Question

An aluminum washer has an outer radius ro = 2.84 cm and an inner radius of ri = 0.58 cm. The temperature of the washer is raised from 343 K to 784 K.

4. What is the change in area of the washer?

Answer 1

Linear Temperature Expansion Coefficient of aluminium , a = 2.22 *10^-5 1/degree C

ro = 2.84 cm

ri = 0.58 cm

change in tempearture , del T = 784 - 343

del T = 441 K

outer radius , ro1 = 2.84 * (1 + 2.22 *10^-5 * 441 )

ro1 = 2.868 cm

new inner radius , ri1 = 0.58 * (1 + 2.22 *10^-5 * 441 )

ri1 = 0.5856 cm

new area, Ai = pi ( 2.868^2 - 0.5856^2) cm^2

Ai = 24.76 cm^2

initial area ,A = pi * (2.84^2 - 0.58^2) cm^2

A = 24.28 cm^2

change in area of washer = 24.76 - 24.28 cm^2

change in area of washer = 0.483 cm^2

the change in area of washer is 0.483 cm^2