e coefficient of linear expansion for some common materials are listed in ne tab

Question

e coefficient of linear expansion for some common materials are listed in ne 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), a6.26 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 0.0238 cm, the button will be activated, turning on the alarm. Material Polycarbonate 70.2x10 Aluminum 22.2x1 Brass Copper Steel Cast Iron Titanium Glass a( lrc) 0-6 18.7x106 16.6x10-6 13.0x10-6 10.4x106 8.60x106 5.92x10-6 At what temperature will the alarm be triggered if the cylinder is made out of polycarbonate? Incorrect Don't forget that the material is initially at room temperature Number 54.1584 C At what temperature will the alarm be triggered if the cylinder is made out of steel? Number 292.455 C

Explanation / Answer

Here ,

initial length , Lo = 6.26 cm

change in length , x = 0.0238 cm

initial temperature , Ti = 23 degree C

Ti = 23 + 273 = 300 K

for polycarbonate

alpha = 70.2 *10^-6 1/degree C

x = alpha * Lo * (Tf - Ti)

0.0238 = 6.26 * 70.2 *10^-6 * (Tf - 23)

Tf = 77.2 degree C

the temperature will be 77.2 degree C

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for steel ,

alpha = 13 *10^-6 1/degree C

x = alpha * Lo * (Tf - Ti)

0.0238 = 6.26 * 13 *10^-6 * (Tf - 23)

Tf = 315.5 degree C

the temperature will be 315.5 degree C

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