The coefficient of linear expansion for some common materials are listed in the
ID: 1793654 • Letter: T
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 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 0.0238 cm, the button will be activated, turning on the alarm. Copper 16.6x10^-6 Cast Iron 10.4x10^-6
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
Given
coefficient of linear expansion of copper is alpha = 16.6*10^-6 / 0C
initial length of the cylinder is l0 = 5.51 cm = 0.0551 m
chang ein length of the cylinder due to change in temperature dT is dL = 0.0238 m
initial temperature of the cylinder is T1 = 23 0C
we know from the relation dL = lo*alpha*dT
dT = dL /L0*alpha
T2-T1 = (dL /L0*alpha )
T2 = (dL /L0*alpha )+T1
T2 = (0.0238*10^-2/(0.0551*16.6*10^-6))+(23)
T2 = 283.205 0C
for cast iron
coefficient of linear expansion of cast iron is alpha = 10.4*10^-6 / 0C
initial length of the cylinder is l0 = 5.51 cm = 0.0551 m
chang ein length of the cylinder due to change in temperature dT is dL = 0.0238 m
initial temperature of the cylinder is T1 = 23 0C
we know from the relation dL = lo*alpha*dT
dT = dL /L0*alpha
T2-T1 = (dL /L0*alpha )
T2 = (dL /L0*alpha )+T1
T2 = (0.0238*10^-2/(0.0551*10.4*10^-6))+(23)
T2 = 438.33 0C