Increase in length of substance `(Deltal)` is directly proportional to original length ..l.. and increase in temperature `..DeltaT..`,
`:.Deltalalphal" and "Deltal alphaDeltaT`
`:.DeltalalphalDeltaT` (combinely)
`:.(Deltal)/(l)alphaDeltaT`
Hence, the fractional change in length. `((Deltal)/(l))` is directly proportional to `DeltaT`.
`:.(Deltal)/(l)propDeltaT`
`:.(Deltal)/(l)=alpha_(l)DeltaT`
`:.Deltal=alpha_(l)lDeltaT` . . . . (1)
Where `alpha_(l)` is coefficient of linear expansion and is characteristic of material.
Value of `alpha_(l)` depends on type of material and temperature.
If the temperature difference is not large then `.alpha_(l).` doesn.t depend on temperature.
Unit of `alpha_(l)` is `(""^(@)C)^(-1)` or `K^(-1)`.
In equation (1), `Deltal=l_(2)-l_(1)` and `DeltaT=T_(2)-T_(1)`,
`l_(2)=l_(1)=alpha_(l)l_(1)(T_(2)-T_(1))`
`:.l_(2)=l_(1)+alpha_(l)l_(1)(T_(2)-T_(1))`
`:.l_(2)=l_(1)[1+alpha_(l)(T_(2)-T_(1))]`
By taking `alpha_(l)=alpha` and `l_(1)=l`
`l_(2)=l[1+alpha(T_(2)-T_(1))]`
In above table, special average values are given for some elements for `0^(@)C` to `100^(@)C` temperature interval.
From this table, if `alpha_(l)` for glass and copper are compared, then it is seen that for the same increases in temperature, copper expands 5 times more than glass.
In general, expansion is more in metals and their values of `alpha_(l)` are high.
