Posted by on Dec 19, 2011 in Physical Chemistry | 0 comments

## Entropy (Part 6): Randomness and ensembles

After rolling 2, 3, 4, 10 and Avogadro’s dice, as seen in the entries below, it becomes clear that the most random states (most number of ways of rolling a number) always dominate while those with fewer arrangements occur less frequently: 1 Entropy: Randomness by rolling two dice 2 Entropy: Randomness by rolling three dice 3 Entropy: Randomness by rolling four dice 4 Entropy: Randomness by rolling ten dice 5 Entropy: Randomness by rolling Avogadro’s dice In this final entry of randomness and entropy, the concept of an ensemble is discussed. We are using a die to represent a particle that has six states that come up randomly.  Hence we have treated systems with 2, 3, 4, 10 and Avogadro’s constant (let’s use 1023) of particles (dice) and have shown that as the number increases, the total number of accessible states, is given by 6n. Clearly the number of states in Avogadro’s case is  61023 : an enormous number!! If you start to roll this many dice, every roll gives...

Posted by on Dec 12, 2011 in Physical Chemistry | 0 comments

## Entropy (Part 5): Randomness by rolling Avogadro’s dice

With Avogadro’s number of dice, you can roll them as much as you want, and the chance that there is an outcome other than the one that corresponds to the position of the spike is so unlikely you can safely ignore them.

Posted by on Dec 5, 2011 in Physical Chemistry | 2 comments

## Entropy (Part 4): Randomness by rolling ten dice

For 10 dice there are over 60 million arrangements and Figure 1 shows the outcomes for 30,000 rolls.

Posted by on Nov 21, 2011 in Physical Chemistry | 0 comments

## Entropy (part 3): Randomness by rolling four dice

The basic idea is that a physical system has many different arrangements (states) of particles which are consistent with some macroscopic quantity, like the temperature. Boltzmann found that out of all possible ways those particles can be arranged, only those that are consistent with the actual temperature need be considered. The chance of any other arrangements is negligible in comparison. Rolling dice illustrates this nicely.