Question

Each side of a box made of metal sheet in cubic shape is $a$ at room temperature $T$. The coefficient of linear expansion of the metal sheet is ‘$\alpha$’. The metal sheet is heated uniformly, by a small temperature $\Delta$$T$, so that its new temperature is $T+\Delta$$T$. Calculate the increase in the volume of the metal box.

• A. $\frac{4}{3}\pi a^3\alpha \Delta T$
• B. $4\pi a^3\alpha \Delta T$
• C. $3a^3\alpha \Delta T$
• D. $4a^3\alpha \Delta T$

Answer 1

The correct option is C $3a^3\alpha \Delta T$

Coefficient of volumetric expansion,
$\gamma =3\alpha$

$\frac{\Delta V}{V}$ $=$ $\gamma \Delta T$

$\Rightarrow \Delta V=V\gamma \Delta T$

$\Rightarrow \Delta V=3a^3\alpha \Delta T$