Two systems, each composed of two particles represented by circles, have 20 J of total energy. Which system, A or B, has the greater entropy? Why?

Video transcript

Hi everyone for this problem we're told to consider the two systems below. Each system is composed of four particles that have a total energy of 40 jewels. Identify how many energetically equivalent ways the particles can be distributed for each system and identify the system that has the greater entropy. Okay, so we have two things that we need to answer here. So let's take a look at the first one. The first one says identify how many energetically equivalent ways the particles can be distributed for each system. So for this question we're dealing with what's known as permutations. And permutations are useful to determine the different number of ways to arrange something and in permutations, the order matters. So looking at A we see that so we'll write out our answer for the first one. Okay, so for our system a looking at the different number of ways we can arrange something. There's only one way to arrange these four particles. Okay, so because there's only one way to arrange them, we're going to say that it has one permutation. Okay, so there's only one energetically equivalent way that the particles can be distributed in system A let's take a look at system be So for system B we have four ways to arrange our particles. Okay, But we need to take a look at their different number of ways to arrange those particles. Okay, so we have four different ways. We can arrange these four particles and The number of permutations can be calculated by getting the factory of the number of positions. So we're going to take four and multiply it by four to get 24 permutations for System B. Okay, So that is the answer to Part one. Part two asks identify the system that has the greater entropy. Okay, So now we're dealing with entropy. Okay. And with entropy we're going to have greater entropy where there's more permutations. And here we can see that B, system B has more permutations than system A. So our answer for greater entropy is going to be system be Okay. So these are our answers to this question and that is the end of this problem. I hope this was helpful.