Thermal Expansion · 6 min read

Linear expansion

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Introduction to expansion

Have you noticed how electric poles' wires sag more during a very hot afternoon than at night? Or why there are gaps in railway tracks? This happens because solids grow longer when they get hot. This increase in length is what we call Linear Expansion.

When you heat a metal rod, the tiny particles inside start vibrating faster and pushing each other apart. This makes the whole rod stretch. Some materials, like copper, stretch a lot, while others, like steel, stretch only a little.

What is Linear Expansion

Simply put, linear expansion is how much longer a wire or rod becomes when its temperature goes up.

Linear Expansivity

Not all metals expand at the same rate. We use a number called Linear Expansivity (represented by the Greek letter alpha, alpha) to measure how much a material expands. A material with a high expansivity will grow very long with just a little heat.

It is a constant for each material and its unit is per Kelvin (K^-1) or per degree Celsius (°C^-1).

Mathematical Formula

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To calculate how much a rod expands, we use this formula:

Linear Expansivity (alpha) = (Change in Length) / (Original Length x Temperature Change)

We can also write it as: alpha = (L₂ - L₁) / (L₁ x (theta₂ - theta₁))

Where L₁ is the starting length, L₂ is the new length, theta₁ is the first temperature, and theta₂ is the final temperature.

Worked Example

A copper rod has an original length of 10.0 meters at a temperature of 20°C. If it is heated until it reaches 70°C, and the linear expansivity of copper is 0.000017 K^-1, calculate the new length of the rod.

1. Identify the given values: L₁ = 10 m, theta₁ = 20°C, theta₂ = 70°C, alpha = 0.000017 K^-1.

2. Calculate temperature change (delta theta): 70 - 20 = 50 K.

3. Use the formula for expansion: Change in length (e) = alpha x L₁ x delta theta.

4. Calculate: e = 0.000017 x 10 x 50 = 0.0085 m.

5. Find new length (L₂): L₁ + e = 10 + 0.0085 = 10.0085 meters.

Key points

•Linear expansion refers to increase in length only.
•The unit of linear expansivity is K^-1 or °C^-1.
•Different materials have different rates of expansion.
•The increase in length depends on the original length and the rise in temperature.