A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods a
ID: 1421319 • Letter: A
Question
A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0 C. The rods are placed in line with a gap of 1.2 cm between them. The distance between the far ends of the rods is maintained at 120 cm throughout. The temperature is raised until the two rods are barely in contact. The coefficient of linear expansion of brass and aluminum are 2.0 * 10^-5 and 2.4 *10 ^-5, respectively. What is the temperature at which contact of the rods barely occurs, in Celsius?
Explanation / Answer
we know that
L1 = Lo1*(1 + a1 t)
L2 = Lo2*(1 + a2 t)
L1 + L2 = d =120 cm
Solving
t = {d - (Lo1+Lo2)}/(a1Lo1+a2Lo2)
t = (120 -118.8)/(2*69.5 + 2.4*49.3)*10^-5 = 466 °C
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