Question

The radius of a metal sphere at room temperature $T$ is $R$, and the coefficient of linear expansion of the metal is $\alpha$. The sphere is heated a little by a temperature $\Delta T$ so that its new temperature is $T+\Delta T$. The increase in the volume of the sphere is approximately

• A. $2\pi R\alpha \Delta T$
• B. $\pi R^2\alpha \Delta T$
• C. $4\pi R^3\alpha \Delta T/3$
• D. $4\pi R^3\alpha \Delta T$

Answer 1

The correct option is D $4\pi R^3\alpha \Delta T$

$\Delta V=\gamma V\Delta T=3\alpha \frac{4}{3}\pi R^3\Delta T=4\pi R^3\alpha \Delta T$