Q 11-10-089JEE MainJEE Main 2021 (24 Feb, Shift 1)Easy
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.
Answer: (B) $3a^3\alpha\Delta T$
The enclosed volume expands as if the box were solid metal, with volume coefficient $\gamma = 3\alpha$:
$$\Delta V = \gamma V\Delta T = 3a^3\alpha\Delta T$$
Solution by Sreeraj P, M.Sc Physics