[Physics Class Notes] on Coefficient of Linear Expansion Pdf for Exam

What is Coefficient of Linear Expansion?

To put simply, linear expansion is the phenomena of increase in the length of a specimen or material because of the rising temperature of this same material. Consequently, the coefficient of linear expansion is expressed as the per degree Celsius, or change in the length of a 1 unit long material when there is a 10 C rise in temperature. 

 

Coefficient of Linear Expansion Formula

As per the definition, the formula is expressed as 

αL₁ = ∆L / ∆T, or 

αL₁ = dL / dT,

Where, 

• α define coefficient of linear expansion. 

• L₁ is the initial length of the material.

• dL indicates a unit change in length. 

• dT indicates a unit change in temperature.

 

SI unit & Dimension 

The SI unit of coefficient of linear expansion can be expressed as °C^-1 or °K^-1. Here, C indicates Celsius and K indicates Kelvin. 

The dimension of coefficient of linear expansion will be [M^{0}L^{0}T^{0} K^{-1}]

Solved Numericals

1. A metal rod is of length 64.576 cm at a temperature 90°C whereas the same metal rod has a length of 64.522 cm at a temperature 12°C. Calculate the coefficient of linear expansion. 

Ans: Consider L₂ as 64.576 cm and L₁ as 64.5222; then the value of dL will be 0.054. Consider T₂ as 90°C and T₁ as 12°C then the value of dT will be 78. Subsequently, from the formula, α will be 1.073 x 10-5/ °C.

 

Functions of Linear Expansion 

Every material is packed with numerous atoms and the extent to which it can expand entirely depends upon the cohesive force between these particles. In simpler words, if the cohesive force is high, then the expansion in length of the material will be low even when the temperature is increased. 

 

From the above, it can be concluded that the coefficient of linear expansion is an inherent property of a material, and it will vary from one element to another. For instance, soft metals expand quickly as the cohesive force between their atoms is low.

 

Coefficient of Linear Expansion Value for a Few Compounds

Since this is the intrinsic property of a compound, each one has a different value than others, based on their properties. To define coefficient of linear expansion of solid, these have a high coefficient because of the high cohesive force between the atoms in solid. Hard solids have a higher coefficient in the range of 10^-7/K, whereas organic liquids can be in the range of 10^-3/K. 

 

Read on to familiarise yourself with various accessible materials and their coefficient of linear expansion. 

Application 

This concept is popularly used in various industrial applications as well as day to day operations, like opening the lid of a tight bottle by dipping it in hot water. Here are a few other applications related to this same concept. 

• The idea is used in thermometers for measuring temperature. 

• Riveting. 

• Thermostats. 

• Development of firm buildings. 

• In the creation of metal alloys. 

These are a few concepts which will help you understand the idea of the coefficient of linear expansion equation better.

 

To get a better understanding, app can help you get a comprehensive picture of this concept while helping you solve various tricky questions. Download our app to get access to carefully curated study material by proficient teachers.

 

Example question on the concept of the Coefficient of Linear Expansion

Example 1:- At the temperature of 0°C a brass rod was 200 inches long in length and on top of that the coefficient of linear expansion of brass is given at 0·0000188 per degree C, what will be the length of the brass rod at 50°C?

Solution: Given 

Length of the brass rod at the temperature of 0°C = 200 inches.

The Coefficient of Expansion = [ frac{text { Increase/decrease in length} } {text {Original length } } ]  per 1 degree celsius of temperature rise 

From the equation above we can drive the formula for the increase in length

Change in length = 0.0000188 200 50

                               = 0.188 inches. 

Hence the length of the brass rod at the temperature of 50°C is = 200 + 0.188 inches

    = 200.188 inches.