NEB Class 11 • Physics • Heat and Thermodynamics

Thermal Expansion: NEB Class 11 Physics Guide

Build thermal expansion from the particle model, then distinguish length, area, volume, real and apparent expansion without losing the reference temperature or container effect.

Linear, superficial and cubical coefficients
Real versus apparent liquid expansion
Derivations, Nepal examples and exam checks

Expansion depends on original size, temperature change and material coefficient.

Nepal curriculum boundary

What Thermal Expansion includes

The current CDC Physics Grade 11 page and secondary curriculum document place thermal expansion inside Heat and Thermodynamics. The outcomes include the relation among expansion coefficients and the distinction between real and apparent expansion of liquids.

This guide follows the small-expansion treatment in OpenStax thermal expansion. Values of coefficients vary with material and temperature, so use the coefficient supplied in a question rather than treating a table value as exact for every condition.

Physical picture

Why heating usually increases size

Atoms in a solid vibrate about equilibrium positions. The interatomic potential is not perfectly symmetric, so a higher average vibrational energy generally increases the mean separation. The object expands even though individual atoms do not become larger. Cooling usually reverses the change while the material remains in the elastic, single-phase range.

Thermal expansion is not the same as heat capacity. Expansion describes a geometric response; heat capacity describes energy required for temperature change. Two materials may receive the same quantity of heat yet reach different temperatures and expand by different amounts.

Model conditions: homogeneous material, small temperature interval, no phase change, unconstrained body and a coefficient treated as constant over the interval.

One-dimensional change

Linear expansion and its coefficient

For original length L₀ and temperature change ΔT, ΔL = αL₀ΔT. The new length is L = L₀(1 + αΔT). The coefficient α = ΔL/(L₀ΔT) has unit K⁻¹ or °C⁻¹ because a temperature interval has the same numerical size in kelvin and Celsius.

Worked example: steel rail in the Terai

A 12.0 m rail has α = 12×10⁻⁶ K⁻¹ and warms by 35 K. ΔL = 12×10⁻⁶×12.0×35 = 5.04×10⁻³ m = 5.04 mm. A joint must allow at least this ideal expansion plus an engineering safety margin.

Cooling check

If ΔT is negative, ΔL is negative. A 2.0 m rod with α = 20×10⁻⁶ K⁻¹ cooled by 50 K contracts by 2.0 mm. Keep the sign through the equation and describe contraction in words.

From length to area and volume

Why β ≈ 2α and γ ≈ 3α

Let each side of a rectangle scale by (1+αΔT). Then A = A₀(1+αΔT)² = A₀[1+2αΔT+(αΔT)²]. For small αΔT, the squared term is negligible, so ΔA ≈ 2αA₀ΔT. Thus the superficial coefficient β is approximately 2α.

For an isotropic cube, V = V₀(1+αΔT)³. Neglecting second- and third-order small terms gives ΔV ≈ 3αV₀ΔT, so the cubical coefficient γ is approximately 3α. These relations are approximations for isotropic materials and small changes, not universal identities for anisotropic crystals.

Change	Equation	Coefficient relation
Length	ΔL = αL₀ΔT	α
Area	ΔA = βA₀ΔT	β ≈ 2α
Volume	ΔV = γV₀ΔT	γ ≈ 3α

Worked example: metal plate hole

A circular hole of diameter 4.00 cm is cut in a plate with α = 18×10⁻⁶ K⁻¹. For ΔT = 100 K, the hole diameter increases by αdΔT = 0.0072 cm. The hole expands as though it were made of the same material; it does not shrink.

Container and contents

Real and apparent expansion of a liquid

A liquid must be held in a vessel, and both expand on heating. If the liquid’s real cubical coefficient is γ_l and the vessel’s is γ_v, the overflow or observed increase is governed by γ_app = γ_l − γ_v. Therefore γ_real = γ_app + γ_v.

Worked example: flask and liquid

A liquid has γ_real = 9.0×10⁻⁴ K⁻¹ in a glass flask with γ_v = 2.7×10⁻⁵ K⁻¹. Its apparent coefficient is 8.73×10⁻⁴ K⁻¹. For 500 cm³ and a 20 K rise, apparent increase is 500×8.73×10⁻⁴×20 = 8.73 cm³.

