Linear Expansion of Solids

This article mainly discusses the linear expansion of solids. But to properly enter that topic, we have to get a proper idea about what is the thermal expansion of matter and why it happens.

Thermal expansion of matter

When the matter is supplied heat, if the volume of the matter increases with the temperature, it is called a thermal expansion.

The thermal expansion can be a,

• solid expansion,
• liquid expansion, or
• gaseous expansion.

Why does thermal expansion in matter happen?

Very matter exists made out of atoms. When heat energy is provided to any kind of matter including solid, liquid, and gaseous matter, the kinetic energy of atoms that are in the material will be increased. As a result of this increment of kinetic energy, the vibration frequency of atoms will be increased. Also moving distance of atoms will be increased. So the distances between atoms will be increased.

Thermal expansion will affect differently to solids, liquids, and gases. Therefore because of thermal expansion in matter,

• increment in length, surface area, and volume in solids
• Increment in the volume of liquids
• Increment in pressure in gas (in constant volume), increment in volume of gas (at constant pressure).

Thermal expansion of solids

When heat is supplied to a solid, a solid matter will increase its length, surface area, and volume. So there are three types of solid expansion.

1. Linear expansion of solids
2. Superficial expansion (Area expansion) of solids
3. Volume expansion of solids

Linear expansion of solids

When the heat is supplied to an object like a rod, it shows an increase in length. This is known as the linear expansion of solids. Mathematically, when the temperature is increased by Δθ degrees, of a rod-like object with the length of 'l', if it shows the increase of length by Δl, the increase in length is proportional to the initial length and the temperature difference.

Where,

• l - Initial length of the rod
• Δ l - Increase in length
• Δθ - Increase in temperature
• α - Linear expansion coefficient

The linear expansion coefficient (The linear temperature expansion coefficient) - α

The linear expansion coefficient is the proportional coefficient that expresses the ratio between the increased length and the original length when the temperature is increased by one degree of Kelvin or Celsius. Linear temperature expansion coefficient is a material property.

Consider a rod with the length of l₁ at temperature θ₁. When this rod is heated up to θ₂, the length would be l₂. If the linear expansion coefficient of the material is α, the final length of the rod can be expressed in terms of the linear expansion coefficient.

Linear expansion coefficients (α) of different solid materials

Functionality of a bimetallic strip

Two metallic strips with the same dimensions but different linear expansion coefficients are joined together. When it is heated, two metals are expanded according to their linear expansion coefficients. The metal with a higher thermal expansion coefficient will show a higher increase in length than the other metal. This will result in a bend in the bimetallic strip.

Bimetallic strips are used in some electric circuits to protect the device from high heat. When the temperature increases, the bimetallic strip will bend and the circuit will be disconnected. Thus, the temperature is decreasing and the bimetallic strip will become the original state. Therefore, the circuit is connected again.

Solving questions about the Linear expansion of solids

Question 01

When the temperature of a rod is increased by 100 °C, it will show 0.002 of rational increase in length. What is the linear expansion coefficient of the material?

Answer