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 ${\alpha }_F={\alpha }_C($ change in $T_C/$ change in $T_F)$
$<br/>={\alpha }_C\left(\text{ change in }{T}_C/(9/5)\text{ change in }{T}_C\right)<br/>$
$={\alpha }_C\times (5/9)$
$=(20/3)\times 10^{-6}$