# Thermal Expansion

THERMAL EXPANSION.

Thermal expansion is a small, but not always insignificant effect. Typical coefficients are measured in parts per million per kelvin (10-6/K).

Almost all materials expand on heating, the most famous exception being water, which contracts as it is warmed from 0 degrees Celsius to 4 degrees. when water at 00C is heated, it decreases in volume until it reaches 40C. Above 4oC water behaves normally and expands in volume as the temperature is increased. This is referred to as the anomalous behaviour of water.

This is actually a good thing, because as freezing weather sets in, the coldest water, which is about to freeze, is less dense than slightly warmer water, so rises to the top of a lake and the ice begins to form there( on the surface). For almost all other liquids, solidification on cooling begins at the bottom of the container.

Because of the unusual behaviour of water, it is hard for any large body of water to freeze completely. This is made possible, by the layer of ice on the surface, acting as an insulator to reduce the flow of heat out of the water into the cold air.

NOTE: Water expands as it freezes to ice, and this is why pipes break when the water inside them freezes.

Linear Expansivity of Materials.

The coefficient of linear expansion,α is defined as the increase in length per unit length per degree change in temperature, hence

α = ΔL/(LoΔT)

where ΔL is the change in length, Lo is the original length, and ΔT(Tf – Ti) is the change in temperature.

The change in Length,ΔL(L – L0), can be written as:

ΔL = αL0ΔT

where ΔT is the difference between the original temperature and the temperature T, while ΔL is the change in length of the material, and is also equal to how much an Object expands or contracts.

It is customary to choose the standard length Lo to be the length as measured at 0oC.

Then the above equation can be written as

L = Lo (1 +αΔT)

where L is the new Length.

Examples on linear Expansivity

1.An iron of length 50m and at a temperature of 600C is heated to 700C. Calculate its new length .[linear expansivity of iron = 1.2 x 10-5/k]

Solution

Lo=50m, Ti= 600oC, Tf= 700oC, L = ?

L = Lo (1 +αΔT) ,

Substituting the given values into the equation,

L = 50 ( 1 + 1.2 x 10-5 x ( 700 – 600))

L = 50 (1 + 1.2 x 10-5 x 100)

L = 50 ( 1 + 0.0012), 50( 1.0012)

= 50( 1.0012)

L = 50.06m