Question (continuation)
(a) What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to E S from parallel to perpendicular?
(b) At what absolute temperature T is the average translational kinetic energy 3/2kT of a molecule equal to the change in potential energy calculated in part (a)?
Answer:
a. 9.0 * 10^-24 Joules
b. 0.44K
Explanation:
Given
Let p = dipole moment = 5.0 * 10^-30 Cm
Let E = Magnitude = 1.8 * 10^6 N/m
a.
The charge in electric potential = Final Charge - Initial Charge
Initial Charge = Potential Energy
Initial Energy = -pE cosФ where Ф = 0
So, initial Energy = - 5.0 * 10^-30 * 1.8 * 10^6
Initial Energy = -9 * 10^-24 Joules
Final Energy = 0
Charge = 0 - (-9.0 * 10^-24)
Charge = 9.0 * 10^-24 Joules
b.
Absolute Temperature
Change in Kinetic Energy = Change in Potential Energy = 9.0 * 10^-24
Change in Kinetic Energy = 3/2kT where k is Steven-Boltzmann constant = 1.38 * 10^-23
So,
9.0 * 10^-24 = 3/2 * 1.38 * 10^-23 * T
T = (9.0 * 10^-24 * 2)/(3 * 1.38 * 10^-23)
T = (18 * 10^-24)/(4.14 * 10^-23)
T = 0.44K
