Heat capacity

Internal Energy: What It Means

The internal energy of a body is the total energy of its particles, made up of:

Kinetic energy due to random motion of particles, and

Potential energy due to forces between particles.

Temperature and Internal Energy: The Core Link

Temperature is a measure of the average kinetic energy of the particles in a substance.

When the temperature of a body rises:

particles gain kinetic energy,

particles move faster and more vigorously,

the internal energy of the body increases.

This increase occurs even if the body does not change state.

Molecular Interpretation

In a solid: particles vibrate more strongly about fixed positions.

In a liquid: particles move faster and collide more frequently.

In a gas: particles move faster in random directions and collide more energetically.

In all cases, a rise in temperature means an increase in random thermal motion, which increases internal energy.

[Insert diagram showing particles moving faster at higher temperature compared to lower temperature]

Energy Transfer and Temperature Rise

When energy is supplied to a body (for example by heating):

energy is transferred to the particles,

their kinetic energy increases,

the temperature rises,

internal energy increases.

Important clarification:

Adding energy increases internal energy,

Rising temperature is the observable result of increased random motion.

Key Conceptual Distinction (Exam-Critical)

Internal energy depends on:
- temperature, and
- the amount and type of substance.

Two objects at the same temperature can have different internal energies if they contain different amounts of matter.

Key Exam-Ready Statements

A rise in temperature causes an increase in internal energy.

This is due to increased random kinetic energy of particles.

Temperature measures average kinetic energy, not total energy.

Internal energy increases whenever particles move more vigorously.

Questions

Question 1

What is meant by internal energy?

Question 2

Describe what happens to the internal energy of a body when its temperature rises.

Question 3

Explain, in terms of particle motion, why heating a substance increases its internal energy even if no change of state occurs.

Solutions

Solution 1

Internal energy is the total energy of the particles of a body due to their random motion and the forces between them.

Solution 2

When the temperature of a body rises, its particles gain kinetic energy and move faster.

This increase in random motion causes the internal energy of the body to increase.

Solution 3

Heating transfers energy to the particles of the substance.

This increases their kinetic energy and makes them move more vigorously.

As a result, the internal energy increases even though the substance remains in the same state.

Examiner-Level Guidance

Always link temperature rise → increased particle motion → increased internal energy.

Do not confuse internal energy with heat.

Mention random motion explicitly for full marks.

Avoid stating that temperature measures total energy.

Why Heat Capacity Is Needed

Different objects require different amounts of energy to raise their temperature by the same amount.

For example:

a metal spoon heats up quickly,

a large pot of water heats up slowly.

This difference is explained using heat capacity and specific heat capacity.

Meaning of Heat Capacity

The heat capacity of a body is:

the amount of thermal energy required to raise the temperature of the entire body by 1 °C (or 1 K).

Key points:

it depends on the mass of the body,

it depends on the material the body is made of,

larger or heavier objects usually have greater heat capacity.

Interpretation

If a body has a large heat capacity:

a large amount of energy is needed to raise its temperature slightly,

it warms up slowly.

If a body has a small heat capacity:

a small amount of energy produces a noticeable temperature rise,

it warms up quickly.

Specific Heat Capacity

Meaning of Specific Heat Capacity

The specific heat capacity of a substance is:

the amount of thermal energy required to raise the temperature of 1 kg of the substance by 1 °C (or 1 K).

Specific heat capacity:

is a property of the material,

does not depend on mass,

allows fair comparison between different substances.

Conceptual Importance

Specific heat capacity explains why:

water heats up slowly but stores large amounts of energy,

metals heat up quickly and cool down quickly.

Substances with high specific heat capacity:

require more energy to change temperature,

are good for thermal storage.

Substances with low specific heat capacity:

change temperature easily,

respond quickly to heating or cooling.

Key Differences Between Heat Capacity and Specific Heat Capacity

Feature	Heat Capacity	Specific Heat Capacity
Depends on mass	Yes	No
Depends on material	Yes	Yes
Definition basis	Whole object	Per kilogram
Use	Describes an object	Describes a substance

Relationship to Internal Energy

When energy is supplied to a body:

internal energy increases,

temperature rises depending on the heat capacity,

the rise is smaller if heat capacity is large.

Specific heat capacity controls how much energy per kilogram is needed for a temperature change.

