**TYPES OF THERMAL EXPANSION **

There are three types of thermal expansion:

(1) Linear Expansion

(2) Superficial Expansion

(3) Volumetric Expansion

**1-LINEAR EXPANSION**

Expansion in length of solid bodies on heating is called linear expansion.

**MATHEMATICAL REPRESENTATION**

Consider a metallic bar of length “Li” at temperature “Ti”. Let the bar is heated to “T2″. From experiments it is observed that linear expansion depends on two factors:

- The increase in length of a solid bar is directly proportional to its original length.

ΔL ∞ L_{1 ——–} (1)

- The Increase in length is directly proportional to temperature.

ΔL ∞ ΔT —– (2)

Combining (1) and (2),

ΔL ∞ L_{1 }ΔT

OR

**COEFFICIENT OF LINEAR EXPANSION**

It is a characteristic property of a material of solid and is defined as:

“Increase in length per unit original length per Kelvin rise in temperature is known as coefficient of linear expansion.”

It is denoted by “α” (alpha). Value of a’ is constant for a given material but different for different materials. It is independent of mass & dimensions of body. Coefficient of linear expansion depends on the nature of material.

Unit of “α”

1/K or K^{-1}

**2- VOLUMETRIC EXPANSION**

Increase in volume of a body on heating is referred to as Volumetric expansion or Cubical expression.

**MATHEMATICAL EXPRESSION**

Consider a metallic body of volume V_{1}. Let its temperature is released by ΔT, then experimentally:

Increase in volume “ΔV” is directly proportional to its initial volume “V_{1}”.

ΔV ∞ V_{1} ————(1)

Increase in volume “ΔV” is directly proportional to its rise in temperature “ΔT”.

ΔV ∞ ΔT ————(2)

Combining (1) and (2)

ΔV ∞ V_{1} ΔT

“OR”

ΔV = ᵝ V_{1} ΔT

Where “ᵝ” is constant known as “Coefficient of Volumetric expansion”

**EXPRESSION FOR FINAL VOLUME**

We know that,

Final volume = Initial volume + increase in volume |

V |

Putting the value of ΔV

V_{2} = V_{1} + ᵝ V_{1 } + ΔT

V_{2} = V_{1} + (1 + ᵝ + ΔT)

**COEFFICIENT OF VOLUMETRIC EXPANSION**

Coefficient of volumetric expansion (ß) is defined as:

**“Increase in volume per unit original volume per Kelvin rise in temperature is called coefficient of volumetric expansion”**

**Unit of ß**

**1/K or K ^{-1}**

**RELATION BETWEEN “α” AND “ß”**

Coefficient of volumetric expansion is three times the coefficient of linear expansion i.e

**ß**** = 3α**