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 5.51 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 0.0268 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 polycarbonate? At what temperature will the alarm be triggered if the cylinder is made out of glass?

Explanation / Answer

given

T1 = 23 C

L1 = 5.51 cm

delta_L = 0.0268 cm

T2 = ?

a) for polycarbonate,

delta_L = L1*alfa*(T2-T1)

delta_L/(L1*alfa) = T2 - T1

==> T2 = T1 + delta_L/(L1*alfa)

= 23 + 0.0268/(5.51*70.2*10^-6)

= 92.29 C <<<<<<----------Answer

b)

for glass,

delta_L = L1*alfa*(T2-T1)

delta_L/(L1*alfa) = T2 - T1

==> T2 = T1 + delta_L/(L1*alfa)

= 23 + 0.0268/(5.51*5.92*10^-6)

= 844.6 C <<<<<<----------Answer

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