A bolt hole in a brass plate has a diameter of 1.2 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 per degree C.)

Question

Quizplus · Accepted Answer

The diameter of the hole at the new temperature can be calculated using the formula for linear expansion: $\Delta L = L_0 \alpha \Delta T$, where $\Delta L$ is the change in length (diameter in this case), $L_0$ is the original length (1.2 cm), $\alpha$ is the coefficient of linear expansion (19 × 10^-6 /°C), and $\Delta T$ is the change in temperature (220°C - 20°C = 200°C). Plugging in the values: $\Delta L = 1.2 \times 19 \times 10^{-6} \times 200 = 0.00456$ cm. Adding this change to the original diameter gives a new diameter of 1.20456 cm, which rounds to 1.205 cm.

A Bolt Hole in a Brass Plate Has a Diameter