# Question #e675f

Jun 30, 2015

Linear expansion coefficients have units of K^(-1) and typical values around $1 \times {10}^{- 5} {K}^{- 1}$, so we rewrite the question as: If an object initially at 29C with a length of 5.00 m and expansion coefficient of $1 \times {10}^{- 5} {K}^{- 1}$ is heated to 29C, what is the new length of the expanded object?

#### Explanation:

The strain that occurs during expansion (fractional change in length) is
$\epsilon = \frac{\mathrm{dL}}{L} = \alpha \left({T}_{2} - {T}_{1}\right) = 1 \times {10}^{- 5} \left(29 - 28\right) = 1 \times {10}^{- 5}$

The expansion is
$\mathrm{dL} = L \times \alpha = 5 m \times 1 \times {10}^{- 5} = 5 \times {10}^{- 5} m$

The new length is
$L + \mathrm{dL} = 5 m + 1 \times {10}^{- 5} m = 5.00005 m$