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