The volume of a metal sphere increases by 0.2 | vedclass

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(A) The coefficient of volume expansion $\gamma$ is given by the formula: $\gamma = \frac{\Delta V}{V \cdot \Delta T}$.
Given, $\frac{\Delta V}{V} =

Vedclass · Accepted Answer

$2 	imes 10^{-5}$

Vedclass · Answer

(A) The coefficient of volume expansion $\gamma$ is given by the formula: $\gamma = \frac{\Delta V}{V \cdot \Delta T}$.
Given, $\frac{\Delta V}{V} = 0.24\% = \frac{0.24}{100}$ and $\Delta T = 40^{\circ}C$.
Substituting the values: $\gamma = \frac{0.24}{100 	imes 40} = \frac{0.24}{4000} = 0.00006 = 6 	imes 10^{-5} 	ext{ } ^\circ	ext{C}^{-1}$.
The relationship between the coefficient of linear expansion $\alpha$ and volume expansion $\gamma$ is $\alpha = \frac{\gamma}{3}$.
Therefore, $\alpha = \frac{6 	imes 10^{-5}}{3} = 2 	imes 10^{-5} 	ext{ } ^\circ	ext{C}^{-1}$.

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40^{\circ}C$. The coefficient of linear expansion of the metal is .......... $^{\circ}C^{-1}$.

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