The densities of a liquid at `0^(@)C` and `100^(@)C` are respectively `1.0127` and 1. A specific gravity bottle is filled with 300 g of the liquid at `0^(@)C` upto the brim and it is heated to `100^(@)C`. Then, the mass of the liquid expelled in gram is
Coefficient of linear expansion of glass `= 9 xx 10^(-6)//^(@)C`)

Options

A. `(3)/(10.1)`
B. `(3)/(1.01)`
C. `(3.81)/(1.0127)`
D. `(3.81)/(0.0127)`

Answer

B

Explanation

Coefficient of real expansion`= (Po-P100)/(P100xxDeltat)`
`gamma_(real) =(1.0127-1)/(1xx100)=0.0127xx10^(-2)`
`gamma_(app)=gamma_(real)+gamma_(g)`
`= gamma_(real) +(3 alpha)`
`= (0.0127xx10^(-2)) + (3xx9xx10^(-6))=1xx10^(-4).`
`gamma_(app) = ("Expelled liquid")/("Remaining liquid "xx Deltat)`
`1xx10^(-4)= (m_(1)-m_(2))/(m_(2)xxDeltat)`
`1xx10^(-4)=(300-m_(2))/(m_(2)xx(100)`
`m_(2)= (300)/((1+0.01))=(300)/(1.01)`
`therefore` Expelled liquid, `m_(1)-m_(2)=300-(300)/(1.01)=(3)/(1.01)`