Question

Fused quartz possesses an exceptionally low coefficient of linear expansion, 5.50 × 10 − 7 ( ∘ C ) − 1 . Suppose a bar of fused quartz of length 2.99 m at 20.0 ∘ C is heated to 235 ∘ C . By how much, in millimeters, would the bar expand?

Answer 1

To solve this problem it is necessary to apply the concepts related to thermal linear expansion. Mathematically this concept can be expressed under the Equation:

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

Where,

$L_0 =$ Initial Length

$\alpha =$Thermal Expanssion constant

$\Delta T =$Change in Lenght

Our values are given as

$L_0 = 2.99m$

$\alpha = 5.50*10^{-7} ( \∘C )^{-1}$

$\Delta T = T_2-T_1 = 213-20$

Replacing at our equation we have,

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

$\Delta L = (2.99) (5.5 x 10^{-7}) (213 - 20)$

$\Delta L = 0.317*10^{-3}m\approx 0.317mm$

Therefore the expantion of the bar is 0.317mm