Question

The coefficient of linear expansion of a
metal rod is 12x10-6 / °C, its value in per
°F is​

Answer 1

Given : The coefficient of linear expansion of a metal rod is 12 × 10¯⁶ /°C

To find : The value of coefficient of linear expansion of that metal rod in per °F.

solution : we know, change in length due to increase temperature ∆T is given by, ∆l = lα∆T

where α is coefficient of linear expansion of rod.

here it is clear that dimensions of α is related to change in temperature, ∆T.

we know, (change in temperature in °C)/5 = (change in temperature in °F)/9

so, ∆T in °F = 9/5 × (∆T in °C)

now α value per °F = 12 × 10¯⁶/(9/5) /°F

= 12 × 5/9 × 10¯⁶ /°F

= 6.67 × 10¯⁶ /°F

Therefore the coefficient of linear expansion of a metal rod in per °F is 6.67 × 10¯⁶ /°F