Question

An iron plate of dimensions $50cm\times 20cm$ and at ${20}^{\circ }C$ is heated in a furnace, when the final area of plate is $1006c{m}^2$. If the coefficient of linear expansion of iron is $0.000012{/}^{\circ }C$. Find the temperature of the furnace

• A. ${200}^{\circ }C$
• B. ${250}^{\circ }C$
• C. ${270}^{\circ }C$
• D. $4^{\circ }C$

Answer 1

The correct option is C ${270}^{\circ }C$

Initial Area, $A_o=50\times 20c{m}^2=1000c{m}^2$
final area of plate, $A_t=1006c{m}^2$
Coefficient of linear expansion $(\propto )=0.000012{/}^{\circ }C$
$\therefore B=2\times 2=0.000024{/}^{\circ }C$
$A_t-A_o=A_o{B}_t$
$t=\frac{A_t-A_o}{A_o\times B}$
$=\frac{1006-1000}{1000\times 0.000024}=\frac{6}{0.024}={250}^{\circ }C$
Temperature of furnace $=$ Initial temp $+$ Rise in temperature
$=(20+250{)}^{\circ }C={270}^{\circ }$