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Physics Question on Thermal Expansion

The coefficient of linear expansion of a metal rod is 12×10−6/∘C12 \times 10^{-6} / ^{\circ}C , its value in per its value in per ∘F^{\circ}F

A

203×10−6/∘F\frac{20}{3} \times 10^{-6}/^{\circ}F

B

154×10−6/∘F\frac{15}{4} \times 10^{-6}/^{\circ}F

C

21.6×10−6/∘F21.6\times 10^{-6}/^{\circ}F

D

12×10−6/∘F12\times 10^{-6}/^{\circ}F

Answer

203×10−6/∘F\frac{20}{3} \times 10^{-6}/^{\circ}F

Explanation

Solution

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