Question

The volume of a metal block is $4000 cm ^{3}$ at $273 K$. What would be its volume at $373 K$ ? (give $\alpha$ of the metal is 18 $\left.\times 10^{-6} K ^{-1}\right)$

• A. $5.001 m ^{3}$
• B. $4 \times 10^{-3} m ^{3}$
• C. $4.002 \times 10^{-3} m ^{3}$
• D. $1.002 \times 10^{-2} m ^{3}$

Answer 1

Answer: (C)

$V_{t}=V_{0}(1+\gamma \Delta T)$
$ \Rightarrow V_{0}=4 \times 10^{3} m ^{3}$
$\alpha=\frac{\gamma}{3} $
$ \Rightarrow \gamma=3 \alpha=3 \times 18 \times 10^{-6}$
$\therefore V _{ t }= V _{ o }(1+\gamma \Delta T )$
$ \Rightarrow V _{ t }=4 \times 10^{-3}\left(1+3 \times 18 \times 10^{-6} \times 10^{2}\right)$
$V =4 \times 10^{-3}\left(1+5.4 \times 10^{-3}\right)$
$V =4.002 \times 10^{-3} m ^{3}$