Thermal Expansion of Solids

In order to demonstrate the expansion of solid we can use following method

1. The ball and ring experiment
2. The bar and gap experiment

The ball and ring experiment

1st Case: When the ball is not heated then it will pass through the ring very easily because it has a small volume.

2nd Case: When the ball is heated, it will expand and increase in volume, so itwill not pass through the ring.

The bar and gap experiment

1st Case: When the Bar not heated (Not raised with temperature) then the dimension will remain constant.

2nd Case: When the Bar is heated (raised with temperature) then the dimension of the Bar will increase and eventually will not pass thought the Gap.

When a solid is heated, its atoms vibrate faster about their fixed points. The relative increase in the size of solids when heated is therefore small.

Normally Expansion and contraction is accompanied by tremendous forces; The presence of force indicates the expansion and contraction is Resisted.

Bar breaker

1. Consists a strong metal blocker with a pair of vertical jaws J and a strong metal Bar R. The metal bar has a wing nut N at one end and an eye at the other end.
2. The bar is placed between the two pair of Jaws
3. A short cast iron C is inserted in the eye of the bar.
4. The bar is then heated it expands and the wing not screwed to tighten the bar R against the jaws.
5. The bar is then allowed to cool as it cools, it contracts the short cast Iron rod C which presses against the jaws of the bar breaker, Resists the contraction of the Metal bar R.
6. The resistance to the contraction of the bar sets up very large forces, which breaks the short cast Iron rod C in the eye of metal bar, because the contracting bar is trying to pull itself through the small gap in the frame.

The amount by which the linear dimension of a given solid expands depends on:

1. The length of the solid
2. The temperature to which the solid is heated
3. The nature of solid

Definition: The coefficient of linear expansivity ($x$) is the fractional increase in the length of a solid per original length per degree Celsius rise in temperature.

Mathematical formula

$\Delta L = L_0 \times x \times \Delta T$

Where:

• $\Delta L$ = Increase in length
• $L_0$ = Original length
• $x$ = Coefficient of linear expansivity
• $\Delta T$ = Change in temperature

SI Unit of Coefficient of Linear Expansivity:

$^\circ C^{-1} \quad \text{or} \quad K^{-1}$

Example 1

Problem: A copper rod has a length of 40 cm at 22.3°C. What will be its length when the temperature is 30°C? (Given: Linear expansivity of copper $x = 0.000017/^\circ C$)

Solution:

Given:

$L_0 = 40\, \text{cm}$

$\Delta T = 30 - 22.3 = 7.7^\circ C$

$x = 0.000017/^\circ C$

Now apply the formula:

$\Delta L = L_0 \times x \times \Delta T$

$\Delta L = 40 \times 0.000017 \times 7.7 = 0.005236\, \text{cm}$

$L = L_0 + \Delta L = 40 + 0.005236 = \boxed{40.0052\, \text{cm}}$

Table of coefficients of linear expansivity

Applications of expansion of solids in daily life

1. Railway Tracks Small gaps are left between rail segments to allow for expansion on hot days and prevent bending or buckling.
2. Iron Tyres on Wooden Wheels Iron tyres are heated before being fitted on wheels. Heating causes them to expand, and as they cool, they shrink tightly onto the wheel.
3. Bridges and Metal Structures Expansion joints are used to absorb expansion and contraction caused by temperature changes.
4. Thermostats Use bimetallic strips made of two metals with different expansion rates to control temperature automatically.