Question

Problem: Mercury fills 90% of the volume of a sealed glass container at 20 ?C. What temperature does the glass/Mercury have to be heated so that the mercury completely fills the container? (?Hg = 6x10-5 ?C-1, and ?glass = 0.4x10-5C-1). Show all working.

Answer 1

We have V_m = 0.9V_g (Initial volumes)

We want to heat the mercury and glass till the mercury completely fills the glass container.

Which means V'_m = V'_g

which are the respective final volumes.

The initial temperature = T_i = 20 ^oC = 20 + 273 = 293 K.

Let us denote the final temperature as T_f

Now, the volume expansion equation is given as

For mercury

For glass

Equating V'_m = V'_g, we get

0.9(1 + 3 * 6x10^-5(T_f - 293)) = 1 + 3*0.4x10^-5(T_f - 293)

0.9 + 16.2x10^-5(T_f - 293) = 1 + 1.2x10^-5(T_f - 293)

15x10^-5(T_f - 293) = 0.1

T_f - 293 = 666.67

T_f = 959.67 K

Ans. The glass/mercury needs to be heated upto 959.67 K or 686.67 ^oC.