[Insert diagram comparing temperature rise of equal masses of different materials when same heat energy is supplied]

Key Exam-Ready Statements

Heat capacity refers to the entire object.

Specific heat capacity refers to 1 kg of a substance.

Large heat capacity means slow temperature rise.

Specific heat capacity allows comparison between materials.

Questions

Question 1

Define heat capacity.

Question 2

Define specific heat capacity.

Question 3

Explain why a large metal block and a small metal block made of the same material have different heat capacities.

Question 4

Water has a high specific heat capacity.

State one practical advantage of this property.

Solutions

Solution 1

Heat capacity is the amount of thermal energy required to raise the temperature of a body by 1 °C (or 1 K).

Solution 2

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

Solution 3

The large metal block has a greater mass than the small block.

Since heat capacity depends on mass, the larger block requires more energy to raise its temperature by the same amount.

Solution 4

Water’s high specific heat capacity allows it to absorb large amounts of heat with only a small temperature rise, making it useful for cooling systems or temperature regulation.

Examiner-Level Guidance

Do not confuse heat capacity with specific heat capacity.

Always include “per kilogram” in specific heat capacity definitions.

Temperature change must be 1 °C or 1 K in definitions.

Real-life applications strengthen extended answers.

Core Principle Behind the Experiments

Specific heat capacity, ccc, relates:

the energy supplied to a substance,

the mass of the substance,

the temperature change produced.

The relationship is:

E = mc\Delta T

where:

E = energy supplied (J),

m = mass (kg),

c = specific heat capacity (J kg °C),

ΔT = change in temperature (°C or K).

In experiments:

E is usually supplied electrically or by heating,

temperature rise is measured,

mass is measured accurately.

Experiment 1: Measuring the Specific Heat Capacity of a Solid

Apparatus

solid metal block with holes,

electric heater,

power supply,

ammeter and voltmeter,

thermometer,

stopwatch,

insulation (cotton wool or foam),

balance.

[Insert labelled diagram of a metal block with heater, thermometer, insulation, ammeter and voltmeter]

Method (Procedure)

Measure the mass of the metal block using a balance.

Insert the heater and thermometer into the block.

Wrap the block with insulation to reduce heat loss.

Record the initial temperature of the block.

Switch on the power supply and start the stopwatch.

Record the current and voltage.

Heat the block for a measured time.

Record the final temperature.

Switch off the heater.

Measurements and Calculations

Energy supplied electrically:

E = VIt

Then calculate specific heat capacity:

c = \frac{E}{m\Delta T}

Sources of Error and Improvements

Some energy is lost to the surroundings.

Insulation reduces, but does not eliminate, heat loss.

Using a short heating time and good insulation improves accuracy.

Experiment 2: Measuring the Specific Heat Capacity of a Liquid

Apparatus

liquid (e.g. water),

electric heater,

insulated container or calorimeter,

thermometer,

ammeter and voltmeter,

stopwatch,

balance.

[Insert labelled diagram of calorimeter with liquid, heater, thermometer, and insulation]

Method (Procedure)

Measure the mass of the empty container.

Add the liquid and measure the total mass.

Calculate the mass of the liquid.

Place the heater and thermometer into the liquid.

Insulate the container.

Record the initial temperature.

Switch on the heater and start the stopwatch.

Record voltage, current, and heating time.

Record the final temperature.

Measurements and Calculations

Energy supplied:

E = VIt

Specific heat capacity of the liquid:

c = \frac{E}{m\Delta T}

Experimental Considerations

Stirring ensures uniform temperature.

Insulation reduces energy loss.

The container also absorbs some energy (often neglected at BGCSE level or discussed as a limitation).

Comparison of the Two Experiments

Feature	Solid	Liquid
Heating method	Electric heater	Electric heater
Temperature measurement	Thermometer in solid	Thermometer in liquid
Heat loss	Reduced by insulation	Reduced by insulation
Key difficulty	Heat loss to surroundings	Heat absorbed by container

Key Exam-Ready Statements

Energy supplied is usually calculated using E=VItE = VItE=VIt.

Mass and temperature change must be measured accurately.

Insulation is used to reduce heat loss.

Errors mainly arise from energy losses.

Questions

Question 1

Describe an experiment to measure the specific heat capacity of a solid.

