# Thermal Expansion

With the increase in temperature of a body, there is an increase in its dimension also. This property is known as thermal expansion. The thermal expansion of a body can be studied as a function of temperature.

One of the common examples of thermal expansion is seen while opening a tight metal jar lid. People often loosen a tight metal jar lid by holding it under hot water. By doing so, the metal of the lid and the glass of the jar, both expand because the hot water adds energy to their atoms. But the metal expands more as compared to glass and gets loosen up.

## Types Of Thermal Expansion

Linear expansion

Now let us consider a rod at a temperature T and suppose its length is L at the same temperature. When the temperature is increased to ($T + ?T$), the length also increases to ($L~ +~ ?L$).

$frac{Delta L}{L}$ = $?~ ?T$

Where,

$?$ is a constant called the coefficient of linear expansion. Unit of $?$ is ‘per degree’ or ‘per Kelvin’. It depends on the material.

Area expansion

$frac{Delta A}{A}$= $2? ~?T$

Here $2?$ is the coefficient of surface expansion.

Volume expansion

$frac{Delta V}{V}$ = $3?~ ?T$

Here $3?$ is the coefficient of volume expansion.

Example: Suppose two rods of different materials are placed between massive walls as shown in the figure.  The cross-section of the rods is $A$, and their respective lengths are $L_1$ and $L_2$. The temperature increases by $t$. Now we have to calculate the force which the rods will exert on each other if the coefficient of linear thermal expansion is $?_1$ and $?_2$, and modulus of elasticity are $E_1$ and $E_2$ respectively.

The total increment in the length of the rods when the temperature is increased is:

$?L$ = $?L_1~+~?L_2$

= $(?L_1~+~?L_2)~t$

= $?t~(L_1~+~L_2)$    ……………… (1)

Compression by the same amount $?L$ will reduce the length of the rods by $?L’_1$ and $?L’_2$ such that

$?L’_1~+~?L’_2$ = $?L$        ………………… (2)

This will require some force, say $F$ $F$ = $frac{E_1 A Delta L’_1}{L_1}$ = $frac{E_2 A Delta L’_2}{L_2}$  ……… (3)

The value of force F can be calculated using the equations 1, 2, and 3.

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