Specific Heat Capacity

Why a beach is hot but the sea is cool

On a sunny day the sand can burn your feet while the sea stays refreshingly cool — even though both have been under the same Sun for the same time. The difference is a property called specific heat capacity: a measure of how much energy a material needs to change its temperature. Sand needs very little; water needs a great deal. Understanding this single number explains everything from why radiators use water to why coastal climates are mild.

Before this lesson it helps to be clear on what temperature actually is — see what is temperature.

Temperature versus thermal energy

These two ideas are easy to confuse, so let's pin them down.

• Temperature tells you how hot something is — the average kinetic energy of its particles. It is measured in °C (or kelvin).
• Thermal energy is the total energy stored in all the random motion of an object's particles. It depends on temperature, mass and the material.

A spark from a sparkler can be at 1000 °C but barely warms your skin, because it is tiny and holds very little thermal energy. A bath of warm water is much cooler but holds enormously more energy. Specific heat capacity is the bridge between temperature and energy.

Defining specific heat capacity

Specific heat capacity (c) is the amount of energy needed to raise the temperature of 1 kilogram of a substance by 1 degree Celsius.

Its units are joules per kilogram per °C (J/kg°C). Some typical values:

Material	Specific heat capacity (J/kg°C)
Water	4200
Ice	2100
Aluminium	900
Glass	670
Iron / steel	~450
Copper	385
Lead	130

Look at the spread. Water needs 4200 J to warm a single kilogram by one degree, while lead needs only 130 J — over thirty times less. That is why a metal spoon left in a hot drink burns your fingers almost instantly, but the drink itself stays hot for ages.

The key equation

The energy needed to change a substance's temperature is given by:

Q = m × c × ΔT

where:

• Q = energy transferred (joules, J)
• m = mass (kilograms, kg)
• c = specific heat capacity (J/kg°C)
• ΔT = change in temperature (°C) — the symbol Δ ("delta") means "change in".

Worked example 1. How much energy is needed to heat 3 kg of water from 20 °C to 100 °C? (c for water = 4200 J/kg°C.)

First find the temperature change: ΔT = 100 − 20 = 80 °C. Q = m × c × ΔT = 3 × 4200 × 80 = 1 008 000 J (about 1 megajoule).

That is a lot of energy — which is exactly why boiling a full kettle takes a noticeable time.

Worked example 2. A 0.5 kg aluminium block is given 9000 J of energy. By how much does its temperature rise? (c for aluminium = 900 J/kg°C.)

Rearrange Q = m × c × ΔT to make ΔT the subject: ΔT = Q ÷ (m × c). ΔT = 9000 ÷ (0.5 × 900) = 9000 ÷ 450 = 20 °C.

Worked example 3 (finding c). A 2 kg metal block absorbs 23 000 J and warms by 50 °C. What is its specific heat capacity?

c = Q ÷ (m × ΔT) = 23 000 ÷ (2 × 50) = 23 000 ÷ 100 = 230 J/kg°C.

Why water is special

Water has one of the highest specific heat capacities of any common substance, and this has huge consequences:

• Cooling systems. Car engines and power stations circulate water because it can absorb a lot of heat without its own temperature shooting up — making it an excellent coolant.
• Heating systems. Central-heating radiators use hot water for the same reason in reverse: water holds plenty of thermal energy and releases it slowly into a room.
• Climate. Oceans store immense amounts of solar energy and release it gradually, moderating Earth's temperature. Coastal towns have milder winters and cooler summers than inland regions.
• Life. Your body is mostly water, which helps keep your internal temperature stable even when the weather changes.

The reason for water's high value lies in the strong hydrogen bonds between its molecules: a lot of energy must be supplied to make them move faster, so it takes plenty of energy to raise the temperature.

The link to thermal energy on the move

Specific heat capacity tells you how much energy to put in, but that energy still has to travel through the material — by conduction, convection or radiation. To see how thermal energy moves, look at conduction, convection and radiation.

Try it yourself! 🧪

Demo — racing temperatures with water and oil. You can feel specific heat capacity in your kitchen.

1. Put the same mass of water and cooking oil into two identical small saucepans (use a balance, or roughly the same depth in matching pans).
2. Heat both on the same hob setting for the same short time, then carefully measure each with a thermometer (a cooking thermometer is ideal).
3. You will find the oil is noticeably hotter than the water, even though both received roughly the same energy.

Why? Cooking oil has a specific heat capacity of around 2000 J/kg°C — less than half that of water. With the same energy in and the same mass, the oil's temperature climbs about twice as fast. This is also why oil reaches frying temperature long before a pan of water would, and why chefs are warned that hot oil heats and cools faster (and more dangerously) than water. You have just measured a fundamental thermal property of two everyday liquids.