(a) Calculate the entropy of the system in the absence of the field. (b) Calcula

Question

(a) Calculate the entropy of the system in the absence of the field.

(b) Calculate the entropy of the system in the applied field.

(c) Does the system become more ordered or disordered when the field is applied?

(12 pts) You have a solution of dipolar molecules with a positive charge at the head and a negative charge at the tail. When there is no electric field applied to the solution, the dipoles point north (n), east (e), west (w), or south (s) with equal probabilities. The probability distribution is shown in part (a) of the figure below. However when you apply a field to the solution, you now observe a different distribution, with more heads pointing north, as shown in part (b) of the figure below. 4. (a) Electric Field Absent (b) Electric Field Present 16 1 16

Explanation / Answer

a) entropy of the system in the absence of the field = 1/4 . 1/4 .1/4 . 1/4 = 1/256

b)  entropy of the system in the applied field = [7/16 . 1/16 ] + [1/4 . 1/4 ] = 7/256 + 1/16 = 23/256

c) when the field is applied, system become more disordered .

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