Question 2

Explain why insulation is used in experiments to measure specific heat capacity.

Question 3

A liquid is heated using an electric heater.

State the measurements needed to calculate its specific heat capacity.

Solutions

Solution 1

The mass of the solid is measured and a heater and thermometer are placed in the solid.

The solid is insulated and its initial temperature is recorded.

The heater is switched on for a measured time while voltage and current are recorded.

The final temperature is measured and the energy supplied is calculated using E = VIt.

The specific heat capacity is calculated using:

c = \frac{E}{m\Delta T}

Solution 2

Insulation reduces heat loss to the surroundings.

This ensures that most of the supplied energy raises the temperature of the substance, improving accuracy.

Solution 3

The required measurements are:

mass of the liquid,

initial temperature,

final temperature,

voltage, current, and heating time.

Examiner-Level Guidance

Always include apparatus, method, measurements, and calculation.

State how energy is calculated.

Mention insulation and heat loss for higher marks.

Clear, logical sequencing is essential in practical descriptions.

Equations Used in Heat Capacity Calculations

At BGCSE level, calculations are based on two closely related equations:

1. Heat Capacity of a Body

E = C\Delta T

where:

E = energy transferred (J),

C = heat capacity of the body (J °C or J K),

ΔT = temperature change (°C or K).

This equation is used when the heat capacity of the whole object is known.

2. Specific Heat Capacity

E = mc\Delta T

where:

mmm = mass of the substance (kg),

ccc = specific heat capacity (J kg °C).

This equation is used when the material and mass are specified.

Important Conceptual Notes

A temperature change of 1 °C is equal to 1 K in calculations.

Energy transferred is usually electrical, thermal, or mechanical, but always measured in joules.

Larger heat capacity → smaller temperature rise for the same energy input.

[Insert diagram showing same energy supplied to two objects with different heat capacities producing different temperature rises]

Worked Examples (Step-by-Step)

Example 1: Calculating Energy Using Heat Capacity

A metal block has a heat capacity of 800 J °C.

Calculate the energy required to raise its temperature by 5 °C.

Step 1: Write the equation

E = C\Delta T

Step 2: Substitute values

E = 800 \times 5

Step 3: Calculate

E = 4000\ \text{J}

Answer: The energy required is 4000 J.

Example 2: Calculating Temperature Rise

A body with a heat capacity of 500 J °C absorbs 2500 J of energy.

Find the temperature rise.

\Delta T = \frac{E}{C} = \frac{2500}{500} = 5^\circ\text{C}

Example 3: Using Specific Heat Capacity

A 2.0 kg block of aluminium (specific heat capacity = 900 J kg °C) is heated so that its temperature rises by 10 °C.

Calculate the energy supplied.

E = mc\Delta T = 2.0 \times 900 \times 10 = 18\,000\ \text{J}

Example 4: Finding Specific Heat Capacity

A 1.5 kg liquid absorbs 6300 J of energy and its temperature rises by 3 °C.

Calculate its specific heat capacity.

c = \frac{E}{m\Delta T} = \frac{6300}{1.5 \times 3} = 1400\ \text{J kg}^{}\,^\circ\text{C}^{}

Key Exam-Ready Statements

Use E=CΔT for whole objects.
$E = C\Delta T$

Use E=mcΔT for materials with known mass.
$E = mc\Delta T$

Temperature change may be in °C or K.

Always show substitution and working.

Questions

Question 1

A body has a heat capacity of 600 J °C.

Calculate the energy needed to raise its temperature by 8 °C.

Question 2

A 3.0 kg substance has a specific heat capacity of 420 J kg °C.

Calculate the energy required to raise its temperature by 5 °C.

Question 3

A block absorbs 10 000 J of energy and its temperature rises by 4 °C.

Calculate its heat capacity.

Solutions

Solution 1

E = C\Delta T = 600 \times 8 = 4800\ \text{J}

Solution 2

E = mc\Delta T = 3.0 \times 420 \times 5 = 6300\ \text{J}

Solution 3

C = \frac{E}{\Delta T} = \frac{10\,000}{4} = 2500\ \text{J}\,^\circ\text{C}^{}

Examiner-Level Guidance

Correct equation choice is essential.

Units must be stated correctly.

Do not confuse heat capacity with specific heat capacity.

Missing units or steps may lose marks even if the final answer is correct.