Rudolph's Disorderly System
Rudolph the red-nosed, statistical mechanist is trying to maximize the entropy of his system. He can either fill his box with 2 particles and 3 unit of energy or 3 particles and 2 units of energy. Assuming that a unit of energy is quantized (i.e. a particle cannot have a part of a unit of energy) and that all energy is assigned to the particles, which arrangement provides for more entropy?
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1 solution
2 particles and 3 units of energy
The possible microstates are:
E 1 = 3 and E 2 = 0
E 1 = 2 and E 2 = 1
E 1 = 1 and E 2 = 2
E 1 = 0 and E 2 = 3
There are 4 possible microstates, so the entropy is S = k B l n ( 4 ) .
3 particles and 2 units of energy
E 1 = 2 , E 2 = 0 , and E 3 = 0
E 1 = 0 , E 2 = 2 , and E 3 = 0
E 1 = 0 , E 2 = 0 , and E 3 = 2
E 1 = 1 , E 2 = 1 , and E 3 = 0
E 1 = 1 , E 2 = 0 , and E 3 = 1
E 1 = 0 , E 2 = 1 , and E 3 = 1
There are 6 possible microstates, so the entropy is S = k B l n ( 6 ) .