Material The coefficient of linear expansion for some common materials are liste
ID: 1462256 • Letter: M
Question
Material 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 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 0.0258 cm, the button will be activated, turning on the alarm Polycarbonate 70.2x106 22.2x106 18.7x106 16.6x10-6 13.0x106 10.4x10-6 8.60x10-6 5.92x106 Aluminum Brass Copper Steel At what temperature will the alarm be triggered if the cylinder is made out of brass? Cast Iron Titanium Glass Number At what temperature will the alarm be triggered if the cylinder is made out of cast iron? NumberExplanation / Answer
delta L = L * (a* delta T)
0.0258 = 5.51* (a* (T-23))
we need to calculate T given the a
for brass:
a = 18.7*10^-6 oC-1
0.0258 = 5.51* (a* (T-23))
0.0258 = 5.51* (18.7*10^-6 * (T-23))
T-23 = 250.4
T= 273.4 oC
Answer: 273.4 oC
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for cast iron:
a = 10.4*10^-6 oC-1
0.0258 = 5.51* (a* (T-23))
0.0258 = 5.51* (10.4*10^-6 * (T-23))
T-23 = 450.2
T= 473.2 oC
Answer: 473.2 oC