A molecule of a substance has permanent electric dipole moment equal to 10 -29 C-m. A mole of this substance is polarized(at low temperature) by applying a strong electrostatic field of magnitude 10 6 V/m. 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. For simplicity assume 100% polarization of sample. Avogadro no.= 6.023 x 10 23 mole -1 (Hint: Total work done in rotating all the dipoles in one mole= heat energy released) Ans: 3J
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Dipole charge = q distance between them: 2a
dipole moment = p = 2aq Electric field : E
Avogadro number = N = 6.023 * 10^23
electrostatic Force on charge +q: F1 = q E in the direction of E acting at A.
Force on -q = -F1 = - q E opposite to that of E acting at B.
Torque about center O of dipole = qE a Sin t + q E a Sin t = 2a q E Sin t = p E Sin t
Work done = Integral Torque dt = p E [ - cos t ] = p E [ cos 0 - cos 60 ] = p E /2
Total Work done in rotating N number of dipoles
= 10^-29 * 10^6 * 1/2 * 6.023 * 10^23 J
= 3.011 J
dipole moment = p = 2aq Electric field : E
Avogadro number = N = 6.023 * 10^23
electrostatic Force on charge +q: F1 = q E in the direction of E acting at A.
Force on -q = -F1 = - q E opposite to that of E acting at B.
Torque about center O of dipole = qE a Sin t + q E a Sin t = 2a q E Sin t = p E Sin t
Work done = Integral Torque dt = p E [ - cos t ] = p E [ cos 0 - cos 60 ] = p E /2
Total Work done in rotating N number of dipoles
= 10^-29 * 10^6 * 1/2 * 6.023 * 10^23 J
= 3.011 J
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Dipole moment of molecule of substance = 10^–29 C-m
| E | applied = 106 Vm^–1
Change of angle of electric field = 60º
No of molecules in one mole = n = 6.023 × 10^23
Amount of heat released in aligning the dipoles along new direction.
= + ΔU = ΔWext
= + (Uf - Ui)
= n [ -PEcos60° - (-PE)]
= n [ -PE/2 + PE] = n PE/2
= ( 6.023 *10^23 * 10^-29 * 10^6) / 2
= 6.023 / 2 ≈ 3.0115 J
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