Question

The coefficient of linear expansion of a metal rod is $12 \times 10^{-6} / ^{\circ}C$ , its value in per its value in per $^{\circ}F$

• A. $\frac{20}{3} \times 10^{-6}/^{\circ}F$
• B. $\frac{15}{4} \times 10^{-6}/^{\circ}F$
• C. $21.6\times 10^{-6}/^{\circ}F$
• D. $12\times 10^{-6}/^{\circ}F$

Answer 1

Answer: (A)

Coefficient of thermal expansion = Change in length / (original length $X$
change in temperature)
So, $\alpha_{ c } / \alpha_{ F }=$ Change in temp in Fahrenheit / change in temp in centigrade
Or $\alpha_{ F }=\alpha_{ C }\left(\right.$ change in $T _{ C } /$ change in $\left.T _{ F }\right)$
$
=\alpha_{ C }\left(\text { change in } T _{ C } /(9 / 5) \text { change in } T _{ C }\right)
$
$=\alpha_{ C } \times(5 / 9)$
$=(20 / 3) \times 10^{-6}$