Question

If the volume of a block of metal changes by $0.12\%$, when it is heated through $20\,{}^{\circ}C$, then the coefficient of linear expansion is

• A. $4 \times 10^{-5}\,{}^{\circ}C^{-1}$
• B. $2 \times 10^{-5}\,{}^{\circ}C^{-1}$
• C. $0.5 \times 10^{-5}\,{}^{\circ}C^{-1}$
• D. $4 \times 10^{-4}\,{}^{\circ}C^{-1}$

Answer 1

Answer: (B)

Here, $\frac{\Delta V}{V}=0.12\%$, $\frac{0.12}{100}$
$\Delta T=20\,{}^{\circ}C$
Now, $\gamma=\frac{\Delta V}{V\Delta T}=\frac{0.12}{100 \times 20}$
$=6 \times 10^{-5}\,{}^{\circ}C^{-1}$
$\therefore \alpha=\frac{\gamma}{3}=2 \times10^{-5}\,{}^{\circ}C^{-1}$