Definition
- The specific heat capacity (c) of a substance is the amount of energy needed to raise the temperature of 1 kg of the substance by 1 °C
- The SI unit is joules per kilogram per degree Celsius (J/(kg °C)) (equivalent to J/(kg K) since temperature differences are the same in °C and K)
- Reference values for a feel:
- water: 4200 J/(kg °C), very high, which is why oceans moderate climate and water-cooled radiators work
- aluminium: 900 J/(kg °C)
- copper: 385 J/(kg °C)
- iron: 460 J/(kg °C)
- air: 1000 J/(kg °C)
Implications of high vs low c
- A substance with a high specific heat capacity:
- heats up slowly for a given energy input
- cools down slowly when energy is removed
- is good for storage heaters, hot-water bottles and household central-heating systems (water carries lots of heat per kilogram)
- A substance with a low specific heat capacity:
- heats up quickly and cools down quickly
- is good for cooking pans and engine pistons (metals heat fast, conduct fast, cool fast)
The energy equation
ΔQ = m × c × ΔT
- where:
- ΔQ = energy supplied to (or removed from) the substance (J)
- m = mass of the substance (kg)
- c = specific heat capacity (J/(kg °C))
- ΔT = change in temperature (°C)
- This equation only applies while the substance is not changing state. During a change of state, the temperature does not change so ΔT = 0 and the equation gives zero, but real energy is still being delivered (into the potential store)
Example — 0.25 kg of aluminium block is heated from 20 °C to 35 °C. Aluminium has a specific heat capacity of 900 J/(kg °C). Calculate the energy supplied.
- ΔT = 35 − 20 = 15 °C
- ΔQ = m × c × ΔT = 0.25 × 900 × 15 = 3375 J
Example — a 1.2 kg saucepan of water receives 50 400 J of energy from a hob. The specific heat capacity of water is 4200 J/(kg °C). Calculate the temperature rise.
- Rearrange ΔQ = m × c × ΔT to ΔT = ΔQ / (m × c)
- ΔT = 50 400 / (1.2 × 4200) = 50 400 / 5040 = 10 °C