Specific Heat Capacity

This lesson explains what specific heat capacity means, introduces the equation linking energy, mass and temperature change, and works through several exam-style calculations. Specific heat capacity is a required equation for the Edexcel GCSE Combined Science specification (1SC0).

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What Is Specific Heat Capacity?

Different materials heat up at different rates. The property that quantifies this is specific heat capacity (SHC).

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

$E = m c \Delta\theta$E=mcΔθ

Symbol	Quantity	Unit
$E$E	Energy transferred	joules (J)
$m$m	Mass	kilograms (kg)
$c$c	Specific heat capacity	joules per kilogram per degree Celsius (J/kg °C)
$\Delta\theta$Δθ	Temperature change	degrees Celsius (°C) or kelvin (K)

Exam Tip: The symbol $\Delta\theta$Δθ (delta-theta) means "change in temperature". You calculate it as: $\Delta\theta = \text{final temperature} - \text{initial temperature}$Δθ=final temperature−initial temperature.

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Rearranging the Equation

To find	Rearrangement
Energy	$E = m c \Delta\theta$E=mcΔθ
Mass	$m = \frac{E}{c \Delta\theta}$m=cΔθE​
Specific heat capacity	$c = \frac{E}{m \Delta\theta}$c=mΔθE​
Temperature change	$\Delta\theta = \frac{E}{m c}$Δθ=mcE​

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Comparing Specific Heat Capacities

Material	Specific Heat Capacity (J/kg °C)
Water	4200
Aluminium	900
Copper	390
Iron	450
Lead	130
Oil	2100
Concrete	800

What Do These Numbers Mean?

• Water has a very high SHC (4200 J/kg °C). This means it takes a lot of energy to heat water up, but it also stores a lot of energy and cools down slowly.
• Lead has a very low SHC (130 J/kg °C). A small amount of energy causes a large temperature rise.

graph LR
    A["Same energy input"] --> B["Water: small temp rise<br/>(high SHC)"]
    A --> C["Copper: large temp rise<br/>(low SHC)"]

Practical Significance of Water's High SHC

• Water is used in central heating systems — it can carry large amounts of thermal energy.
• Coastal areas have milder climates — the sea absorbs and releases energy slowly, moderating temperatures.
• Water is used as a coolant in car engines and power stations.

Exam Tip: If an exam question asks you to explain why water is used in heating systems or as a coolant, always state that water has a high specific heat capacity and then explain what this means (it can absorb or release a large amount of energy for a relatively small temperature change).

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Worked Example 1

How much energy is needed to heat 2.0 kg of water from 20 °C to 100 °C? (SHC of water = 4200 J/kg °C)

Step 1 — Identify the values:

• $m = 2.0$m=2.0 kg
• $c = 4200$c=4200 J/kg °C
• $\Delta\theta = 100 - 20 = 80$Δθ=100−20=80 °C

Step 2 — Substitute into the equation:

$E = m c \Delta\theta = 2.0 \times 4200 \times 80 = 672\,000 \text{ J} = 672 \text{ kJ}$E=mcΔθ=2.0×4200×80=672000 J=672 kJ

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Worked Example 2

A 0.5 kg block of copper is supplied with 15 600 J of energy. By how much does the temperature rise? (SHC of copper = 390 J/kg °C)

$\Delta\theta = \frac{E}{m c} = \frac{15\,600}{0.5 \times 390} = \frac{15\,600}{195} = 80 \text{ °C}$Δθ=mcE​=0.5×39015600​=19515600​=80 °C

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Worked Example 3

A student heats 0.3 kg of oil from 25 °C to 85 °C using an immersion heater that supplies 37 800 J. Calculate the specific heat capacity of the oil.

$c = \frac{E}{m \Delta\theta} = \frac{37\,800}{0.3 \times (85 - 25)} = \frac{37\,800}{0.3 \times 60} = \frac{37\,800}{18} = 2100 \text{ J/kg °C}$c=mΔθE​=0.3×(85−25)37800​=0.3×6037800​=1837800​=2100 J/kg °C

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The Core Practical: Investigating Specific Heat Capacity

In this practical you measure the SHC of a metal block.

Method

1. Measure the mass of the metal block ($m$m) using a balance.
2. Insert a thermometer (or temperature sensor) into the block.
3. Insert an immersion heater and connect it to a joulemeter (or use $E = P \times t$E=P×t with a stopwatch).
4. Record the initial temperature ($\theta_1$θ1​).
5. Switch on the heater and let it run for a set time (e.g. 10 minutes).
6. Record the final temperature ($\theta_2$θ2​) and the energy supplied ($E$E).
7. Calculate: $c = \frac{E}{m \Delta\theta}$c=mΔθE​.

Sources of Error

Source of error	How to reduce it
Energy lost to the surroundings	Insulate the block with a lagging jacket
Poor thermal contact	Add a few drops of oil into the thermometer hole
Reading the thermometer at the wrong time	Stir (liquids) or wait for equilibrium; use a data logger for continuous readings

Exam Tip: In the practical, the measured SHC is usually higher than the accepted value because some energy is lost to the surroundings. You should be able to explain this.

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Energy Stores and Transfers

When an object is heated, energy is transferred from the thermal energy store of the heater (or flame) to the thermal energy store of the substance. The temperature rise depends on:

1. The amount of energy transferred.
2. The mass of the substance.
3. The specific heat capacity of the material.

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Common Misconceptions

Misconception	Correction
Temperature and energy are the same thing	Temperature measures the average kinetic energy of particles; energy is the total amount transferred
All materials heat up at the same rate for the same energy input	Materials with different SHC values heat up at different rates
A higher temperature means more energy stored	Not necessarily — a large mass of water at 30 °C stores more energy than a small mass of iron at 100 °C

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Summary