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.

Options

A. `1.3 xx 10^(-3) //""^(@)C`
B. `5.2 xx 10^(-3) // ""^(@)C`
C. `2.6 xx 10^(-3)//""^(@)C`
D. `0.26 xx 10^(-3)//""^(@)C`

Answer

C

Explanation

`V_(30^@C) = ("Loss of weight")/("Specific gravity" xx g) = ((45 - 25)g)/(1.5 xx g) = 13.33 cm^(3)`
`V_(40^@ C) = ((45 - 27) xx g)/(1.25 xx g) = 14.40 cm^3`
`therefore V_(40) = V_(30) [ 1 + gamma (Delta T)]`
`rArr gamma = (V_40 - V_30)/(V_30 (t_2 -t_1)) = (14.4 - 13.33)/(13.33 (40-30)) = 8.03 xx 10^(-3)//""^(@)C`
`therefore alpha = (gamma)/(3) = (8.03 xx 10^(-3))/(3) = 2.6 xx 10^(-3) //""^(@)C`