A molecule of a substance has a permanent electric dipole moment of magnitude `10^(-29) `C m. A mole of this substance is polarized at low temperature by appling a strong elecrostatic field of magnitude `10^(6) V m^(-1)`. The direction of the field is suddenly changed by an angle of `60^(@)`. Estimate the heat released by the substance in aligning its dipole along the new direction of the field. For simplicity, assume `100%` polarisation of sample.

Explanation

Here,dipole moment of each molecule `1- ^(-29)C `m. As 1 mole of the substance contains `6 xx 10^(23)` molecules ,total dipole moment of all the molecules.
`P = 6 xx 10^(23) xx 10^(-29) C m`
`= 6 xx 10^(-6) C m`
Initial potential energy, `- U _(i) = - p E cos theta = - 6 xx 10^(-6) xx 10^(6) cos 0^(@) = - 6 J`
Final potential energy ( when `theta 60^(@) ) , U _(f) = - 6 xx 10^(-6) xx 10^96) cos 60^(@) = - 3 J `
Change in potential energy ` = - 3J - ( - 6J ) = 3J`
So, there is loss in potential energy. This must be the energy released by the substance in the form of heat in aligning its dipoles.