Question

The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is 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. $\pi R^{2}\alpha\Delta T$
• D. $4\pi R^{3}\alpha\Delta T$

Answer 1

Answer: (D)

$4\pi R^{3}\alpha\Delta T$

Answer 2

As $\gamma = \frac{\Delta V}{V \times \Delta T}$and $\gamma = 3\alpha$

$\therefore 3\alpha = \frac{\Delta V}{\left( \frac{4\pi}{3}R^{3} \right)\Delta T}$

Which gives, $\Delta V = 4\pi R^{3}\alpha\Delta T$