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(A) The change in volume $\Delta V$ is given by the formula $\Delta V = \gamma \cdot V \cdot \Delta T$,where $\gamma$ is the coefficient of volume exp

Vedclass · Accepted Answer

$28.9$

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(A) The change in volume $\Delta V$ is given by the formula $\Delta V = \gamma \cdot V \cdot \Delta T$,where $\gamma$ is the coefficient of volume expansion.For a solid,$\gamma = 3\alpha$,where $\alpha$ is the coefficient of linear expansion.Given: Diameter $d = 20 \; cm$,so radius $r = 10 \; cm$.Initial volume $V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (10)^3 = \frac{4000}{3} \pi \; cm^3$.Change in temperature $\Delta T = 100^{\circ} C - 0^{\circ} C = 100^{\circ} C$.Coefficient of linear expansion $\alpha = 23 	imes 10^{-6} \; /^{\circ} C$.Substituting the values:$\Delta V = 3 	imes (23 	imes 10^{-6}) 	imes (\frac{4}{3} \pi 	imes 10^3) 	imes 100$$\Delta V = 3 	imes 23 	imes 10^{-6} 	imes \frac{4}{3} 	imes 3.14159 	imes 1000 	imes 100$$\Delta V = 23 	imes 4 	imes 3.14159 	imes 10^{-1} = 92 	imes 3.14159 	imes 0.1 \approx 28.9 \; cm^3$.

An aluminium sphere of $20 \; cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{Al} = 23 \times 10^{-6} \; /^{\circ} C$): (in $; cm^3$)

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