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 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 0.0233 cm, the button will be activated, turning on the alarm.

A)At what temperature will the alarm be triggered if the cylinder is made out of aluminum?

B)At what temperature will the alarm be triggered if the cylinder is made out of glass?

Note:both are measured in Celsius

Explanation / Answer

Given: length of rod (at 230C) L0 = 5.51 cm ; change in length needed (L) = 0.0233 cm

Now coefficinet of linear expansion of aluminium (a) = 22.2*10-6 m/m-0C

and coefficinet of linear expansion of glass (g) = 4*10-6 m/m-0C

(a) we have the equation   L = L0*a*T where T is the rise in temperature

so   T = 0.0233/5.51*22.2*10-6 = 190.50C so the actual final temperature T = 23 + 190.5 = 213.50C

(b) again   L = L0*g*T or   T = 0.0233/5.51*4*10-6 = 1057.20C   

so final temperature T = 1057.2 + 23 = 1080.20C

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects