Question

A system consists of molecules that convert between two colors (green and yellow). There are spaces for 10,000 molecules, but there are only 6000 molecules in the system. The system starts in a state with 2000 green molecules and 4000 yellow molecules. What is the entropy of the system? (Hint: Use Stirling’s approximation.)

Answer 1

Step-by-step explanation:

According to Stirling's approximation,

W =
`\frac{\text{spaces}\mid}{\text{green}\mid \text{yellow}\mid \text{empty}\mid}`

Entropy of the system will be calculated as follows.

S =
`K_(B) ln W`

=
`K_(B) ln ((10,000|)/(2000| 4000| 4000|))`

=
`K_(B) [(10,000 ln (10000) - 10000) - 2000 ln (2000) - 2000 + 4000 ln (4000) - 4000 + 4000 ln (4000) - 4000)]`

S =
`10549.2 K_(B)`

Therefore, we can conclude that the entropy of the system is
`10549.2 K_(B)`.