Question

A uniform metal rod of $2mm$${}^2$ cross section is heated from 0${}^o$C to 20${}^o$C. The coefficient of linear expansion of the rod is 12 x 10${}^{-6/0}$C. Its Young's modulus of elasticity is 10${}^{11}$ N/m${}^2$. The energy stored per unit volume of the rod is :

• A. $2880J/m^3$
• B. $1500J/m^3$
• C. $5760J/m^3$
• D. $1440J/m^3$

Answer 1

The correct option is A $2880J/m^3$

$energy=\frac{1}{2}\times stress\times strain\times volume$

$\frac{energy}{volume}=\frac{1}{2}\times stress\times strain$

$=\frac{1}{2}\times Y\times strain\times strain$

$=\frac{1}{2}\times Y\times (strain{)}^2$

$=\frac{1}{2}\times Y\times (\alpha \Delta T{)}^2$

$=\frac{1}{2}\times {10}^{11}\times (12\times {10}^{-6}\times 20{)}^2$

$=2880J/m^3$