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CISCEISC (Science) ISC Class 11
प्रश्नपत्रिका१७
संकल्पना स्पष्टीकरण आणि व्हिडिओ२२०
अभ्यासक्रम

Thermal Expansion

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Estimated time: 9 minutes
  • Introduction
  • Definition: Thermal Expansion
Maharashtra State Board: Class 11

Introduction

It is our common experience that most substances expand on heating and contract on cooling. When heat is supplied to a substance, its temperature increases and its particles gain kinetic energy. This causes them to vibrate more vigorously (in solids) or move faster (in liquids and gases), pushing neighbouring particles farther apart — resulting in expansion.

The extent of expansion depends on:

  • The original size of the body
  • The change in temperature (ΔT)
  • The nature of the material (its coefficient of expansion)

Depending on which dimension changes significantly, thermal expansion is classified into three types:

  • Linear Expansion (Change in length (1-D))

  • Areal Expansion (Change in area (2-D))

  • Volume Expansion (Change in volume (3-D))

Maharashtra State Board: Class 11

Definition: Thermal Expansion

The increase in the dimensions (length, area, or volume) of a body due to an increase in its temperature is called thermal expansion. Conversely, a decrease in temperature causes contraction.

OR

The increase in the dimensions of a body due to an increase in its temperature is called thermal expansion.

Maharashtra State Board: Class 11

Definition: Coefficient of Linear Expansion (α)

The increase in length per unit original length of a rod (at 0°C) per unit rise in temperature is called the coefficient of linear expansion.

Maharashtra State Board: Class 11

Definition: Coefficient of Superficial Expansion (β)

The change in area per unit original surface area of a two-dimensional body (at 0°C) per unit rise in temperature is called the coefficient of superficial expansion.

Maharashtra State Board: Class 11

Definition: Coefficient of Cubical Expansion (γ)

The increase in volume of a body per unit original volume (at 0°C) per unit rise in temperature is called the coefficient of cubical expansion.

Maharashtra State Board: Class 11

Key Points: Thermal Expansion

  • Solids have three types of expansion - Linear (1D), Superficial (2D), and Cubical (3D) - with β = 2α and γ = 3α.
  • Change in dimensions: ΔL = L0αΔT, ΔA = A0βΔT, ΔV = V0γΔT.
  • Liquids have only volume expansion; real expansion = apparent expansion + vessel expansion, i.e., γr = γa + γv.
  • Gases have only real expansion as the container expansion is negligible.
  • Final quantity after heating: L = L0(1 + αΔT), A = A0(1 + βΔT), V = V0(1 + γΔT).

Test Yourself

Related QuestionsVIEW ALL [38]

If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.

A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:

S.No. l(m) ∆T (C) ∆l (m)
1. 2 10 `4 xx 10^-4`
2. 1 10 `4 xx 10^-4`
3. 2 20 `2 xx 10^-4`
4. 3 10 `6 xx 10^-4`

If the first observation is correct, what can you say about observations 2, 3 and 4.

Solve the following problem.

In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10–5K–1 for the material of the rail section?

The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?

A rail track made of steel having length 10 m is clamped on a raillway line at its two ends (figure). On a summer day due to rise in temperature by 20° C, it is deformed as shown in figure. Find x (displacement of the centre) if αsteel = 1.2 × 10–5/°C.

A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z

The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new temperature is T + ∆T. The increase in the volume of the sphere is approximately ______.

A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5 K–1

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