Heat, mass, specific heat and temperature change
The energy Q needed to change a substance’s temperature is its mass times its specific heat c times the temperature change ΔT. Specific heat is the energy to raise one gram by one degree. For water c = 4.186 J/g°C, so warming a gram of water by one degree takes 4.186 joules. Rearrange to solve for any term: m = Q ÷ (cΔT), c = Q ÷ (mΔT), ΔT = Q ÷ (mc).
Specific heat of common materials
| Material | c (J/g°C) | Relative to water |
|---|---|---|
| Water | 4.186 | 1.00 |
| Ice | 2.09 | 0.50 |
| Wood | 1.76 | 0.42 |
| Air | 1.01 | 0.24 |
| Aluminium | 0.897 | 0.21 |
| Concrete | 0.88 | 0.21 |
| Sand | 0.835 | 0.20 |
| Iron | 0.449 | 0.11 |
| Copper | 0.385 | 0.09 |
| Lead | 0.129 | 0.03 |
Ice, water and steam are the same molecule but have different specific heats, so use the value for the phase you are actually heating.
Points that trip people up
- Specific heat vs heat capacity. Specific heat c is per gram; heat capacity C = mc is for the whole object. A cup and a pool of water share the same c but not the same C.
- ΔT is the same in °C and K. A change of one degree Celsius equals a change of one kelvin, so either works in the formula.
- Q can be negative. Cooling gives a negative ΔT and a negative Q, meaning heat is released. That is correct, not an error.
- Mind the mass unit. J/g°C pairs with grams; mixing in J/kg°C without converting throws the answer off by 1000.
Common questions
How do you calculate heat energy?
Multiply mass, specific heat and temperature change: Q = m x c x delta-T. Heating 100 g of water by 60 degrees Celsius takes 100 x 4.186 x 60, about 25,100 joules.
What is the specific heat of water?
4.186 joules per gram per degree Celsius, the highest of any common liquid. Its dense network of hydrogen bonds soaks up energy, which is why water heats and cools slowly.
Why does metal heat up faster than water?
Metals have a low specific heat, often 0.1 to 0.9 J/g degrees Celsius, so the same energy raises their temperature far more. Copper at 0.385 heats about eleven times faster than water for equal mass.
