A molecule of a substance has a permanent electric dipole moment of magnitude $10^{-31} Cm$. A mole of this substance is 100% polarised by applying a strong electrostatic field of magnitude $10^8 Vm^{-1}$. The direction of field is suddenly changed by an angle of 60°. Find the heat released by substance in aligning its dipoles along the new direction of the field.

[Take 1 mole = $6 × 10^{23}$ molecules]

3 J

The correct answer is Option (4) → 3J

The potential energy of a dipole is,

$U=-pE\cos(θ)$

Change in potential energy (ΔU) is,

$ΔU=U_{final}-U_{initial}$

$ΔU=-pE(\cos 60°)-(-pE\cos(0°))$

$=-\frac{pE}{2}-(-pE)=\frac{pE}{2}$

and,

$ΔU_{mole}=\frac{pE}{2}×N_A$

$=\frac{10^{-31}×10^8}{2}×6.022×10^{23}$

$=3J$