# Warm-Up Exercise 12

## Due 12:15 pm, Mon 24 Sep 2012

Physics 123, Fall 2012

Reading assignment: 22.6-22.7

Imagine a system like a checkerboard (8x8 grid) where 8 of the 64
spaces may be occupied, the rest empty. Selecting the 8 occupied
squares at random, there are a lot of possible outcomes (how
many?).

The 5 cases above are possible outcomes. Rank these in order of least
likely to most likely. Explain your reasoning.

Using the same situation as in the first problem, imagine a
*macrostate* that is composed of all of the microstates where all of the
occupied squares touch at least one other occupied square (diagonally or
adjacent). Compare that to a second macrostate where only 2 or fewer of the 8 occupied squares are
touching each other. Which of these macrostates is more likely? Explain.

What's the difference between a macrostate and a microstate? How does
that difference come into play in your answers to questions 1 and 2?

Consider all of the gas particles in the room where you are sitting
right now. Thinking about all the positions, speeds, and directions of the
particles in the room, is this a likely macrostate? or an unlikely
one? Also, describe a macrostate (not microstate), for the gas
particles in this room, *with the same energy* that is quite
different from this one.