11.1 Temperature, Internal Energy and Thermal Expansion — American System Physics Revision Notes & Topical Questions

Part 1 of 7Key ideas

Key ideas

Kelvin conversion

T (K) = θ (°C) + 273; e.g. 27 °C = 300 K.

0 K = −273 °C

Absolute zero = 0 K = −273 °C; nothing can be colder.

A temperature change of 1 K is identical to a change of 1 °C.

Average kinetic energy of gas particles is proportional to kelvin temperature: doubling T in K doubles average KE.

Thermal energy always flows from hotter to colder, never the reverse on its own.

Order of expansion for the same temperature rise

Order of expansion for the same temperature rise gases > liquids > solids.

Linear expansion (extension)

ΔL = αL₀Δθ, where α is the coefficient of linear expansion (per K).

Part 2 of 7Learning objectives

1

Distinguish between temperature and internal energy.

2

Describe the kinetic particle model and Brownian motion.

3

Convert between the Celsius and Kelvin scales.

4

Describe thermal expansion of solids, liquids and gases and its uses and consequences.

Part 3 of 7Essential knowledge

1

11.1 Temperature, Internal Energy and The… concept map: Kelvin conversion, Order of expansion for the sa, Linear expansion (extension), Brownian motion, Thermal expansion — Visual guide to the key ideas explained in this lesson.

2

All matter is made of particles in constant random motion. The hotter the substance, the faster (on average) its particles move. Temperature is linked to the average kinetic energy per particle; internal energy is the total energy of all particles.

3

Brownian motion

Brownian motion under a microscope, smoke particles in air move in random, zig-zag paths. They are being hit unevenly by much smaller, fast-moving air molecules. This is evidence that gas molecules are in rapid random motion.

4

When an object is heated its internal energy increases. This either raises its temperature (particles move faster) or changes its state (particles gain potential energy as they separate) — not both at the same time for a pure substance.

5

Temperature decides the direction of thermal energy transfer, not the amount of internal energy. A spark at 1000 °C has less internal energy than a warm swimming pool, but energy flows from the spark to your skin.

6

The kelvin scale starts at absolute zero, where particles have the minimum possible kinetic energy. Temperatures in gas-law calculations must be in kelvin.

7

A liquid-in-glass thermometer works because the liquid (mercury or coloured alcohol) expands as it is heated and rises up a narrow capillary tube. A thin tube and thin-walled bulb increase sensitivity and responsiveness; a longer tube increases range.

8

Thermal expansion

Thermal expansion when heated, particles in a solid vibrate with larger amplitude and push each other slightly further apart, so the solid gets bigger. The particles themselves do not expand.

9

Consequences and uses of expansion

Consequences and uses of expansion gaps in railway tracks and expansion joints on bridges prevent buckling; power cables are hung with slack in summer; bimetallic strips in thermostats bend to switch circuits; hot metal lids loosen on glass jars; rivets shrink as they cool to clamp plates tightly.

10

Liquids expand more than solids and gases expand much more than liquids for the same temperature rise, because the forces between particles are weaker.

11

Water is unusual

Water is unusual between 0 °C and 4 °C it contracts when heated, so it is densest at 4 °C. This is why lakes freeze from the top down.

Part 4 of 7Process & sequence

1

Calibrating an unmarked liquid-in-glass thermometer: place the bulb in pure melting ice and mark the liquid level as 0 °C.

2

Place the bulb in steam above pure boiling water at standard atmospheric pressure and mark the level as 100 °C.

3

Measure the distance between the two marks.

4

Divide the distance into 100 equal divisions (assumes the liquid expands linearly).

5

Use the scale to read an unknown temperature from the liquid level.

How a thermostat bimetallic strip workswrite these steps in this order; each step is a marking point.

1

At room temperature the straight strip touches a contact, closing the heater circuit.

2

The heater raises the room temperature and the strip warms.

3

The brass side expands more than the iron side.

4

The strip bends away from the contact (brass on the outside of the curve).

5

The circuit breaks, the heater switches off; as the strip cools it straightens and the cycle repeats.

Part 5 of 7Worked examples

1Convert (a) 37 °C and (b) −196 °C to kelvin.

(a) T = 37 + 273 = 310 K. (b) T = −196 + 273 = 77 K.

29.0 mm

A steel rail 25 m long has α = 1.2 × 10⁻⁵ K⁻¹. How much longer is it when its temperature rises by 30 °C?

ΔL = αL₀Δθ = 1.2 × 10⁻⁵ × 25 m × 30 = 9.0 × 10⁻³ m = 9.0 mm. So gaps of about 1 cm are needed between rails.

Part 6 of 7Summary

1

Temperature measures average particle kinetic energy; internal energy is the total.

2

Heating always transfers energy from higher to lower temperature.

3

T(K) = θ(°C) + 273; absolute zero is 0 K.

4

Substances expand when heated because particles move more and separate slightly; the particles themselves do not get bigger.

Part 7 of 7Compare: Compare

Temperature vs internal energy
Feature	Temperature	Internal energy
What it measures	Average kinetic energy per particle	Total kinetic + potential energy of all particles
Depends on amount of substance?	No	Yes (more mass → more internal energy)
Unit	°C or K	J
Example	A cup and a bath of water can both be 40 °C	The bath at 40 °C has far more internal energy

Relative thermal expansion of states of matter
State	Expansion on heating	Reason
Solid	Smallest	Strong forces hold particles in fixed positions; they only vibrate more
Liquid	Medium	Weaker forces; particles move further apart
Gas	Largest	Almost no forces; particles move freely and fast

Key terms

Command terms

Identify / Describe (FRQ)

A short, specific statement; describing requires relevant characteristics, not a single word.

Explain / Justify (FRQ)

Give the cause-and-effect reasoning or evidence; a restated fact does not score.

Calculate

Show setup, substitution and the answer with units.

Predict

State the expected outcome; add a reason only if asked to justify.

MCQ technique

Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Exam technique

Keywords the mark scheme looks for in this lesson

Temperature · Internal (thermal) energy · Thermal energy transfer (heating) · Thermal equilibrium · Absolute zero · Kelvin scale · Thermometer · Fixed point · Thermal expansion · Kinetic particle model · Brownian motion · Bimetallic strip

Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1

Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).

2

Use precise vocabulary, never “it/stuff/things”.

3

Show units and working in calculations.

4

In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1

the particles expandthe particles vibrate/move more and move further apart.

2

temperature is the amount of heattemperature is a measure of the average kinetic energy of the particles.

3

cold flows into the objectthermal energy is transferred from the hotter object to the colder one.

4

0 K = 0 °C0 K = −273 °C.

5

Brownian motion is smoke particles moving by themselvessmoke particles move randomly because they are bombarded by fast-moving air molecules.

Temperature, Internal Energy and Thermal Expansion — American System Physics Revision Notes & Topical Questions