Consider the changes in the distribution of nine particles into three interconnected boxes shown

Consider the changes in the distribution of nine particles...

Key Concepts

Entropy

Entropy is a fundamental thermodynamic quantity that measures the level of disorder or randomness in a system. In statistical mechanics, it is directly connected to the number of microscopic configurations (microstates) that correspond to a macroscopic state, with more microstates resulting in higher entropy.

Multiplicity

Multiplicity refers to the number of microstates associated with a particular macrostate of a system. A higher multiplicity indicates that there are more ways to arrange the particles, which in turn corresponds to a higher entropy. Conversely, a lower multiplicity implies a decrease in entropy.

Statistical Distribution of Particles

The statistical distribution of particles across available states or compartments (boxes) determines the number of microstates. Alterations in this distribution can lead to a change in the system’s entropy. The most negative change in entropy (?S) corresponds to a configuration where the system has fewer microstates, indicating a more ordered state.

Transcript

00:01 So today we're going to be talking about changes in entropy, which is just the entropy of the final state, minus the entropy of the initial state.

00:15 So an easy way to think about entropy is that it's how dispersed, random, or disordered something is.

00:23 So like a crystal lattice, which is very rigid ordered, has low entropy, a gas that is evenly dispersed, throughout a container has high entropy.

00:35 However, if a gas for any reason were to be clustered in a corner somewhere, that would be low entropy.

00:44 So for the examples we're thinking about today, it would be really good to think about people entering a room.

00:50 So when people enter a room, they tend to spread out throughout the room.

00:55 If you enter a room and everybody's clustered in the corner, you'd think what's going on.

01:02 So we're going to be looking at several scenarios and we are going to try to find where the change in entropy is less than zero.

01:10 So this is the scenario where the entropy of the initial state is higher than the entropy of the final state.

01:20 So let's consider a box with three imaginary compartments and particles are moving through these compartments and we freeze them in time.

01:31 So, and this is the initial state, and we can see that eight particles are occupying two -thirds of the box.

01:42 There's this one low -knee particle in one -third of a box, and it doesn't seem very evenly distributed.

01:49 This would be a very strange room if you walk in, you're wondering, what did this blue person do to everybody else? why are they staying away from him? and so the initial state has a low entropy.

02:05 And then you look at the final state and you see that there are three particles in each compartment.

02:11 It's very evenly distributed.

02:14 It's very probable.

02:16 And that is very high entropy.

02:19 So since the final state has a higher entropy than initial state, the change in entropy is positive...

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