# Worksheet: Calculating Entropy by Counting Microstates

In this worksheet, we will practice using the Boltzmann equation to calculate the entropy of particles from the logarithm of the number of microstates.

**Q1: **

A system contains six particles distributed between two boxes.

Calculate the fractional probability of all particles occupying one of the two boxes.

- A
- B
- C
- D
- E

The system originally contains an equal number of particles in each box. The particles are redistributed so that one box contains only one particle. Calculate to 4 significant figures the entropy change for this process.

- A J/K
- B J/K
- C J/K
- D J/K
- E J/K

Calculate to 4 significant figures the maximum value of when one distribution converts to another in this system.

- A J/K
- B J/K
- C J/K
- D J/K
- E J/K

**Q2: **

A system contains four particles evenly distributed between two boxes. Before heat transfer, two units of energy are distributed between the particles in one box and the particles in the other box have zero energy. After heat transfer, the two units of energy are evenly distributed between the two boxes. Calculate to 4 significant figures the entropy change for this process.

- A J/K
- B J/K
- C J/K
- D J/K
- E J/K

**Q5: **

There are sixteen microstates associated with placing four particles in two boxes. The microstates may be collected into five distributions, (a)–(e), involving the same numbers of particles in each box.

Calculate the entropy change when distribution (a) converts to distribution (d).

- A J/K
- B J/K
- C J/K
- D J/K
- E J/K

Calculate the entropy change when distribution (c) converts to distribution (b).

- A J/K
- B J/K
- C J/K
- D J/K
- E J/K

Calculate the maximum value of when one distribution converts to another in this system.

- A J/K
- B J/K
- C J/K
- D J/K
- E J/K