Question

A 5-m-long cylinder of solid aluminum has a radius of 2 cm.

(a) If the cylinder is at a temperature of 5 °C, how much will the length change when the temperature rises to 30 °C?

(b) Due to the temperature increase, by how much would the density of the aluminum cylinder change?

The density decreases by % upon heating.

c) By what percentage does the volume of the cylinder increase?

The volume increases by % upon heating.

Answer 1

coefficient of linear expansion of aluminium = 22.2 * 10^-6 m/(m K)

change in length / original length = coefficient of linear expansion * change in temperature

change in length / 5 = 22.2 * 10^-6 * (30 - 5)

a) change in length = 0.002775 m

initial density = mass / volume

initial density = mass / (pi * 0.02^2 * 5)

final density = mass / (pi * 0.02^2 * 5.002775)

change in density = mass / (pi * 0.02^2 * 5) - mass / (pi * 0.02^2 * 5.002775)

change in density = 0.0882819969 * mass

% change in density = 0.0882819969 * mass * 100 / (mass / (pi * 0.02^2 * 5))

density is decreased by = 0.0554692146 %

increase in volume = (pi * 0.02^2 * 5.002775 - pi * 0.02^2 * 5) * 100 / (pi * 0.02^2 * 5)

increase in volume = 0.0555 %