Question

A container is filled to the brim with 1.5 L of mercury at 20

Answer 1

Solution:

Volume of mercury = V1 = 1.5 L.

initial temperature of mercury = t1 = 20 C

Final temperature of the container + mercury= 54 C

Spilled volume of mercury = V2 -V1 = 7.7 mL = 7.7 x 10^-6 m^3

volume of overflow = change in volume of mercury - change in volume of glass

7.7e-6 = [V_m *3*m (54-20) ] - [Vg * 3 * g (54-20)]

Vm=Vg since both the mercury and glass have same initial volume = 1.5 x 10^-3 m^3

=> 7.7e-6 = 3* (1.5e-3) *34( m - g)

=> m - g = 7.7e-6/ 3*(1.5e-3)*34

                    = 7.7 e -6 / 0.153

                   = 0.0000503

=> g = m - 0.0000503

           = 61x10^-6 - 0.0000503

           = 0.00001067 /K

           = 1.1x10^-5 /K =11x10^-6 /K

[Note : volume coefficient of expansion = 3 * linear coefficient of expansion. so we use 3 * ]