# A 2-m long pipe at 27"^oC is heated until it is 2.00024 m at 77"^oC. What is the coefficient of linear expansion of the pipe?

Oct 19, 2016

$\textsf{\alpha = 2.4 \times {10}^{- 6} \textcolor{w h i t e}{x} {\text{degC}}^{- 1}}$

#### Explanation:

The coefficient of linear expansion is the fractional increase in length for a rise in temperature of 1 degree (deg C or Kelvin).

This means that if the length was doubled with a rise of 1 degree then the coefficient would be 2.

For most materials the numbers are much smaller.

$\therefore$$\textsf{\alpha = \frac{\Delta L}{{L}_{0} \times \Delta T}}$

$\textsf{\Delta T = 77 - 27 = 50 \textcolor{w h i t e}{x} \text{degC}}$

$\therefore$$\textsf{\alpha = \frac{0.00024}{2 \times 50} = 2.4 \times {10}^{- 6} \textcolor{w h i t e}{x} {\text{degC}}^{- 1}}$