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]
Answer & explanation
Correct answer: option 4
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,
$ΔU_{mole}=\frac{pE}{2}×N_A$
$=\frac{10^{-31}×10^8}{2}×6.022×10^{23}$
$=3J$