The hidden energy of melting and boiling
Put a pot of ice on the stove with a thermometer in it. The temperature climbs to 32 °F and then stops while the ice melts, even though the burner keeps supplying heat. Later it stops again at 212 °F while the water boils away. The energy absorbed at those plateaus does not change the temperature; it breaks the bonds holding the solid or liquid together. Joseph Black named it latent heat, meaning hidden heat, in the 1760s.
The two kinds of heat
- Sensible heat changes the temperature: Q = m × c × ΔT, with c the specific heat of ice, water or steam.
- Latent heat changes the phase: Q = m × L, with L the heat of fusion (melting) or vaporization (boiling).
| Quantity | Value for water |
|---|---|
| Specific heat of ice | 2.09 kJ/kg·K |
| Specific heat of liquid water | 4.186 kJ/kg·K (1 BTU/lb·°F) |
| Specific heat of steam | 2.01 kJ/kg·K |
| Heat of fusion at 32 °F | 334 kJ/kg (144 BTU/lb) |
| Heat of vaporization at 212 °F | 2,257 kJ/kg (970 BTU/lb) |
The calculator adds up every segment between your start and end temperatures.
Worked example
Take 2 lb of ice from a freezer at −4 °F and heat it until it reaches 212 °F, just about to boil:
- Warming the ice to 32 °F: 36 BTU.
- Melting it: 287 BTU.
- Heating the water from 32 to 212 °F: 360 BTU.
- Total: 683.1 BTU (720.7 kJ), of which 42% is latent heat.
- A 1,500 W electric kettle with no losses would need about 8 minutes.
Boiling all of it away would take another 1,940 BTU, almost three times as much again.
Why it matters
- Cooling: ice cools drinks so well because melting absorbs a lot of heat at a steady 32 °F.
- Steam burns: steam at 212 °F releases its heat of vaporization as it condenses on skin, which makes it far more dangerous than water at the same temperature.
- Weather: water vapor carries huge amounts of energy into the atmosphere and releases it in clouds, powering thunderstorms and hurricanes.
- Air conditioning and heat pumps move heat by evaporating and condensing a refrigerant.
Limits
The values apply at sea-level pressure. At high altitude water boils at a lower temperature, and in a pressure cooker at a higher one. Real heating also loses energy to the pot and the air, so actual times are longer. If the end temperature is below the start, the calculator gives the heat that must be removed instead.