Question

Consider a solid copper sphere that is 15.8 cm in diameter at 97°C. By how much will its volume change if it is cooled to 19°C?

Answer 1

Change in Volume due to temperature change is given by:

dV = V0**dT

= Volume expansion coefficient = 3*

= linear expansion coefficient of copper = 17*10^-6 /C

So, = 3* = 3*17*10^-6 = 51*10^-6 /C

dT = Final temperature - Initial temperature = Tf - Ti

dT = 19 - 97 = -78 C

V0 = Initial Volume of sphere = 4*pi*R^3/3

R = radius of sphere = 15.8/2 = 7.9 cm = 0.079 m

So,

dV = (4*pi*0.079^3/3)*(51*10^-6)*(-78)

dV = -8.22*10^-6 m^3 = -8.22 cm^3 (-ve sign means Volume is reduced)

So Volume of sphere is reduced by 8.22 cm^3

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