Question

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by ${40}^{o}C$. The coefficient of linear expansion of the metal is

• A. $2\times {10}^{-5}{}^o{C}^{-1}$
• B. $6\times {10}^{-5}{}^o{C}^{-1}$
• C. $18\times {10}^{-5}{}^o{C}^{-1}$
• D. $1.2\times {10}^{-5}{}^o{C}^{-1}$

Answer 1

Answer: (A)

$2\times {10}^{-5}{}^o{C}^{-1}$

The change in the volume is given by,

$V_T=V_0(1+\gamma △T)$

$\Rightarrow \frac{V_T-V_0}{V_0}=\left(\gamma △T\right)$

$\frac{0.24}{100}=\gamma \times {40}^{o}C$

$\gamma =\frac{0.24}{100\times 40}=6\times {10}^{-5}{}^o{C}^{-1}$

Therefore, Coefficient of linear expansion,
$\alpha =\frac{\gamma }{3}=\frac{6\times {10}^{-5}}{3}=2\times {10}^{-5}{}^o{C}^{-1}$