Question

A building made with a steel structure is 565 m high on a winter day when the temperature is 0◦F. How much taller is the building when the temperature is 103◦F? The linear expansion coefficient of steel is 1.1 × 10−5 ( ◦C)−1 . Answer in units of cm.

Answer 1

To solve this problem we apply the thermodynamic equations of linear expansion in bodies.

Mathematically the change in the length of a body is subject to the mathematical expression

$\Delta L = L_0 \alpha \Delta T$

Where,

$L_0 =$ Initial Length

$\alpha =$ Thermal expansion coefficient

$\Delta T =$ Change in temperature

Since we have values in different units we proceed to transform the temperature to degrees Celsius so

$0\°F \Rightarrow (0-32)*\frac{5}{9} = -17.77\°C$

$103\°F \Rightarrow (103-32)*(\frac{5}{9})= 39.44\°C$

The coefficient of thermal expansion given is

$\alpha = 1.1*10^{-5}/\°C$

The initial length would be,

$L_0 = 565m$

Replacing we have to,

$\Delta L = L_0 \alpha \Delta T$

$\Delta L = (565)(1.1*10^{-5})(39.44-(-17.77))$

$\Delta L = (565)(1.1*10^{-5})(39.44-(-17.77))$

$\Delta L = 0.355m$

This means that the building will be 35.5cm taller