A piece of metal weighs 46g times g in air. It weighs 30g times g in a liquid of specific gravity 1.24 at 27^(@)C. At 42^(@)C, when the specific gravity of the liquid is 1.20, the weight of the piece immersed in it is 30.5g times g.Find the coefficient of linear expansion (alpha) of the metal.

A piece of metal weighs 46g times g in air. It weighs 30g times g in a

1.	A piece of metal weighs 46g times g in air. It weighs 30g times g in a liquid of specific gravity 1.24 at 27^(@)C. At 42^(@)C, when the specific gravity of the liquid is 1.20, the weight of the piece immersed in it is 30.5g times g.Find the coefficient of linear expansion (alpha) of the metal.
Answer» SOLUTION :Mass of the displaced liquid at `27^(@)C` `""=46-30=16g` Volume of the displaced liquid at `27^(@)C, V_(27)=16/1.24 cm^(3)` Similarly volume of the displaced liquid at `42^(@)C`, `""V_(42)=(46-30.5)/1.20=15.5/1.20cm^(3)` So the volume of the PIECE at `27^(@)C " and " 42^(@)C` are `16/1.24cm^(3) " and " 15.5/1.20cm^(3)` respectively. Now, `V_(42)=V_(27){1+gamma(42-47)}` [where `gamma`= COEFFICIENT of volume expansion of the metal] or, `""15.5/1.20=16/1.24{1+gamma times 15} " or, " 1+15gamma=(15.5 times 1.24)/(1.20 times 16)` or, `"" 15gamma=1.001-1` or, `"" gamma=0.001/15=3alpha` `therefore` Coefficient of linear expansion of the metal, `"" alpha=gamma/3=0.001/45=2.2 times 10^(-5@)C^(-1).`