Question

Define the linear expansion in solids due to change in temperature.

Answer 1

Hint: Here we are using the concept of thermal expansion; we know that atoms and molecules in solids are constantly rotating about its equilibrium. When we increase the temperature, the kinetic energy of atoms increases but the potential energy remains the same, the atoms vibrate and move at a higher velocity thus creating a larger average separation between them, this happens because of the increase in temperature. These in turn make solids (mostly metals) increase their length. Its reverse is also true if we decrease the temperature of solids the atoms vibrate and move at lower velocity and thus creating a smaller average separation between them, this happens because of the decrease in temperature.

Complete step by step answer:
There are basically three types of thermal expansion namely linear expansion, area expansion, and volumetric expansion.
The linear expansion is given as: \[\dfrac{{\Delta L}}{L} = {\alpha _L}\Delta T\]
 where L = Initial length of solid, \[\Delta L\]= change in length, \[{\alpha _L}\]= Length expansion coefficient, \[\Delta T\]= Temperature Difference.
Area expansion is given as \[\dfrac{{\Delta A}}{A} = {\alpha _A}\Delta T\]
 where \[\Delta A\]= Change in the area, \[A\]= Area, \[{\alpha _A}\]= Area expansion coefficient, \[\Delta T\]= Temperature Difference.
Volumetric expansion is given as \[\dfrac{{\Delta V}}{V} = {\alpha _V}\Delta T\]
 where \[\Delta V\]= Change in volume, \[V\]= Volume, \[{\alpha _V}\]= Volume expansion coefficient, \[\Delta T\]= Temperature Difference.
The linear expansion is described as the change in the length of the solid due to the change in temperature. For example while in the construction of railway tracks there is always a certain amount of gap given, so that in summers when the temperature is high the railway tracks have space to expand, similarly one may have noticed that in summers the wooden door of a house closes tightly and in winters in fits loose, this is because in summers the temperature is high and in winters the temperature is low. At high temperature the length of the wooden door expands and in winters the length of the wooden door contracts.

Final Answer:
The linear expansion is defined as. \[\dfrac{{\Delta L}}{L} = {\alpha _L}\Delta T\]

Note: Here we have to explain thermal expansion on the molecular level and then we have to relate how thermal expansion at the molecular level makes an increase in the length of the whole solid. Give practical examples and relate them well with the given equation\[\dfrac{{\Delta L}}{L} = {\alpha _L}\Delta T\].