Thermal Expansion and Specific Heat Capacity

Q: What is the difference between heat and temperature for SHC calculations?

Temperature is a measure of how hot a substance is (units °C/K), while heat is the thermal energy transferred between substances (units J). Specific heat capacity links energy transferred to the temperature change of a fixed mass of material.

Q: Do I need to memorise the specific heat capacity of water?

Yes, CIE IGCSE exams expect you to recall that the specific heat capacity of water is 4200 J/(kg °C) unless it is explicitly provided in the question.

Physics· 2.2.1, 2.2.2 (2026-2028 syllabus)· 18 min read

1. 1. Thermal Expansion (Core)★★☆☆☆⏱ 4 min

📘 Definition

Thermal Expansion

The increase in volume or length of a substance when heated, caused by particles gaining kinetic energy and moving further apart, with no change of state.

Example:

A 1 m long steel rod expands by 1 mm when heated by 100 °C.

The extent of expansion for the same temperature rise follows the order: solids < liquids < gases. This is because interparticle forces are strongest in solids, holding particles close together, and negligible in gases, so particles can move much further apart when heated.

📐 Worked Example

Explain why glass tumblers often crack when very hot water is poured into them, using particle theory.

1
1. When hot water is poured into the cold glass, the inner surface of the glass heats up rapidly, and its particles gain kinetic energy and expand.
2
1. Glass is a poor conductor of heat, so the outer surface of the glass remains cool and does not expand at the same rate.
3
1. The uneven expansion creates stress in the glass, causing it to crack.

Exam tip:

Core questions frequently ask for applications/hazards of thermal expansion: common examples include railway track gaps, bimetallic strips in thermostats, and overhead power line slack in summer.

2. 2. Internal Energy and Temperature (Core)★☆☆☆☆⏱ 3 min

Everything is made of particles that are always moving, so every object stores energy in the movement and arrangement of its particles. This stored energy is called the object's internal energy.

📘 Definition

Internal energy

The total energy stored in an object in the movement (kinetic energy) and arrangement (potential energy) of its particles.

📐 Worked Example

A metal block is heated by a flame so its temperature rises. State and explain what happens to the internal energy of the block.

1
Step 1: State the change:
2
The internal energy of the block increases.
3
Step 2: Explain why:
4
Raising the temperature makes the particles of the block move faster, so the total energy stored in the block - its internal energy - increases.

Exam tip:

For Core (Paper 1/3) you only need the link between temperature and internal energy - the specific heat capacity equation, calculations and measuring experiments are all Extended (Supplement) content.

3. 3. Specific Heat Capacity and Its Formula (Extended)★★★☆☆Extended only⏱ 5 min

📘 Definition

Specific Heat Capacity

$c$

The amount of thermal energy required to raise the temperature of 1 kg of a substance by 1 °C, measured in J/(kg °C).

Example:

Water has a specific heat capacity of 4200 J/(kg °C).

Q = m c \Delta T

Where $Q$ = thermal energy transferred (J), $m$ = mass of substance (kg), $c$ = specific heat capacity, and $Δ T$ = change in temperature ( $T_{f ina l} - T_{ini t ia l}$ ). Always convert mass from grams to kilograms before substituting values into the formula.

📐 Worked Example

Calculate the energy required to heat 3 kg of water from 15 °C to 65 °C. Use $c_{w a t er} = 4200$ J/(kg °C).

1
Step 1: Identify known values: $m = 3$ kg, $c = 4200$ J/(kg °C), $Δ T = 65 - 15 = 50$ °C
2
Step 2: Substitute into the formula $Q = m c Δ T$ :
3
$Q = 3 \times 4200 \times 50$
4
Step 3: Calculate the result: $Q = 630, 000$ J = 630 kJ

Exam tip:

Always show full substitution steps for SHC calculations to earn all available marks, even if you can solve the problem mentally.

4. 4. Measuring Specific Heat Capacity (Extended)★★★☆☆Extended only⏱ 5 min

You are expected to describe the method to measure the specific heat capacity of a solid (e.g. aluminium block) or liquid (e.g. water) in the exam:

1. Measure the mass of the substance using a balance, and record its initial temperature with a thermometer.
1. Wrap the substance in insulating material (e.g. foam) to reduce thermal energy loss to the surroundings.
1. Heat the substance using an electric heater of known power for a measured time, then record the final maximum temperature.
1. Calculate energy supplied by the heater: $Q = p o w er (W) \times t im e (s)$ , then rearrange $c = Q / (m Δ T)$ to find specific heat capacity.

📐 Worked Example

A 1 kg copper block is heated by a 100 W heater for 90 seconds. Its temperature rises from 22 °C to 47 °C. Calculate the specific heat capacity of copper.

1
Step 1: Calculate energy supplied: $Q = P \times t = 100 \times 90 = 9000$ J
2
Step 2: Calculate $Δ T = 47 - 22 = 25$ °C, $m = 1$ kg
3
Step 3: Rearrange the formula to $c = Q / (m Δ T)$ :
4
$c = 9000 / (1 \times 25)$
5
Step 4: Calculate $c = 360$ J/(kg °C)

Exam tip:

You may be asked to identify sources of error in SHC practicals: the most common error is thermal energy loss to the surroundings.

