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Question:

Two rods A and B of identical dimensions are at temperature 30°C. If A is heated up to 180°C and B up to T°C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4:3, then the value of T is?

270oC

230oC

250oC

200oC

Solution:

Δl1 = Δl2
lα1ΔT1 = lα2ΔT2
α1/α2 = ΔT2/ΔT1
4/3 = (T - 30)/(180 - 30)
4/3 = (T - 30)/150
4 * 150 = 3 * (T - 30)
600 = 3T - 90
690 = 3T
T = 230°C