The coefficient of linear expansion for some common materials are listed in the
ID: 1632579 • 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 degree C), a 5.01 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. 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
Coefficient of thermal expansion of copper = 16.6*10-6 /oC
Length of cylinder at 23oC = 5.01 cm
Lengthened length of cylinder = 5.01+0.0258 = 5.0358 cm
5.0358 = 5.01(1+16.6*10-6*(T-23))
T = 333.22oC
Alarm will be trigerred at 333.22 oC
Coefficient of thermal expansion of cast iron = 10.4*10-6 /oC
Length of cylinder at 23oC = 5.01 cm
Lengthened length of cylinder = 5.01+0.0258 = 5.0358 cm
5.0358 = 5.01(1+10.4*10-6*(T-23))
T =518.16 oC
Alarm will be trigerred at 518.16 oC