# Please Fill Out Questions On Case 1 2 And 3 (Physics Entropy)

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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