Question

You have two equal length rods of aluminum and steel which are to be heated separately. What temperature, in degrees Celsius, would the steel need to be heated to so that its length increases by the same amount as aluminum at 1000 degrees Celsius? Assume both start at 20 degrees Celsius. Linear expansion coefficients: aluminum = 2.55x 10^-5 1/*C, steel = 1.2 x 10^-5 1/*C.

Answer 1

Put 1000 in the aluminum formula find the expansion. Then equate that for the steel equation and find the temperature

Answer 2

Or another way: Steel expands 1.2 / 2.55 as much as aluminum, so must have temp increase 2.55 / 1.2 times as much. The aluminum rod had 980 degrees temp increase, so the steel rod must have 2.55 / 1.2 * 980 degrees increase (above 20).