A molecule of a substance has a permanent electric dipole moment of magnitude `10^(-29) Cm.` A mole of this substance is polarised (at low temperature) by applying a strong electrostatic 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 dipoles along the new direction of the field. Assume 100% polarisation of the sample.

Explanation

Here, dipole moment of each molecules `= 10^(-29)Cm`
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) Cm = 6 xx 10^(6)Cm`
Initial potential energy, `U= - pE 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 10^6 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.