Question

A uniform metal rod of $2\, mm ^{2}$ cross-section is heated from $0^{\circ} C$ to $20^{\circ} C$. The coefficient of linear expansion of the rod is $12 \times 10^{-6}$ per ${ }^{\circ} C , Y =10^{11} N / m ^{2}$. The energy stored per unit volume of the rod is :

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

Answer 1

Answer: (C)

Energy stored per unit volume of the rod
$=\frac{1}{2} \times$ stress $\times$ strain
$=\frac{1}{2} Y \alpha \Delta T \times \alpha \Delta T$
$=\frac{1}{2} Y[\alpha \Delta T]^{2}$
$=\frac{1}{2} \times 10^{11} \times\left(12 \times 10^{-6} \times 20\right)^{2}$
$=2880\, J / m ^{3}$