Question: One way to construct a device with two points whose separation remains the same in spite of temperature changes is to bolt together one end

One way to construct a device with two points whose separation remains the same in spite of temperature changes is to bolt together one end of two rods having different coefficients of linear expansion as in the arrangement shown in figure.

(a) Show that the distance L will not change with temperature if the lengths L_A and L_B are chosen such that L_A/L_B = a_B/a_A.

(b) If material B is steel, material A is brass, and L_A = 250 cm at 0^oC, what is the value of L?

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