Different substances need different amounts of energy to warm by the same number of degrees. Specific heat capacity, written c, is the energy needed to raise one kilogram by one kelvin. It is the reason a metal spoon in hot soup burns your hand while the soup itself does not.
Q is energy in joules, m is mass in kilograms, c is specific heat in J/kg·K, and ΔT is the temperature change. Because it is a change rather than an absolute temperature, a difference in Celsius equals a difference in kelvin — you do not need to convert.
Water is the outlier
Water’s specific heat of 4186 J/kg·K is extraordinarily high — about eleven times copper’s and thirty times lead’s. Heating a kilogram of water by one degree takes as much energy as heating a kilogram of aluminium by nearly five.
This single fact shapes a great deal of the world. Oceans moderate coastal climates because they absorb enormous heat with little temperature change. Water is the default coolant in engines and power stations. Your body, mostly water, resists temperature swings that would otherwise be fatal.
Common values
| Substance | c (J/kg·K) |
|---|---|
| Water (liquid) | 4186 |
| Ice | 2090 |
| Steam | 2010 |
| Wood | 1700 |
| Air | 1005 |
| Aluminium | 897 |
| Glass | 840 |
| Iron | 449 |
| Copper | 385 |
| Lead | 129 |
The phase change trap
Q = mcΔT only holds while the substance stays in one phase. During melting or boiling the temperature stops rising even though energy keeps going in — that energy is breaking bonds rather than increasing molecular motion. This is latent heat, and it is large: turning 1 kg of 100 °C water into 100 °C steam takes 2,260,000 J, more than five times the energy needed to heat that same kilogram all the way from freezing to boiling.
So a problem that crosses 0 °C or 100 °C has to be broken into segments: heat the ice, melt it, heat the water, boil it, heat the steam. Each segment uses a different c, and the phase changes use latent heat instead.
Why real heating takes longer
This calculation gives the theoretical minimum. In practice heat escapes to the surroundings the whole time, the container absorbs some, and no heater is perfectly efficient. A kettle rated 2000 W delivers rather less than 2000 W into the water. Use the calculated figure as a lower bound and expect reality to be 10–30% worse.