Heating takes energy
Raising the temperature of a material takes energy, and some materials need much more than others. The quantity that measures this is the specific heat capacity: the energy needed to warm one kilogram of the material by one degree Celsius (or one kelvin). Water has one of the highest values of any common substance, which is why a pot of water takes so long to boil and why oceans moderate coastal climates.
The formula
Q = m × c × ΔT
- Q is the heat energy in joules,
- m is the mass in kilograms,
- c is the specific heat in J/(kg·K),
- ΔT is the temperature change, in °C or kelvins (one degree Fahrenheit is 5/9 of a kelvin).
The calculator also gives the energy in kilowatt-hours and kilocalories, and the time a heater of a given power would need if no heat were lost.
Worked example
You heat 2 lb of water from 68 °F to 212 °F with a 1,500 W kettle.
- Mass: 0.907 kg. Temperature change: 144 °F, which is 80 K.
- Q = 0.907 × 4,186 × 80 = 303.8 kJ, or 288 BTU.
- In other units: 0.084 kWh, or 72.6 kcal.
- Heating time with no losses: 303,800 ÷ 1,500 = 3 minutes 23 seconds. A real kettle takes a little longer, since some heat warms the kettle and escapes to the air.
Specific heat of common materials
| Material | Specific heat, J/(kg·K) |
|---|---|
| Water | 4,186 |
| Ice | about 2,100 |
| Olive oil | about 1,970 |
| Wood | about 1,700 |
| Air (constant pressure) | 1,005 |
| Aluminum | 897 |
| Concrete | about 880 |
| Glass | about 840 |
| Iron and steel | about 450 |
| Copper | 385 |
Why it matters
- Cooking: an aluminum pan heats up in seconds, while the water inside takes minutes, because water’s specific heat is more than four times higher.
- Heating systems: water is used in radiators and hot water tanks because it stores a lot of heat per kilogram.
- Climate: large bodies of water warm up and cool down slowly, keeping coastal winters milder and summers cooler.
- Building: heavy materials like concrete store heat during the day and release it at night, an effect called thermal mass.
Changes of state
The formula covers heating or cooling without a change of state. Melting ice or boiling water takes extra energy, the latent heat: 334 kJ per kilogram to melt ice and 2,257 kJ per kilogram to turn boiling water into steam. To go from ice at 32 °F to steam, add those amounts to the result of each heating step.
Energy cost
Multiply the result in kWh by your electricity price to estimate the cost. Heating 2 lb of water to boiling costs well under one cent, while heating a 50-gallon water tank by 70 °F uses about 8.6 kWh.