Question

A building made with a steel structure is 582 m high on a winter day when the temperature is 0◦F. How much taller is the building when the temperature is 120◦F? The linear expansion coefficient of steel is 1.1 × 10−5 ( ◦C)−1 . Answer in units of cm.

Answer 1

L = Lo(1 + Ce*delta T)

where

L = height of the building at any temperature

Lo = original height of the building

Ce = coefficient of linear expansion = 1.1 x 10^-5

delta T = temperature change = 120 F

First, there must be a temperature conversion that needs to be done. The temperature change of 103 F must be

converted to the corresponding temperature in Centigrade.

C = (F - 32)*(5/9)

C = (120 - 32)*5/9

C = 48.89 C

Substituting appropriate values,

L = 582 [1 + (1.1 x 10^-5)(48.89)]

L = 582.31 m

At 120 F, the building is 582.31 m high and therefore at this temperature, it is

582.31 - 582 = 0.31 m = 31 cm