# Thermodynamics: Conceptual Question

1. Jun 5, 2010

### cdlegendary

1.Problem: A thermodynamic system has a large number of possible microscopic states. If you double the number of possible microscopic states, what happens to the entropy of the system?

it decreases
it remains the same
it increases, but by a factor less than 2
it increases by a factor greater than 2
it increases by a factor of 2
it increases, but not enough information is given to decide by what factor

2.Equations: S = k*ln(w), where s is entropy, k is the boltzmann constant, and w is the # of microstates

3.Attempt: I did a couple tests with the equation, subbing in values of microstates. I developed an inconsistency, with it doubling by a factor of two with small numbers, and less than two with larger numbers. So I'm pretty sure the entrophy increases, I just don't know by how much. Any help on explaining this to me would be appreciated.

2. Jun 5, 2010

### kuruman

Why bother using small numbers for the microstates? The problem clearly states that the system has a large number of microstates.