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# Thermal Expansion Formula

Thermal expansion is a very common natural phenomenon. It occurs when an object expands and becomes larger due to a change in the object’s temperature. This is done due to the heat generated by the temperature. Temperature is the average kinetic or movement of the energy of the molecules in a substance. A higher temperature means that the molecules are moving faster on the average. If we heat up an object, the molecules move faster and. As a result, they take up more space. The molecules tend to move into areas that were previously empty. Hence due to this the size of the object increases. In this topic, we will discuss the Thermal Expansion Formula with examples. Let us learn the concept!

Source: en.wikipedia.org

## Thermal Expansion Formula

### Concept of Thermal Expansion:

Thermal expansion describes the tendency of an object to change in its area, volume as well as shape to a shift in temperature through a transfer of heat. Heat is a consistently decreasing function of the average molecular kinetic energy of an object. Heating up a substance increases its kinetic energy.

Thermal expansion leads to changes in dimension either in length or volume or area. Therefore, there are three types of thermal expansion. These are named as Linear expansion, Area expansion, and Volume expansion. Generally, all three expansions are occurring in solid. In liquid material, such expansions are more probable.

### The Formula for Thermal Expansion:

• Linear Expansion: Linear expansion occurs when there is a change in length. Linear expansion formula is given as,

$$\frac{\Delta L}{L_0} = \alpha_L \Delta T$$

Where,

 $$L_0$$ Original length, L Expanded length, $$\alpha_L$$ Length expansion coefficient, $$\Delta T$$ Temperature difference, $$\Delta L$$ Change in length.

• Volume expansion: It occurs when there is a change in volume due to temperature. Volume expansion formula is given as:

$$\frac{\Delta V}{V_0} = \alpha_V \Delta T$$

Where,

 $$V_0$$ Original volume, V Expanded volume, $$\alpha_V$$ Volume expansion coefficient, $$\Delta T$$ Temperature difference, $$\Delta V$$ Change in volume.

• Area expansion: It occurs when there is any change in area due to temperature change. Area expansion formula is given as,

$$\frac{\Delta A}{A_0} = \alpha_A \Delta T$$

Where,

 $$A_0$$ Original area, A Expanded area, $$\alpha_A$$ Area expansion coefficient, $$\Delta T$$ Temperature difference, $$\Delta A$$ Change in area.

## Solved Examples

Q.1: A 4m long rod is heated to 40 degrees C. If the length of the rod expands to 6m after some time, calculate the thermal expansion coefficient for length. Given room temperature is 30 C.

Solution:

Given:

Initial length of the rod , $$L_0 = 4 m$$,

Expanded length of the rod, L = 6 m

Change in length $$\Delta L = 6 – 4 = 2 m$$

Temperature difference $$\Delta T$$

= 40 C – 30 C  = 10 C

= 10 C + 273 K

= 283 K

The linear expansion formula is given by,

$$\frac{\Delta L}{L_0} = \alpha_L \Delta T$$

Rearranging ythe above formula to get Length expansion coefficient: we get,

$$\alpha_L = \frac{\Delta L}{L_0} \times \frac{1}{\Delta T}$$

= $$\frac{ 2 }{4} \times \frac{1}{ 283 }$$

=$$\frac {1}{566}$$

= $$0.0017\; K^{-1}$$

Therefore, thermal expansion coefficient for length will be $$0.0017 \; K^{-1}$$.

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