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A molecule of a substance has a permanent electric dipole moment of magnitude $10^{- 30} Cm$ . A mole of this substance is polarized by applying a strong electrostatic field of magnitude $10^{7} V m^{- 1}$ . The direction of the field is changed by an angle $60 °$ . The heat released by the substance in aligning its dipole along the new direction of the field is (in J)

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Detailed Solution

Dipole moment of each molecule $= 10^{- 30} C m$ .

As $1 m o l e$ of substance contains $6 \times 10^{23}$ molecules,

total dipole moment of all the molecules $p = 6 \times 10^{23} \times 10^{- 30} C m = 6 \times 10^{- 7} C m$ .

Initial potential energy, $U_{i} = - p E \cos (θ) = - 6 \times 10^{- 7} \times 10^{7} \cos (0 °) = - 6 J$

Final potential energy, $U_{f} = - 6 \times 10^{- 7} \times 10^{7} \cos (60 °) = - 3 J$

Heat energy released = Loss of potential energy

$= - [(- 6) - (- 3)] = 3 J$

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