At the instant heating begins, the container may warm before the liquid, so the liquid level can initially fall. The final equilibrium relation assumes both reach the same temperature change. The conceptual prompts in OpenStax thermal-expansion questions help separate this transient behaviour from the equilibrium calculation.

Mixed reasoning

More worked Thermal Expansion examples

Bridge expansion gap

A 40 m steel span with α = 12×10⁻⁶ K⁻¹ experiences a 45 K range. Ideal length change is 0.0216 m, or 21.6 mm. The calculation estimates thermal movement; engineers also consider constraints, load, tolerances and safety standards.

Bimetal strip direction

Brass has a larger α than steel. When bonded strips are heated, brass wants to become longer, so it lies on the outside of the curve and the strip bends toward steel. On cooling, the bending direction reverses.

Density after heating

Mass stays constant while V = V₀(1+γΔT), so ρ = ρ₀/(1+γΔT). For small change, density decreases approximately by fractional amount γΔT. Do not claim mass decreases merely because density does.

Kathmandu and Nepal context

Where expansion matters

Structures

Bridge bearings, roof sheets and long pipelines need controlled movement or flexible joints.

Power lines

Conductors sag more when hot and contract when cold; clearance planning must include temperature.

Thermostats

A bimetal strip converts unequal expansion into bending and switching.

Glass and heat

Unequal temperature across glass creates differential expansion and stress that can cause cracking.

The NASA/JPL thermal expansion model offers an institutional activity for linking particle motion, temperature and observable size change. Adapt any experiment to available equipment and teacher safety guidance.

Practical method

Measure the coefficient of a rod

Measure original rod length between fixed reference points.
Record initial temperature after equilibrium.
Heat uniformly using supervised apparatus.
Measure small extension with a suitable gauge.
Calculate α = ΔL/(L₀ΔT).
Repeat and compare the spread of results.

Major uncertainties include non-uniform temperature, movement of supports, gauge zero error and heat loss before reading. A long rod and measurable safe ΔT increase fractional extension. Do not touch heated metal; follow laboratory supervision and personal-protection requirements.

Exam repair

Common mistakes and study method

Use original dimension, not final dimension, in the elementary formula.
Use temperature difference directly; do not add 273 to ΔT.
Match α, β or γ to length, area or volume.
Include vessel expansion for apparent liquid expansion.
State the small-change and unconstrained assumptions.
Keep coefficient unit K⁻¹ and convert final length units carefully.

Study by drawing “before” and “after” diagrams, predicting expansion or contraction, then deriving the needed relation from dimensions. Review Heat & Temperature for equilibrium language and Elasticity for stresses created when expansion is constrained. For online or physical NEB tuition, call 9846662070.

Practice tasks

Closed-book checkpoint

Derive β ≈ 2α from a rectangle.
Derive γ ≈ 3α from a cube.
Calculate expansion of a 25 m rod for a 30 K rise.
Explain why a hole in a plate expands.
Find real coefficient from apparent and vessel coefficients.
Predict bimetal bending direction.
Explain one thermal-stress failure.
Design a safe rod-expansion experiment.

Frequently asked questions

Questions about Thermal Expansion

Does a hole in a heated plate expand?

Yes. In uniform unconstrained heating, every linear dimension scales, so the hole expands as if it were filled with the same material.

Why is cubical expansion approximately three times linear expansion?

All three perpendicular dimensions scale by about 1+αΔT; expanding the product and neglecting higher-order small terms gives γ≈3α.

Is Celsius acceptable in expansion calculations?

A temperature interval has the same numerical value in Celsius degrees and kelvins, so either is acceptable for ΔT with a matching coefficient unit.

What is apparent expansion of a liquid?

It is the observed liquid-volume increase relative to an expanding vessel, equal to real liquid expansion minus vessel expansion.

Why can glass crack with hot water?

A large temperature gradient makes regions expand unequally, producing thermal stress that may exceed the glass strength.

Where can I get NEB Thermal Expansion help?

For current online or physical tuition options, call 9846662070 and confirm timetable, class mode, teacher availability and fees.

References and next steps

Sources and related study guides

Continue with the Thermal Expansion Study Guide for a focused revision sequence. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

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