A cube of solid aluminum has a volume of 1.00 m3 at 20°C. What temperature change is required to produce a 130 cm3 increase in the volume of the cube?
The linear expansivity of aluminum is 23 x10^-6 /K. Bulk expansivity is 3 x 23 x10^-6 / k For 130 [cm^3] the temperature required is 130 [cm] ^3/ 3 x 23 x10^-6 = 0.00013/[3 x 23 x10^-6] = 1.88 K ========================= If each side of the cube of side 1m expands by e, then its new volume = [1+e]^3 = 1 + 3e + 3e^2 +e^3. Neglecting high powers of e as negligible, the increase in volume is 3e. But e = 23 x10^-6 x rise in temperature 3e = 3*23 x10^-6 x rise in temperature. Given 3e = 0.00013 0.00013= 3*23 x10^-6 x rise in temperature Rise in temperature = 0.00013 / 3*23 x10^-6 = 1.88 K
