Question

The volume of a metal sphere increases by $24\%$ when its temperature is raised by $40K$. The coefficient of linear expansion of the metal is:

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

Answer 1

Answer: (A)

$2\times {10}^{-5}{K}^{-1}$

FROM, $V_T=V_0(1+\gamma \Delta T)$

$⟹\frac{V_T-V_0}{V_0}=\gamma \Delta T$

$\frac{0.24}{100}=\gamma 40$

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

Coefficient of linear expansion,

$\alpha =\frac{\gamma }{3}=\frac{6\times {10}^{-5}}{3}=2\times {10}^{-5}{K}^{-1}$