Question

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

• A. $28.9\text{cc}$
• B. $2.89\text{cc}$
• C. $9.28\text{cc}$
• D. $49.8\text{cc}$

Answer 1

The correct option is A $28.9\text{cc}$

Given, $d=20\text{cm}$
$V=V_0=(1+\gamma \Delta T)=V_0(1+3\alpha \Delta T)$
Where $\gamma$ is coefficient of volumetric expansion.
$\because \gamma =3\alpha$
Volume of sphere =$\frac{4}{3}\pi r^3$
Change in volume $=V-V_0=3V_0\alpha \Delta T$
$=3\times \frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3\times 23\times {10}^{-6}\times 100$
$=3\times \frac{4}{3}\pi {\left(\frac{0.2}{2}\right)}^3\times 23\times {10}^{-6}\times 100$
$=28.9\text{cc}(1\text{cc}={10}^{-6}{\text{m}}^3)$
The correct option is (A).