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Question: A molecule of a substance has a permanent electric dipole moment of magnitude \(10^{- 30}\)cm. A mol...

A molecule of a substance has a permanent electric dipole moment of magnitude 10−3010^{- 30}cm. A mole of this substance is polarized by applying a strong electrostatic field of magnitude 10710^{7}V m−1m^{- 1}. The direction of field is changed by an angle60o60^{o}. The heat released by the substance in aligning its dipole along the new direction of the field is.

A

−6J- 6J

B

−3J- 3J

C

3J3J

D

6J6J

Answer

−3J- 3J

Explanation

Solution

: Dipole moment of each molecules =10−30Cm.= 10^{- 30}Cm. As 1 mole of the substance contains 6×10236 \times 10^{23}molecules Total dipole moment of all the molecules

P=6×1023×10−30Cm=6×10−7CmP = 6 \times 10^{23} \times 10^{- 30}Cm = 6 \times 10^{- 7}Cm

Initial potential energy, Ui=−pEcos⁡θU_{i} = - pE\cos\theta

=−6×10−7×107cos⁡0o= - 6 \times 10^{- 7} \times 10^{7}\cos 0^{o}

=−6J= - 6J

Final potential energy,

Uf=−6×10−6×106×cos⁡60o=−3JU_{f} = - 6 \times 10^{- 6} \times 10^{6} \times \cos 60^{o} = - 3J

Work done = - [change in potential energy]

=−[(−3)−(−6)]=−3J= - \lbrack( - 3) - ( - 6)\rbrack = - 3J