What specific heat capacity means
The specific heat capacity (c) of a substance is the amount of thermal energy needed to raise the temperature of 1 kg of the substance by 1 °C (or 1 K). Its unit is the joule per kilogram per degree Celsius, J/(kg °C). Water has a very high value, c = 4200 J/(kg °C), which is why it heats up and cools down slowly.
Key idea
Q = m c ΔT
where Q = thermal energy transferred (J), m = mass (kg), c = specific heat capacity (J/(kg °C)) and ΔT = temperature change (°C). Rearranged: c = Q / (mΔT).
Using the equation
Worked example
How much energy is needed to heat 2.0 kg of water from 20 °C to 70 °C? Take c = 4200 J/(kg °C).
ΔT = 70 − 20 = 50 °C.
Q = m c ΔT = 2.0 × 4200 × 50 = 420 000 J = 420 kJ.
Why it matters
A substance with a high specific heat capacity needs a lot of energy to warm up but can store a lot of energy. This is why water is used in central-heating systems and car radiators as a coolant. A metal such as copper has a much lower c, so it heats up quickly for the same energy input.
Remember
- Always use the temperature change ΔT, not the actual temperature.
- Mass must be in kilograms for c in J/(kg °C).
- If power P is supplied for time t, energy Q = P×t = m c ΔT.