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  4. A uniform metal rod of 2 mm 2 cross-section is heated from 0° C to 20° C. The coefficient of linear expansion of the rod is 12 × 10-6 per ° C , Y =1011 N / m 2. The energy stored per unit volume of the rod is :

Q. 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 :

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Solution:

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

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