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 grams is: (Coefficient of linear expansion of glass .=9 10⁻⁶ / ^ C )

Step-by-step solution

Density at 0^ C , ₀=1.0127 Density at 100^ C , ₁₀₀=1 Coefficient of real expansion of liquid, _ real = ₀- ₁₀₀ ₁₀₀ t = 1.0127-1 1 100 =0.0127 10⁻²=1.27 10⁻⁴ _ real = _ app + _g _g= coefficient of volume expansion of glass =3 1.27 10⁻⁴= _ app +3 1.27 10⁻⁴= _ app +3 9 10⁻⁶ _ app =1.27 10⁻⁴-27 10⁻⁶=1.27 10⁻⁴-0.27 10⁻⁴=1 10⁻⁴ _ app = mass expelled remaining mass t 1 10⁻⁴= m₁-m₂ m₂ 100 ( m₁ m₂ -1 )=1 10⁻⁴ 100=10⁻² m₁ m₂ =1+10⁻²=1.01m₂= m₁ 1.01 = 300 1.01 Mass expelled =m₁-m₂=300- 300 1.01 = 3 1.01