An aluminum sphere is 8.35 cm in diameter. What will be its change in volume if it is heated from 30 degrees celsius to 200 degrees celsius?
Change in volume = (Coefficient of volume expansion) x (Original volume) x (Change in temperature)
Original volume = 4/3(pi)(r)^3 where r= 4.175cm, and this would make V= 304.8 cm^3.
For aluminum, the coefficient of volume expansion is 75x10^-6 /degC. (This is three times the coefficent of linear expansion).
The change in temperature is 200-30 = 170 degC.
Plugging it in,
Change in volume = (75x10^-6 /degC) x (304.8 cm^3) x (170 degC)
Change in volume = 3.887 cm^3.
Hope this helps, and I hope all my math is right. 🙂Source(s): Giancoli's book, "Physics for Scientists & Engineers with Modern Physics 4th ed."
Chapter 17.4, on pages 460-461.