A rod of length L 0 (fixed at both ends) is supplied heat to raise its temperature by T. If γ is the coefficient of volume expansion of the rod and Y is Young's modulus of the rod then the ener

Question

A rod of length L 0 ​ (fixed at both ends) is supplied heat to raise its temperature by T. If γ is the coefficient of volume expansion of the rod and Y is Young's modulus of the rod then the energy density stored in the rod is:

TestHub · Accepted Answer

The rod cannot expand; its thermal strain is stored as elastic strain.
$α = \frac{γ}{3}$
$ε = α T = \frac{γ T}{3}$
$u = \frac{1}{2} (stress) (strain) = \frac{1}{2} Y ε^{2}$
$u = \frac{1}{2} Y (\frac{γ T}{3})^{2} = \frac{Y γ ^{2} T ^{2}}{18}$
Answer D.

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