A wire of length L is supplied heat to raise its temperature by T. If is the coefficient of volume expansion of the wire and Y is Youngs. Then:-

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Solution

$u = \frac{1}{2} Y * {s t r a i n}^{2}$
$△ T = T$
$Y_{1} = \frac{△ V}{V △ T} = \frac{△ V}{V T}$
$S t r a i n = \frac{△ V}{V} = Y_{1} T$
$u = \frac{{Y_{1}}^{2} T^{2} Y^{- 1}}{2}$

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A wire of length L is supplied heat to raise its temperature by T. If is the coefficient of volume expansion of the wire and Y is Youngs. Then:-

u=12Y∗strain2△T=TY1=△VV△T=△VVTStrain=△VV=Y1Tu=Y12T2Y−12

$u = \frac{1}{2} Y * {s t r a i n}^{2}$
$△ T = T$
$Y_{1} = \frac{△ V}{V △ T} = \frac{△ V}{V T}$
$S t r a i n = \frac{△ V}{V} = Y_{1} T$
$u = \frac{{Y_{1}}^{2} T^{2} Y^{- 1}}{2}$