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 3.45 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 we will use the concepts related to thermal expansion in a body for which the initial length, the coefficient of thermal expansion and the temperature change are related:

$\Delta L = L0\alpha\Delta T$

Where,

$\Delta L$ = Change in Length

$\alpha$ = Coefficient of linear expansion

$\Delta T$ = Change in temperature

$L_0$ = Initial Length

Our values are:

$L_0 = 3.45m$

$\alpha = 5.5*10^{-7} \°C^{-1}$

$\Delta T = 235-20 = 215\°C$

Replacing we have,

$\Delta L = (3.49) (5.5*10^{-7}) [(215)$

$\Delta L = 0.0004126m$

$\Delta L = 0.4126mm$

Therefore the change in milimiters was 0.4126mm