Volume Thermal Expansion Question ?

[cheechnchong]

Volume Thermal Expansion Question!??

a spherical brass shell has an interior volume of 1.60 x 10^-3 m^3. Within this interior volume is a solid steel ball that has a volume of 0.70 x 10^-3 m^3. 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 12 degrees celsius. What is the volume of the mercury that spills out of the hole?

B(brass) = 57 x 10^-6 (degrees celsius)^-1
B(mercury) = 182 x 10^-6 (degrees celsius)^-1
B(steel) = 36 x 10^-6 (degrees celsius)^-1

My Approach:

Change in Velocity = mercury(BVchangeT) - steel(BVchangeT) - brass(BVchangeT)

= (1.6 x 10^-3 - 0.7 x 10^-3)m^3 (182 x 10^-6 celsius^-1)(12 celsius) - (36 x 10^-6 celsius^-1) (0.7 x 10 m^3)(12 celsius) - (1.60 x 10^-3 m^3)( 57 x 10^-6 celsius^-1)(12 celsius)

= 5.70 x 10^.7 m^3

Let Me know if this number is right. I really struggled on this one...kinda tricky for me!

 

[Doc Al]

My Approach:

Change in Velocity = mercury(BVchangeT) - steel(BVchangeT) - brass(BVchangeT)

I assume you meant volume, not velocity!

In any case, you want to compare the increase in volume of the mercury to the increase of volume of the space between steel ball and brass shell: spillover volume = change in mercury volume - change in interior volume.

That change in interior volume is given by: change in brass volume - change in steel volume. Rewrite your equation, being more careful with your signs.