A brass cube,9 cm on a side,is raised in temperature by 226°C.The coefficient of volume expansion of brass is 57 × 10−⁶/C°.By what percentage is any one of the 9-cm edges increased in length? A) 0.32% B) 3.85% C) 0.43% D) 1.73% E) 2.25%

Question

Quizplus · Accepted Answer

First, we need to find the change in volume of the brass cube:

ΔV/V₀ = γΔT
where ΔV/V₀ is the fractional change in volume, γ is the coefficient of volume expansion, and ΔT is the change in temperature.

ΔV/V₀ = (57 × 10⁻⁶ K⁻¹)(226°C) = 0.012882

Next, we can use the fact that the cube has 6 faces of equal area A=9cm², and that the change in volume is equal to the change in each edge length cubed:

ΔV = (Δl)³ = 6A(Δl)

0.012882 = 6(9)(Δl)

Δl/l₀ = 0.000537 = 0.0537%

So any one of the 9-cm edges is increased in length by 0.0537%, which is closest to choice C (0.43%).

A Brass Cube,9 Cm on a Side,is Raised in Temperature