Question

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

• A. $5.001m^3$
• 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)

$V_t=V_0(1+\gamma \Delta T)$
$\Rightarrow V_0=4\times 10^3{m}^3$
$\alpha =\frac{\gamma }{3}$
$\Rightarrow \gamma =3\alpha =3\times 18\times 10^{-6}$
$\therefore V_t=V_o(1+\gamma \Delta T)$
$\Rightarrow V_t=4\times 10^{-3}\left(1+3\times 18\times 10^{-6}\times 10^2\right)$
$V=4\times 10^{-3}\left(1+5.4\times 10^{-3}\right)$
$V=4.002\times 10^{-3}{m}^3$