Question

A glass bottle full of mercury has a mass of 500g being heated through 35 degree celsius. 12.43 g of mercury was expelled Calculate the mass of mercury left in the bottle (cubic expansivity of mecury 1.8 X 10^-4, linear expansivity of glass is 8.0 X10^-6)

Answer 1

volume expansion coefficient of mercury, km = 1.8*10^-4
linear expansion coefficent of glass, kg = 8*10^-6

hence
dT = 35 deg
hence
new radius of glass, r' = r + r*kg*dT
r' = r(1 + kg*dT)

and, new voluem of mercury = V' = V(1 + km*dT)
V = pi*r^2*H
V' - pi*r'^2*H = dV
pi*r^2*H(1 + km*dT) - pi*r^2(1 + kg*dT)^2*H = dV

now dV = 12.43 / 13.69
and pi*r^2*H = 500 / 13.69 = 36.523

36.523(1 + km*dT - 1 - kg^2*dT^2 - 2*kg*dT) = dV
dV = 0.2096391

hence mass left = 500 - 13.69*dV = 497.13 g