Question

The design of some physical apparatus requires that there be a constant difference in length between an iron and a copper cylinder at any temperature. What should be the length of these cylinders at 0°C for the difference in length to be 10 cm at all temperatures? The coefficient of linear expansion of iron is 1.1 X 10-5/°C, that of copper is l.7 x 10-5/°C.

Answer 1

Answer: For the iron cylinder, 28.3 cm; for the copper, 18.3cm.

Explanation:

The lengths of the iron and copper cylinders at any temperature are

l1 = l01(1 + α1t); l2 = l02(1 + α2t), (1)

where the subscripts 1 and 2 refer to the iron and copper cylinders, respectively.

According to the given conditions

l1 — l2 = 10 and l01 — l02 = 10. (2)

From (1) and (2) it follows that

The initial lengths of the cylinders should be inversely proportional to the coefficients of linear expansion. From (3) and (2) it follows that