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10.1aFree

Thermal expansion of solids

Your guide: Sir HamzaBelieves every formula has a story, and units never lie.

Hotter particles need more room

Thermal expansion is the change in length, area or volume of a substance when it is heated. Heated particles gain kinetic energy, vibrate with a larger amplitude and spread out. Cooled particles move closer: this is thermal contraction.

In a solid, atoms sit in a tight, regular pattern. As each atom vibrates harder it pushes on its neighbours, and with no room inwards the solid grows outwards.

Linear expansion (Fig. 10.2)

The increase in length ΔL is proportional to the original length L0 and the rise in temperature ΔT.

ΔL = α L0 ΔT, so L = L0(1 + αΔT). α is the coefficient of linear expansion, in K−1.

Table 10.1: aluminium 2.4, brass 1.9, copper 1.7 and steel 1.2, all × 10−5 K−1.

Volume expansion

ΔV = β V0 ΔT, so V = V0(1 + βΔT). β is the coefficient of volume expansion.

Expansion grows with three things: how long (or big) the object is, how much hotter it gets, and the material, through α or β.

Step 1 / 7

Notes, short questions and MCQs

Read the full notes: key terms, model answers and MCQs with answers

Hotter particles need more room

Thermal expansion is the change in length, area or volume of a substance when it is heated. Heated particles gain kinetic energy, vibrate with a larger amplitude and spread out. Cooled particles move closer: this is thermal contraction.

In a solid, atoms sit in a tight, regular pattern. As each atom vibrates harder it pushes on its neighbours, and with no room inwards the solid grows outwards.

Linear expansion (Fig. 10.2)

The increase in length ΔL is proportional to the original length L0 and the rise in temperature ΔT.

ΔL = α L0 ΔT, so L = L0(1 + αΔT). α is the coefficient of linear expansion, in K−1.

Table 10.1: aluminium 2.4, brass 1.9, copper 1.7 and steel 1.2, all × 10−5 K−1.

Volume expansion

ΔV = β V0 ΔT, so V = V0(1 + βΔT). β is the coefficient of volume expansion.

Expansion grows with three things: how long (or big) the object is, how much hotter it gets, and the material, through α or β.

Key terms

Thermal expansion
The change in length, area or volume of a substance on heating.
Thermal contraction
Particles lose energy and move closer together.
Coefficient of linear expansion (α)
The increase in length per unit length per kelvin.
Coefficient of volume expansion (β)
The increase in volume per unit volume per kelvin.

Short questions with model answers

  1. Q1. Example 10.1 (p. 7): a 1.5 m metal rod expands by 0.025 m when heated from 30 °C to 180 °C. Find α.

    • ΔT = 180 − 30 = 150 K
    • α = ΔL ÷ (L0ΔT) = 0.025 ÷ (1.5 × 150)
    • = 0.025 ÷ 225

    α = 1.11 × 10−4 K−1

  2. Q2. Why do electric transmission wires sag in summer and tighten in winter? (Constructed Response 10.5)

    • Summer.
    • Winter.

    Thermal expansion in heat and contraction in cold change the wire's length.

Common mistakes

  • ✗ A rise of 150 °C must be converted to 423 K before using α.

    ✓ A temperature change of 150 °C equals a change of 150 K.

  • ✗ ΔL is the new length of the rod.

    ✓ ΔL is the increase. The new length is L = L0 + ΔL.

  • ✗ Solids expand because their atoms get bigger.

    ✓ The atoms vibrate more and push further apart; they do not grow.

MCQs

  1. 1. When the temperature of a copper rod is increased, its length:

    1. (a) Remains the same
    2. (b) Increases
    3. (c) Decreases
    4. (d) Becomes double
    Show answer

    (b) MCQ 10.1 (p. 17): heated solids expand.

  2. 2. The increase in length of unit length of a material for a 1 °C rise is called the coefficient of:

    1. (a) Cubic expansion
    2. (b) Volume expansion
    3. (c) Linear expansion
    4. (d) None of these
    Show answer

    (c) MCQ 10.2 (p. 17): that is α, the coefficient of linear expansion.

  3. 3. Which formula gives the new length of a heated rod?

    1. (a) L = L0 ΔT
    2. (b) L = α ΔT
    3. (c) L = L0 − αΔT
    4. (d) L = L0(1 + αΔT)
    Show answer

    (d) Equation 10.1 (p. 3).

  4. 4. From Table 10.1, which expands most for the same length and temperature rise?

    1. (a) Aluminium
    2. (b) Steel
    3. (c) Copper
    4. (d) Pyrex glass
    Show answer

    (a) Aluminium has the largest α of these: 2.4 × 10−5 K−1.

  5. 5. A 1.5 m rod is heated from 30 °C to 180 °C. ΔT is:

    1. (a) 210 K
    2. (b) 423 K
    3. (c) 150 K
    4. (d) 180 K
    Show answer

    (c) Example 10.1: 180 − 30 = 150 °C, which is 150 K.

Quick revision

  • Heating makes particles vibrate more and spread out: thermal expansion. Cooling gives contraction.
  • Linear: ΔL = α L0 ΔT. Volume: ΔV = β V0 ΔT.
  • Each material has its own α and β (Table 10.1).

Before you start

What is Class 10 Physics Thermal expansion of solids?
Thermal expansion of solids is the open Class 10 Physics lesson for Matric Part 2, Punjab board. It is a step-by-step lesson, not a PDF of the book.
Which boards is this Class 10 Physics lesson for?
The same Punjab textbook: Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, Sargodha, Bahawalpur, Dera Ghazi Khan, Sahiwal.
Can I study this in Urdu?
Yes. English, Urdu or Roman Urdu. Science terms stay as the exam writes them.
Is this a notes PDF?
No. The book stays with you. This page is the lesson and the check.

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