The coefficient of linear expansion for some common materials are listed in the
ID: 1619049 • 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 7.26 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 steel?Explanation / Answer
For Copper Cylinder,
ALpha A = 16.6*10^-6 per Deg C
Change of length dL = 0.0258 cm
Original length L = 7.26 cm
so
from the Definition of Coefficeint of linear Expansion
A = dL/(L *dT)
dT = change of temperature = dL/(A*L)
dT = 0.0258/(16.6 *10^-6* 7.26)
dT = 214.08 deg C
-------------------------
if it is made of Steel
then
A = dL/(L *dT)
dT = change of temperature = dL/(A*L)
dT = 0.0258/(13 *10^-6* 7.26)
dT = 273.36 deg C