Heating Formulas: Energy and Heater Power
Heating formulas for the energy to warm water or another material, heater power for a heat-up time with efficiency, and kJ to kWh, with worked examples.
The formulas
| To find | Formula |
|---|---|
| Heat energy | Q (kJ) = m × c × ΔT |
| Energy in kWh | E (kWh) = Q (kJ) / 3600 |
| Heater power | P (kW) = E / (t × η) |
| Heat-up time | t (h) = E / (P × η) |
m is the mass in kg and c the specific heat in kJ/(kg·K), which is 4.186 for water. One litre of water weighs about 1 kg. ΔT is the temperature rise in kelvin (the same number as in °C) and t the time in hours. η is the heater efficiency as a fraction and allows for losses to the surroundings.
Worked example: 200 L of water from 15 °C to 60 °C in 2 hours
The heater and tank have a combined efficiency of 90%.
- Q = 200 × 4.186 × 45 = 37,670 kJ
- E = 37,670 / 3600 = 10.46 kWh
- P = 10.46 / (2 × 0.9) = 5.814 kW
Energy to heat 100 L of water
| Temperature rise | Energy |
|---|---|
| 10 K | 1.163 kWh |
| 20 K | 2.326 kWh |
| 30 K | 3.488 kWh |
| 40 K | 4.651 kWh |
| 50 K | 5.814 kWh |
Frequently asked questions
Does the formula include heat losses?
Only through the efficiency factor. A tank that stays warm for hours also loses heat to the room, so a larger allowance may be needed.
What if the material is not water?
Use its own specific heat. Oil and metals need much less energy per kilogram than water, because their specific heat is lower.
Why do I need the time?
The energy to heat the water is fixed, but a shorter heat-up time needs a more powerful heater to deliver it.
What about a phase change?
Melting, boiling or freezing needs extra energy, called latent heat, on top of this formula.
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