For 1 mol of molecules randomly distributed among bulbs A, B, and C, use Boltzmann's formula to calculate the entropy of the state. If the number of microstates is 27, what is the entropy?

• A. R ln(9)
• B. R ln(3)
• C. 3R ln(3)
• D. R ln(27)

Answer: (D)

Verified step by step guidance

1. Understand that entropy (S) in statistical mechanics can be calculated using Boltzmann's formula: S = k * ln(W), where k is the Boltzmann constant and W is the number of microstates.
2. In this problem, we are given that the number of microstates (W) is 27.
3. Since we are dealing with 1 mol of molecules, we use the molar form of Boltzmann's formula: S = R * ln(W), where R is the gas constant.
4. Substitute the given number of microstates (W = 27) into the formula: S = R * ln(27).
5. Recognize that the expression R * ln(27) is the correct representation of the entropy for the given state, as it directly uses the number of microstates provided.