**Thermal Expansion Definition:**

When matter is heated without any change in its state, it usually expand. This phenomena of expansion of matter on heating, is called thermal expansion.

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## Thermal Expansion in Physics | Definition, Types, Applications – Thermometry and Calorimetry

**Thermal Expansion Types:
**There are three types of thermal expansion

- Expansion of Solids
- Expansion of Liquids
- Thermal Expansion of Gases

1. **Expansion of Solids**

Three types of expansion takes place in solid

(i) **Linear Expansion:**

Expansion in length on heating is called linear expansion.

Increase in length,

l_{2} = l_{1} (1 + α Δt)

where, l_{1}, and l_{2} are initial and final lengths, Δt = change in temperature and α = coefficient of linear expansion.

Coefficient of linear expansion,

α = \(\frac{\Delta l}{l \times \Delta t}\)

where, l =real length and Δl = change in length and Δt = change in temperature.

(ii) **Superficial Expansion:**

Expansion in area on heating is called superficial expansion.

Increase in area,

A_{2} = A_{1} (1 + β Δt)

where, A_{1} and A_{2} are initial and final areas and β is a coefficient of superficial expansion.

Coefficient of superficial expansion,

β = \(\frac{\Delta A}{A \times \Delta t}\)

where, A = area, ΔA = change in area and Δt = change in temperature.

(iii) **Cubical Expansion:**

Expansion in volume on heating is called cubical expansion.

Increase in volume,

0V_{2} = V_{1} (1 + γ Δt)

where, V_{1} and V_{2} are initial and final volumes and γ is a coefficient of cubical expansion.

Coefficient of cubical expansion,

γ = \(\frac{\Delta V}{V \times \Delta t}\)

where V =real volume, ΔV = change in volume and Δt = change in temperature.

Dimension of α, β and γ are same [θ^{-1}] and units are K^{-1} or (°C)^{-1}

Relation between coefficients of linear, superficial and cubical expansions.

β = 2a and γ = 3a

or

α : β: γ = 1 : 2 : 3

2. **Expansion of Liquids**

In liquids only expansion in volume takes place on heating.

(i) **Apparent Expansion of Liquids:**

When expansion of the container containing liquid, on heating is not taken into account, then observed expansion is called apparent expansion of liquids.

Coefficient of apparent expansion of a liquid

(γ_{a}) = \(\frac{\text { apparent(or observed) increase in volume }}{\text { original volume } \times \text { change in temperature }}\)

(ii) **Real Expansion of Liquids:**

When expansion of the container, containing liquid, on heating is also taken into account, then observed expansion is called real expansion of liquids.

Coefficient of real expansion of a liquid

(γ_{r}) = \(\frac{\text { real increase in volume }}{\text { original volume } \times \text { change in temperature }}\)

Both γ_{r} and γ_{a} are measured in °C^{-1}.

We can show that

γ_{r} = γ_{a} + γ_{g}

where, γ_{r} and γ_{a} are coefficient of real and apparent expansion of liquids and γ_{g} is coefficient of cubical expansion of the container (vessel).

**Note:**

Some substances contract with rising temperature because transverse vibration of atoms of substance dominate on the longitudinal vibration which is responsible for contraction.

**Anamalous Expansion of Water**

When temperature of water is increased from 0°C, then its volume decreases upto 4°C, becomes minimum at 4°C and then increases. This behaviour of water around 4°C is called anamalous expansion of water.

3. **Thermal Expansion of Gases**

There are two types of coefficient of expansion in gases

- Volume Coefficient
- Pressure Coefficient

(i) **Volume Coefficient (γ _{V}):**

At constant pressure, the change in volume per unit volume per degree Celsius is called volume coefficient.

γ_{V} = \(\frac{V_{2}-V_{1}}{V_{0}\left(t_{2}-t_{1}\right)}\)

where V_{0}, V_{1} and V_{2} are volumes of the gas at 0°C, t_{1}°C and t_{2}°C.

(ii) **Pressure Coefficient (γ _{p}):**

At constant volume, the change in pressure per unit pressure per degree Celsius is called pressure coefficient.

γ_{p} = \(\frac{p_{2}-p_{1}}{p_{0}\left(t_{2}-t_{1}\right)}\)

where p_{0}, p_{1}, and p_{2} are pressure of the gas at 0°C, t_{1}°C and t_{2}°C.

### Variation of Density with Temperature

Most substances expand when they are heated i.e. volume of a given mass of a substance increases on heating, so density decreases. Hence

ρ ∝\(\frac{1}{V}\),

ρ’ = ρ(1 + γΔT)^{-1}, as γ is small (1 + γΔT)^{-1} ≈ 1 – γΔT

ρ’ ≈ ρ(1 – γΔ T)

**Practical Applications of Thermal Expansion**

- When rails are laid down on the ground, space is left between the end of two rails.
- The transmission cables are not tightly fixed to the poles.
- The iron rim to be put on a cart wheel is always of slightly smaller diameter than that of wheel.
- A glass stopper jammed in the neck of a glass bottle can be taken out by heating the neck of the bottle.

**Thermometry and Calorimetry:**

The thermometer is a device used to check the temperature of an object. This branch of measurement of the temperature of a substance is called thermometry. It is measured in degrees or Fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.