Question

The densities of a liquid at 0${}^0$C and 100${}^0$C are respectively 1.0127 and 1. A specific gravity bottle is filled with 300gm of the liquid at 0${}^0$C up to the brim and it is heated to 100${}^0$C. Then the mass of the liquid expelled in grams is [Coefficient of linear expansion of glass =$9\times {10}^{-6/0}C$]

• A. $\frac{3}{10.1}$
• B. $\frac{3}{1.01}$
• C. $\frac{3.81}{1.0127}$
• D. $\frac{3.81}{0.0127}$

Answer 1

The correct option is B $\frac{3}{1.01}$

${\rho }_{{100}^{\circ }C}=\frac{{\rho }_{0^{\circ }C}}{1+{\gamma }_r\Delta \theta }$

$⟹1=\frac{1.0127}{1+\left({\gamma }_r\right)\left(100\right)}$

$⟹{\gamma }_r=1.27\times {10}^{-4}{/}^{\circ }C$

${\gamma }_a={\gamma }_r-{\gamma }_g={\gamma }_r-3{\alpha }_g={10}^{-4}{/}^{\circ }C$

If the mass spilled out of the bottle due to apparent expansion of liquid is x,

${\gamma }_a=\frac{x}{(300-x)\left(100\right)}$

$⟹x=\frac{3}{1.01}gm$