Question

The volume of a block of metal at 30°C changes by 0.12% when its temperature is increased to 70°C. The coefficient of linear expansion of the metal is ______.

Options

• 2 × 10⁻⁵ °C

• 3 × 10⁻⁵ °C

• 4 × 10⁻⁵ °C

• 1 × 10⁻⁵ °C

Answer 1

The volume of a block of metal at 30°C changes by 0.12% when its temperature is increased to 70°C. The coefficient of linear expansion of the metal is 1 × 10⁻⁵ °C.

Explanation:

Given: Temperature change (ΔT) = 70 − 30 = 40°C

Volume change = 0.12% = 0.0012

`(Delta V)/V` = 3αΔT

0.0012 = 3α ×  40

0.0012 = 120α

α = `0.0012/120`

= 1 × 10⁻⁵ °C