5. 5. Extended: Multi-Substance Energy Transfers★★★★☆Extended only⏱ 4 min

For Extended tier, you will solve problems where thermal energy is transferred from a hotter substance to a cooler one, with the assumption that no energy is lost to the surroundings. This means: energy lost by hot substance = energy gained by cold substance.

📐 Worked Example

A 0.3 kg block of brass heated to 180 °C is dropped into 0.4 kg of water at 18 °C. Assuming no energy loss, calculate the final temperature of the mixture. Use $c_{b r a ss} = 380$ J/(kg °C) and $c_{w a t er} = 4200$ J/(kg °C).

1
Step 1: Let $T$ = final temperature of the mixture. Set energy lost by brass equal to energy gained by water:
2
$m_{brass} c_{brass} (180 - T) = m_{water} c_{water} (T - 18)$
3
Step 2: Substitute known values:
4
$0.3 \times 380 \times (180 - T) = 0.4 \times 4200 \times (T - 18)$
5
$114(180 - T) = 1680(T - 18)$
6
Step 3: Expand and rearrange to solve for T:
7
$20520 - 114T = 1680T - 30240$
8
$50760 = 1794T$
9
Step 4: Calculate final temperature: $T \approx 28.3$ °C

Exam tip:

For energy transfer problems, always ensure temperature change terms are positive: use $T_{h o t} - T_{f ina l}$ for the hot substance, and $T_{f ina l} - T_{co l d}$ for the cold substance.

6. Common Pitfalls

Wrong move:

Using mass in grams instead of kilograms in SHC calculations

Why:

SHC units are J/(kg °C), so mass in grams will produce an incorrect energy value 1000x larger or smaller than the true value

Correct move:

Always convert mass from grams to kilograms by dividing by 1000 before substituting into $Q = m c Δ T$

Wrong move:

Calculating $Δ T$ as initial minus final temperature for a substance being heated

Why:

$Δ T$ measures the increase in temperature for heated substances, so it must be a positive value

Correct move:

$Δ T = T_{f ina l} - T_{ini t ia l}$ for heated substances; use the magnitude of the change for cooled substances

Wrong move:

Stating liquids expand more than gases for the same temperature rise

Why:

Interparticle forces in gases are negligible, so gas particles move much further apart than liquid particles when heated

Correct move:

Recall the expansion order: solid < liquid < gas for equal temperature change, linked to interparticle force strength

Wrong move:

Claiming practical SHC values are lower than true values due to heat loss

Why:

Heat loss means the energy absorbed by the test substance is less than the energy supplied by the heater, so calculated SHC will be higher

Correct move:

State that calculated SHC from practicals is higher than the true value, and suggest improvements like better insulation

Wrong move:

Using the same SHC value for both substances in Extended energy transfer problems

Why:

Every substance has a unique specific heat capacity, so using the wrong $c$ value will produce an incorrect final temperature

Correct move:

Label $c$ , $m$ and $Δ T$ values for each substance clearly before substituting into the energy balance equation

7. Quick Reference Cheatsheet

Concept	Core Rule/Formula	Extended Add-on
Thermal expansion	Solids, liquids and gases expand when heated at constant pressure; gases expand most and solids least; used in railway-track gaps and bimetallic strips	Explain the relative order (solid < liquid < gas) in terms of the motion and arrangement of particles
Internal energy	A rise in the temperature of an object increases its internal energy	A temperature rise corresponds to an increase in the average kinetic energy of all the particles
Specific heat capacity	Not required at Core	Define SHC as energy per unit mass per unit temperature rise; recall and use $Q = m c Δ T$ (official form $c = Δ E / (m Δ θ)$ ); $c_{w a t er} = 4200$ J/(kg °C)
Measuring SHC	Not required at Core	$Q = P \times t$ for the energy supplied; insulate to reduce heat loss, so the measured $c$ comes out slightly too high
Multi-substance transfers	Not required at Core	Energy lost by the hot substance = energy gained by the cold substance (assuming no losses)

8. Frequently Asked

What is the difference between heat and temperature for SHC calculations?

Temperature is a measure of how hot a substance is (units °C/K), while heat is the thermal energy transferred between substances (units J). Specific heat capacity links energy transferred to the temperature change of a fixed mass of material.

Do I need to memorise the specific heat capacity of water?

Yes, CIE IGCSE exams expect you to recall that the specific heat capacity of water is 4200 J/(kg °C) unless it is explicitly provided in the question.

Going deeper

syllabusCIE IGCSE Physics 0625 2026-2028 SyllabusRefer to section 2.2 for full thermal physics outcomes

What's Next

Now that you have mastered thermal expansion and specific heat capacity, you are ready to progress to other thermal physics topics in the CIE IGCSE Physics 0625 syllabus. Next, you will learn about the three mechanisms of thermal energy transfer (conduction, convection, radiation), which explain how heat moves between substances, and thermal processes associated with changes of state. This knowledge builds the foundation for combined thermal physics questions in both Core and Extended papers, which frequently test SHC alongside energy transfer and practical skills. Be sure to practice both single-substance Core calculations and multi-substance Extended problems to build confidence before your exam.