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Thermal Expansion

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Thermal Expansion - Lesson Summary

An increase in the dimensions of a body due to an increase in its temperature is called thermal expansion.
Examples of thermal expansion:
Rails are produced in fixed lengths and fishplates are used to join them.
The gaps provided between rails allow them to expand during summer.
Expansion joints are provided while constructing bridges.
When the temperature of any metallic body is increased, its length, surface area and volume may increase.
Expansion along length is defined as linear expansion.
Expansion of the surface area of a solid is called areal expansion and expansion of its volume is called volume expansion or cubical expansion.
Let us consider a thin metal rod of length L at a temperature T.
It is experimentally observed that the change in the length of the rod (D L) is directly proportional to the change in its temperature, (D T) and also directly proportional to the initial length of the rod.
Thus we get
, where  is the proportionality constant called coefficient of linear expansion and is characteristic of the material of the rod.
The fractional change in length
Similarly, the fractional change in the area is experimentally found to be directly proportional to the change in the temperature.

therefore fractional change in the area
, where is the coefficient of areal expansion.
If the volume of a solid body is “V” and “D V” is the change in volume for a change of temperature “D T then

  , where alpha V is called the coefficient of volume expansion.
Though the coefficient of expansion is a characteristic of the substance, its value depends on its temperature.
Substances that expand at the same rate in all directions are called isotropic substances.
For a perfect isotropic material, the coefficients of thermal expansion are related as

Let us now look at the expansion of solids at an atomic level.
In a solid, the atoms are arranged in fixed positions.
Potential energy curve is an asymmetric curve, the average separation between atoms increases as temperature increases.
As liquids do not have a specific shape, they do not have linear and areal expansion as solids do. They have expansion in volume only.

Unlike other liquids, water exhibits irregular expansion between zero degrees Centigrade and four degrees Centigrade.
If the temperature of water is raised from zero degrees Centigrade to four degrees Centigrade instead of expanding, it actually contracts.
This means a given mass of water occupies least volume and as a consequence will have maximum density at four degrees Centigrade.
This anomalous expansion of water enables aquatic animals and plants to survive in winter.
For ideal gas,  

For gases, the coefficient of volume expansion is inversely proportional to the absolute temperature of the gas.
The stress developed in a body when not allowing it to expand while heating is called thermal stress.


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