Definition
The specific heat capacity c of a substance is the amount of heat required to raise the temperature of 1 kg of the substance by 1 °C (or 1 K). Its SI unit is J kg⁻¹ °C⁻¹. Water has a very high specific heat capacity of about 4200 J kg⁻¹ °C⁻¹, which is why it heats up and cools down slowly.
Key formula / 关键公式
Q = mcθ
Q = heat absorbed or released (J); m = mass (kg); c = specific heat capacity (J kg⁻¹ °C⁻¹); θ = change in temperature (°C).
Rearranged: c = Q / (mθ).
What it means physically
- A material with a high specific heat capacity needs a lot of heat to warm up and releases a lot of heat when it cools.
- A material with a low specific heat capacity heats up and cools down quickly (e.g. metals).
- The large value for water is used in car cooling systems and to moderate the climate near the sea.
Everyday applications
Water is used as a coolant because it can absorb large amounts of heat with only a small temperature rise. Sea breezes occur because land (low c) heats up faster than the sea (high c) during the day.
Worked example / 例题
How much heat is needed to raise the temperature of 2.0 kg of water from 25 °C to 55 °C? (c = 4200 J kg⁻¹ °C⁻¹)
θ = 55 − 25 = 30 °C.
Q = mcθ = 2.0 × 4200 × 30 = 252 000 J = 252 kJ.
Remember / 记住
- Use the temperature change θ, not the actual reading.
- Mass must be in kilograms.
- High c means slow to heat and slow to cool.