A piece of metal weighs `50g` in air. It weighs `45g` when immersed in a liquid at `25^(@)C`, and `45.1 g" at " 100^(@)C.` If the coefficient of linear expansion of the metal is `12 times 10^(-6@)C^(-1)`, find the coefficient of real expansion of the liquid.

Explanation

Apparent loss in weight at `25^(@)C`
`=M_(1)g=(50-45)g times g=5g times g`
Apparent loss in weight at `100^(@)C`
`=M_(2)g=(50-45.1)g times g=4.9 g times g`
As `" " M_(2)=M_(1)[1-(gamma-gamma_(s))(t_(2)-t_(1))]`
`therefore " " 4.9=5[1-(gamma-12 times 10^(-6) times 3)(100-25)]`
or, `therefore " " 4.9=5[1-(gamma-12 times 10^(-6) times 3) times 75] [" as " gamma_(s)=3 times alpha_(s)]`
or, `" " (gamma-36 times 10^(-6)) times 75 times 5=5-4.9`
or, `" " gamma-36 times 10^(-6)=0.1/(75 times 5)`
or, `gamma=36 times 10^(-6)+2.67 times 10^(-4)=3.03 times 10^(-4@)C^(-1).`