The coefficient of linear expansion for some common materials are listed in the

Question

The coefficient of linear expansion for some common materials are listed in the table to the right. You would like to design an emergency overheating alarm using one of these materials. In your design, at room temperature (23.0 degree C), a 6.51 cm long cylinder of the material will sit with one end against a wall and the other just barely touching a button. Once the heat causes the cylinder to lengthen by 0.0273 cm, the button will be activated, turning on the alarm At what temperature will the alarm be triggered if the cylinder is made out of copper? At what temperature will the alarm be triggered if the cylinder is made out of cast iron?

Explanation / Answer

here ,

(a)

length of wire , l = 6.51 cm

l = 0.0651 m

change in lenth , ld = 0.0273 * 10^-2 m

room temp ,Tr = 23 degree C

let the final temp be Tf

then ,

change in length = l*change in temp *(heat expansion coefficient)

for copper

heat expansion coefficient = 16.6 *10^-6

so,

0.0273 * 10^-2 = 0.0651 * (Tf - 23) * 16.6 *10^-6

Tf = 275.62 degree C

the alarm will be triggered if the cyclinder is made up of copper at 275.62 degree C

for cast iron

heat expansion coefficient = 10.4 *10^-6

so,

0.0273 * 10^-2 = 0.0651 * (Tf - 23) * 10.4 *10^-6

Tf = 426.226 degree C

the alarm will be triggered if the cyclinder is made up of cast iron at 426.226 degree C

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