Specific Heat Capacity

Specific heat capacity tells us how much energy is needed to raise the temperature of 1 kg of a substance by 1°C. Different materials need different amounts of energy to heat up. The formula Q = mcΔT connects energy, mass, specific heat capacity, and temperature change.

What is Specific Heat Capacity?

Specific heat capacity (c) is the amount of energy needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K).

Symbol: c
Unit: J/(kg·°C) or J/(kg·K)

Substance	Specific heat capacity (J/kg°C)
Water	4200
Aluminium	900
Iron	450
Copper	385
Air	~1000

Water has a very high specific heat capacity, which is why it is used as a coolant in car engines.

The Formula

$Q = mc\Delta T$

Where:

$Q$ = energy transferred (J)
$m$ = mass (kg)
$c$ = specific heat capacity (J/kg°C)
$\Delta T$ = temperature change (°C or K)

Q = mc\Delta T

Energy transferred equals mass times specific heat capacity times the change in temperature.

Heating Water

How much energy is needed to heat 2 kg of water from 20 °C to 80 °C?

Given: m = 2 kg, c = 4200 J/kg°C, ΔT = 80 − 20 = 60 °C

$Q = mc\Delta T = 2 \times 4200 \times 60 = 504{,}000 \text{ J} = 504 \text{ kJ}$

Real world: Coastal climates

Water has a very high specific heat capacity (c = 4200 J/kg°C), while sand and rock have much lower values (~800 J/kg°C). This means the sea heats up and cools down far more slowly than the land. Coastal cities like Lisbon or Sydney therefore have milder, more stable temperatures year-round than inland cities at the same latitude.

Real world: Cast iron vs. aluminium pans

A 1 kg cast iron pan (c ≈ 460 J/kg°C) and a 1 kg aluminium pan (c = 900 J/kg°C) are placed on the same hob. To raise each by 100 °C:

$Q_{\text{iron}} = 1 \times 460 \times 100 = 46{,}000 \text{ J}$ $Q_{\text{alum}} = 1 \times 900 \times 100 = 90{,}000 \text{ J}$

Cast iron needs less energy to reach cooking temperature, but also loses heat faster when food is added — which is why professional chefs favour cast iron for searing.

Real world: Car engine cooling system

A car engine generates enormous heat. The cooling system circulates water (c = 4200 J/kg°C) around the engine. Water can absorb huge amounts of thermal energy per kg before its temperature rises significantly, making it far more effective as a coolant than oil (c ≈ 2000 J/kg°C) or air.

Tip Where do you see this in real life? Coastal weather patterns, cooking equipment choices, engine coolants, and storage heaters all exploit the differences in specific heat capacity between materials!

Practice Problems

How much energy is needed to heat 0.5 kg of aluminium from 25 °C to 125 °C? (c = 900 J/kg°C)

Show answer

ΔT = 125 − 25 = 100 °C. Q = 0.5 × 900 × 100 = 45,000 J = 45 kJ

3 kg of water cools from 90 °C to 30 °C. How much energy does it release? (c = 4200 J/kg°C)

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ΔT = 90 − 30 = 60 °C. Q = 3 × 4200 × 60 = 756,000 J = 756 kJ

Why is water used as a coolant in car engines?

Show answer

Water has a very high specific heat capacity (4200 J/kg°C), meaning it can absorb a large amount of heat energy before its temperature rises significantly.