A hole in a brass plate has a diameter of 1.200 cm at 20°C.What is the diameter of the hole when the plate is heated to 220°C? The coefficient of linear thermal expansion for brass is 19 × 10^-6 K^-1. A)1.205 cm B)1.195 cm C)1.200 cm D)1.210 cm

Question

Quizplus · Accepted Answer

The diameter of the hole increases with temperature due to thermal expansion. The change in diameter can be calculated using the formula Δd = d0 * α * ΔT, where Δd is the change in diameter, d0 is the original diameter, α is the coefficient of linear expansion, and ΔT is the change in temperature. Here, d0 = 1.200 cm, α = 19 × 10^-6 /°C, and ΔT = 220°C - 20°C = 200°C. Thus, Δd = 1.200 * 19 × 10^-6 * 200 = 0.00456 cm. The new diameter is 1.200 cm + 0.00456 cm = 1.20456 cm, which rounds to 1.205 cm.

A Hole in a Brass Plate Has a Diameter of 1.200