Question

A brass cube, 10 cm on a side, is raised in temperature by 150°C. The coefficient of volume expansion of brass is 57 × 10−6/°C. By what percentage is any one of the 10-cm edges increased in length?

Answer 1

Answer: To find the percentage increase in the length of any one of the 10-cm edges of the brass cube, we can use the coefficient of volume expansion and the formula for volumetric expansion.

Given data:

Side length of the brass cube (L) = 10 cm = 0.1 m

Temperature change (ΔT) = 150°C

Coefficient of volume expansion (β) for brass = 57 × 10^-6/°C

The volumetric expansion (ΔV) of a solid is given by:

ΔV = V₀ * β * ΔT

where V₀ is the initial volume of the solid.

For a cube, the initial volume (V₀) is given by:

V₀ = L³

Now, let's calculate ΔV and the final volume (V_f) of the cube:

ΔV = (0.1 m)^3 * 57 × 10^-6/°C * 150°C

ΔV ≈ 0.001281 m³

V_f = V₀ + ΔV

V_f = (0.1 m)^3 + 0.001281 m³

V_f ≈ 0.001381 m³

The final side length of the cube (L_f) is given by:

L_f = (V_f)^(1/3)

L_f ≈ (0.001381 m³)^(1/3) ≈ 0.109 m

Now, let's find the increase in length (ΔL) of any one of the 10-cm edges:

ΔL = L_f - L

ΔL ≈ 0.109 m - 0.1 m ≈ 0.009 m

Finally, we can calculate the percentage increase in length:

Percentage increase = (ΔL / L) * 100

Percentage increase ≈ (0.009 m / 0.1 m) * 100 ≈ 9%

Therefore, any one of the 10-cm edges of the brass cube increases in length by approximately 9%.