Physics 1 question on finding density of copper cube

Question

A copper cube with density 8.96 ✕ 10³ kg/m³ and mass 20.0 kg at 29.0°C is heated to 150°C.

What is the density of the copper cube at this new temperature? (Give your answer to at least three significant figures.)

Answer 1

The mass of the copper will not change, but the volume will change due to thermal expansion. We can calculate the new density (mass/volume) by dividing the mass by the new volume. To find the new volume we need to know the coefficient of volumetric expansion copper. Tabular value from the internet is 51.0x10^-6 /ºC. Your value may be slightly different.

To find the new volume, we will use V2 = V1(1 + ß∆T)

V2 = new volume

V1 = initial volume = mass/density = 20.0 kg / 8.96x10³ kg/m³ = 2.232x10^-3 m³

ß = coefficient of volumetric expansion = 51.0x10^-6 /ºC

∆T = change in temperature = 150º - 29.0º = 121º

Solving for V2, we have...

V2 = 2.232x10^-3 m³ (1 + 51.0x10^-6 /ºC * 121º)

V2 = 2.232x10^-3 m³ (1.006) = 2.245x10^-3m³

New density = mass/V2 = 20.0 kg / 2.245x10^-3m³ = 8909 kg / m³ = 8.91x10³ kg/m³

(be sure to check all of the math, and remember if you use a different value for the coefficient of expansion, your answer will be different.)