Answer to Question #119913 in Physics for Hussain Ousman Darboe

Question

A glass bottle mercury has mass of 500g. On heating through 35 degree Celsius, 2.43g of mercury are expelled. Calculate the mass of mercury remaining in the bottle. (cubic expansivity of mercury is 1.8 ×10^-4 per K and r expansivity of glass is 8×10^-6 per K)

Answer 1

The 500 g consist of mass of the glass and the mass of the mercury:

$$m=m_1+m_2=\rho_1V_1+\rho_2V_2.$$

The volume of the glass will increase while its density will decrease. The volume of mercury will increase as well, while its density will proportionally decrease. Therefore, to solve the problem, we may assume that the 500 g relate to the mercury. Therefore, the mass of mercury remaining in the bottle is

$$m'=500-2.43=497.57\text{ g}.$$