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A steel rod of length $\ell$, cross sectional area $A$, young's modulus of elasticity $Y$, and thermal coefficient of linear expansion $'a'$ is heated so that its temperature increases by $t\,^oC$. Work that can be done by rod on heating will be
  • A$(YA\, \alpha\, t)\times(\ell\, \alpha\, t)$
  • B$\frac{1}{2}\left( {YA\,\alpha \,t} \right) \times \left( {\ell \,\alpha \,t} \right)$
  • C$\frac{1}{2}\left( {YA\,\alpha \,t} \right) \times \left( {1/2} \right)\left( {\ell \,\alpha \,t} \right)$
  • D$2(YA\, \alpha\, t)\,(\ell\, \alpha\, t)$
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