A piece of metal weighs 46 g in air and 30 g in lipuid of density `1.24 xx 10^3 kg m^(-3)` kept at `27^0C`. When the temperature of the liquid is raised to `42^0C` the metal piece weights 30.5 g . The density of the liqued at `42^0 C` is `1.20 xx 10^3 kg m^(-3)`. Calculate the coefficient of linear expandsion of the metal.

Explanation

At `27^(@)C` : `p_(27)=1.24xx10^(3)kg//m^(3)`
AT `42^(@)C : P_(42)=1.20XX10^(3)KG//M^(3)`
Loss of weight `=pVg`
`46-30=p_(27)V_(27)g`
`46-30.5=p_(42)V_(42)g`
(ii)/(i)
`(p_(42)V_(42))/(p_(27)V_(27))=(46-30.5)/(46-30)=(15.5)/(16)`
`(1.2xx10^(3)xxV_(27)[1+gamma(42-27)])/(1.24xx10^(3)V_(27))=(15.5)/(16)`
`1+15gamma=(15.5xx1.24)/(16xx1.2)=1.00104`
`gamma=(0.00104)/(15)=6.94xx10^(-5)//^(@)C`
`alpha=(gamma)/(3)=2.3xx10^(-5)//^(@)C`