N – # of particles

N!

(total spaces)

W = # of accessible

W =

microstates

no!n1!n2!n3! …

(multiplicity)

n, = # of particles with i

units of energy (tokens)

So the entropy is

S = k In W = k In

30!

no!n1!n2!n3!quot;..

The Boltzmann constant is 1.38 x 10-23 J/K

Case 1: Arrange the tokens so that there is just one on every square of the grid. Calculate

the multiplicity (W), the entropy divided by the Boltzmann constant (S/k) and entropy (S) of

this very unlikely situation (where n1 = 30 and all of the other n; = 0):

W=

S/k =

S =

J/K

Case 2: Arrange the tokens so that all 30 are on a single square of the grid. Calculate both

the multiplicity and the entropy divided by the Boltzmann constant and entropy of this very

unlikely situation (where no = 29, n30 = 1 and all of the other n; = 0):

W =

S/k =

S=

J/K

Case 3: Use the dice to randomly place the 30 tokens onto the grid.

Penny

#Place penny on square

1

W N

14

509

10

4

21

11

6

10

7

9

29

23

12

17

16

29

23

16

28

20

18

22

19

17

20

7

21

5

22

16

23

11

24

23

25

28

26

12

27

24

28

12

29

30

30

20

According to the list placing pennies on the grid until all 30 pennies are gone. Record the

distribution numbers (no, nj, etc.) and calculate both the multiplicity and the entropy

divided by the Boltzmann constant and entropy of this situation:

n3 =

no =

n1 =

n2=

n4 =

ns =

n6 =

n7 =

ng =

ng =

n10 =

n1 =

W =

S/k =

S =

J/KScience