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°C), a 7.01 cm long cylinder of the material will it with one end against a wall and the other just barely touching a button. Once the heat causes the cylinder to lengthen by 0.0243 cm, the button will be activated, turning on the alarnm Material Polycarbonate 70.2x106 Aluminum 22.2x106 Brass Copper Steel Cast Iron Titanium Glass 18.7x106 16.6x106 13.0x106 10.4x106 8.60x10-6 5.92x106 At what temperature will the alarm be triggered if the cylinder is made out of brass? Number At what temperature will the alarm be triggered if the cylinder is made out of cast iron? Number

Explanation / Answer

Change in length due to temperature is given by:

dL = L0*alpha*dT

for Brass

alpha = 18.7*10^-6

dL = 0.0243 cm

L0 = 7.01 cm

dT = Tf - Ti = dL/(L0*alpha)

Tf = Ti + dL/(L0*alpha)

Tf = 23 + 0.0243/(7.01*18.7*10^-6)

Tf = 208.37 C

for Cast iron

alpha = 10.4*10^-6 C

Tf = 23 + 0.0243/(7.01*10.4*10^-6)

Tf = 356.31 C

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