A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods 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

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 0ºC. 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 120.0 cm throughout. The temperature is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are 2.0 Å~ 10-5 K-1 and 2.4 Å~ 10-5 K-1, respectively. In the figure, the temperature at which contact of the rods barely occurs, in degreeC, is closest to?

Explanation / Answer

L = L0_1*(1+a_1*delT) + L0_2*(1+a_2*delT) = 120
L0_1 = 69.5 cm
L0_2 = 49.3 cm
a_1 = 2e-5
a_2= 2.4e-5

(L - L0_1 - L0_2) = L0_1*a_1*delT + L0_2*a_2*delT
delT = (L-L0_1-L0_2)/(L0_1*a_1 + L0_2*a_2)
delT = (120 - 69.5 - 49.3) /(69.5*2e-5+49.3*2.4e-5)
delT = 446.3454. C ~ 446C

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