The energy needed for a temperature change is Q = mcθ, where θ is the rise in temperature. If an electric heater supplies the energy, Q also equals the power times the time.
This lesson is part of heat. It follows explaining thermal equilibrium.
What do the symbols mean?
Write each symbol with its unit before you start.
| Symbol | Meaning | Unit |
|---|---|---|
| Q | Heat energy | J |
| m | Mass | kg |
| c | Specific heat capacity | J kg⁻¹ °C⁻¹ |
| θ | Change in temperature | °C |
If the mass is in grams, convert it to kilograms first.
Worked example: a heater and a tank
A 500 W heater warms 2.0 kg of water from 28°C to 78°C. Use c = 4200 J kg⁻¹ °C⁻¹ and ignore heat loss. How long does it take?
- Temperature change θ = 78 − 28 = 50°C.
- Energy needed Q = 2.0 × 4200 × 50 = 420 000 J.
- Power is energy per second, so t = Q ÷ P = 420 000 ÷ 500 = 840 s, which is 14 minutes.
The link between the heater and the water is the energy. Both sides equal 420 000 J, which is how you check your working.
Why do real experiments give a higher c?
In a real experiment, some of the heater’s energy warms the container and the air. The water gets less than the energy supplied.
If you use the full energy supplied in Q = mcθ, the calculated c is larger than the true value. Insulating the container reduces the error.
The mistake that costs marks
The slips are in θ, in the mass units, and in the power step.
| Slip | Effect | Fix |
|---|---|---|
| Using 78 as θ | Energy far too large | θ = 78 − 28 = 50 |
| Mass 2000 g left as 2000 | Energy 1000 times too large | Convert to 2.0 kg |
| t = Q × P | Wrong by a large factor | t = Q ÷ P |
Write the change in temperature as a subtraction on its own line. The units and significant figure checker can flag mismatched units.
Check yourself
A 200 W heater warms a 0.50 kg aluminium block from 30°C to 70°C. Use c = 900 J kg⁻¹ °C⁻¹ and ignore heat loss. Find the time taken.
Answer
θ = 70 − 30 = 40°C. Q = 0.50 × 900 × 40 = 18 000 J.
Time = Q ÷ P = 18 000 ÷ 200 = 90 s.
What to study next
Go on to using specific latent heat, where the temperature does not change. Then try the heat practice set.
For a teacher to work through heater questions with you, see online one-to-one Physics tuition.