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  • The coefficient of linear expansion of crystal in one direction is  and that in other two di

The coefficient of linear expansion of crystal in one direction is \alpha_{1} and that in other two directions perpendicular to it is \alpha _{2} . The coefficient of cubical expansion is -

Option: 1

\alpha _{1} + \alpha _{2}


Option: 2

2\alpha _{1} + \alpha _{2}


Option: 3

\alpha _{1} + 2 \alpha _{2}


Option: 4

None of these


Answers (1)

best_answer

V = V_{o} \left ( 1+Y\Delta Q \right )

L^{3} = L_{o} \left ( 1+\alpha _{1}\Delta Q \right )L_{0}^{2} \left ( 1+\alpha _{2 }\Delta Q \right )^{2}

       = L_{o}^{3} \left ( 1+\alpha _{1}\Delta Q \right ) \left ( 1+\alpha _{2 }\Delta Q \right )^{2}

          Since, L_{o}^{3} = V_{o}

           and, L^{3} = V

Hence, 

  1+ Y\Delta Q= \left ( 1+\alpha _{1}\Delta Q \right ) \left ( 1+\alpha _{2 }\Delta Q \right )^{2}    

                      = \left ( 1+\alpha _{1}\Delta Q \right ) \left ( 1+ 2\alpha _{2 }\Delta Q \right )

                      = \left ( 1+\alpha _{1}\Delta Q + 2\alpha _{2 }\Delta Q \right )

                 Y = \alpha _{1} + 2 \alpha _{2}

Posted by

vishal kumar

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