Question

A spherical steel ball bearing has a diameter of 2.540 cm at 29.00°C. (Assume the coefficient of linear expansion for steel is 11 ✕ 10−6 (°C)−1. )

(a) What is its diameter when its temperature is raised to 96.0°C? (Give your answer to at least four significant figures.) cm

(b) What temperature change is required to increase its volume by 0.800%?

Answer 1

Part A

For any given linear dimension, the change in length is given by

where is the coefficient of linear expansion and is the temperature change.

In this case

The new diameter is

Part B

The volume of a sphere is dependent on the cube of the radius.

Let the sphere be heated through a change in temperature .

Then, let its new radius be , and new volume be

We know that

Now, we write the equations for the initial volume and final volume, and divide to eliminate the constants

Dividing the second by the first, we get

Substituting our values for final volume in terms of the initial volume, and similarly for the radius, we get