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Explain linear expansion . |
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Answer» Solution :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. |
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