion of water = 334,000 J/kg; c of water = 4200 J/kg °C. (4 marks)
- Stage 1, melt the ice at 0 °C: E = m L = 0.20 × 334,000 = 66,800 J
- Stage 2, warm the water from 0 °C to 20 °C: ΔE = m c Δθ = 0.20 × 4200 × 20 = 16,800 J
- Total = 66,800 + 16,800
- Total energy = 83,600 J
If the ice starts below 0 °C, there is an extra first stage: warming the ice to 0 °C with ΔE = mcΔθ, using the specific heat capacity of ice given in the question.
How to tell which one a question wants
- Look for words like melt, freeze, boil, condense, evaporate or change of state. These point to E = mL.
- Look for two temperatures, or "rises by", "warms to" or "cools from". These point to ΔE = mcΔθ.
- Check the unit of the value you are given. J/kg °C is specific heat capacity; J/kg is specific latent heat.
- If the temperature is stuck at 0 °C or 100 °C for water, the state is changing.
Check each stage with the specific heat capacity calculator and the specific latent heat calculator.
Practice
1. Which equation would you use to find the energy needed to freeze 2 kg of water at 0 °C? Explain why.
E = mL (with the latent heat of fusion), because the water changes state at a constant temperature of 0 °C.
2. Calculate the energy needed to melt 0.10 kg of ice at 0 °C and then warm the water to 30 °C. L = 334,000 J/kg; c = 4200 J/kg °C.
Melt: 0.10 × 334,000 = 33,400 J → Warm: 0.10 × 4200 × 30 = 12,600 J → Total = 46,000 J
3. A value is given as 2100 J/kg °C. Is this a specific heat capacity or a specific latent heat?
A specific heat capacity, because its unit includes °C.
Frequently asked questions
What is the difference between specific heat capacity and specific latent heat?
Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Specific latent heat is the energy needed to change the state of 1 kg of a substance without changing its temperature.
Which equation do I use for melting ice?
E = mL, using the specific latent heat of fusion, because the ice melts at a constant 0 °C.
Why is the heating curve flat during melting and boiling?
The energy being transferred changes the state by breaking bonds between particles, rather than raising the particles’ kinetic energy, so the temperature stays the same.
What are the units of specific heat capacity and specific latent heat?
Specific heat capacity is in J/kg °C. Specific latent heat is in J/kg. The extra °C is a quick clue to which quantity you have.
Written by Engr. Mehmood Kakar
Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)
Checked against the AQA GCSE Physics (8463) specification on 14 November 2026.