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 7.51 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 0.0258 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 brass? Material a( 1/°C) Polycarbonate 70.2x10-6 Aluminum 22.2x10-6 Brass 18.7x10-6 Copper 16.6x106 Steel 13.0x106 Cast Iron 10.4x106 Titanium 8.60x106 Glass 5.92x10-6 Number Incorrect. Don't forget that the material is initially at room temperature. 183.7 At what temperature will the alarm be triggered if the cylinder is made out of cast iron? Number 1°c

Answer 1

initial temperature Q = room temperature ) 0 = 23.0°C Original length lä 7.51 cm After heat is supplied change in length is De = 0.0258 cm To find: Temperature at which se becomes 0.0258 cm - Such that it presses button and alarm Starte. - we have formula for linear expansion Dea lo aso mo on 25 18.78 10-6 oct for Brass :: 0.0258 = 7.56 x 187 XL9–6 x (02-02) or, 02-0 =183.713 or 0 = 183.712*23.0 - 16096 1025 206-70J - Answer part a] Similany for part 0 2= 20.4 x 100 %- - for cart iron ng Jormula, De = loa Do or, 000258 = 752x10.4x10-6 (02-23 Lan 02 = 330-33+23:0 202=353:33° 7 Answer part b] Usina

Part C Arca 20.0579 x 0.0847 m2 d=0.807M, K=385 W/m.) Heat Current, that is heat now rate is given by formula, 9 . kl 102-DJA - 3854697.3 -55.9)x(0.0539 X0.0842 0.807 = 96.86 JIS m 96.9 DIS Answer part C7