Question

a). A spherical brass shell has an interior volume of 1.65 × 10-3 m³. Within this interior volume is a solid steel ball that has a volume of 5.00 × 10-4 m³. The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole is drilled through the brass, and the temperature of the arrangement is increased by 13 °C. What is the volume of the mercury that spills out of the hole? THE ANSWER IS NOT 0.0000019604 m

Answer 1

given that

Vo(brass) = 1.65 × 10^-3 m³
Vo(steel) = 5.0 × 10^-4 m³
Vo(hg) = Vo(brass) - Vo(steel) = 1.15 × 10^-3 m³

we know that the Coefficients of Thermal expansion ( α )
α(brass) = 19 × 10^-6 /C
α(steel) = 13 × 10^-6 /C
α(hg) = 61 × 10^-6 /C

The formula for Volume (bulk) Expansion

∆V
----- = 3α ∆T
Vo

For the Mercury Volume expansion

∆Vв= V_o x 3αx ∆T

      =( 1.15 × 10^-6 m³ )x 3x(61 × 10^-6 /C)x13 (given ΔT=13)
       =2.73 × 10^-9

Volume of steel ball expanded

∆Vs = V_o x 3αx ∆T
         = (5.0 × 10^-4 m³ )x3x(13 × 10^-6)x (13)
        =2.53 × 10^-7