Question

A metal cube of length $10.0\text{mm}$ at $0^{\circ }\text{C}\left(273\text{K}\right)$ is heated to ${200}^{\circ }\text{C}\left(473\text{K}\right)$. Given its coefficient of linear expansion is $2\times {10}^{-5}{\text{K}}^{-1}$, the percent change in its volume is

• A. $0.1$
• B. $0.2$
• C. $1.2$
• D. $0.4$

Answer 1

The correct option is C $1.2$

Here, percentage change in volume is given as
$\frac{\Delta V}{V}\times 100=\gamma \Delta T\times 100$
We know that, $\gamma =3\alpha$
So,
$\frac{\Delta V}{V}\times 100=3\alpha \times (T_1-T_2)\times 100$
$\Rightarrow \frac{\Delta V}{V}\times 100=3\times 2\times {10}^{-5}\times (473-273)\times 100$
$\therefore$ % Change in volume $=1.2$