Consider the distribution of 1000 ideal gas molecules among three bulbs (A, B, and C) of equal volume. For each of the following states, determine the number of ways (W) that the state can be achieved, and use Boltzmann’s equation to calculate the entropy of the state. (a) 1000 molecules in bulb A

Question

Consider the distribution of 1000 ideal gas molecules among three bulbs (A, B, and C) of equal volume. For each of the following states, determine the number of ways (W) that the state can be achieved, and use Boltzmann’s equation to calculate the entropy of the state.

(a) 1000 molecules in bulb A

(b) 1000 molecules randomly distributed among bulbs A, B, and C

STRATEGY

Use the equation [latex]W = B^{N}[/latex] to calculate the number of ways that N molecules can occupy B boxes. Then use Boltzmann’s equation to calculate entropy.

Accepted Answer

(a) [latex]W = B^{N} = 1^{1000} = 1[/latex]

S = k ln W = [latex](1.38 imes 10^{-23} J/K)( ln 1) = 0[/latex]

(b) [latex]W = B^{N} = 3^{1000}[/latex]

S = k ln W = [latex](1.38 imes 10^{-23} J/K)( ln 3^{1000})[/latex]

[latex]=(1.38 imes 10^{-23} J/K)(1000)( ln 3)[/latex]

[latex]=1.52 imes 10^{-20} J/K[/latex]

IDENTIFY
Known	Unknown
Number of molecules (N = 1000)	Number of ways (W)
Number of bulbs or “boxes” (B = 3)	Entropy (S)
Boltzmann’s equation: S = k ln W

Question 17.2: Consider the distribution of 1000 ideal gas molecules among ......

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