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Predict the sign of $\Delta S_{\mathrm{sys}}$ for…

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North Carolina State University

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Problem 14

Predict the sign of $\Delta S_{\mathrm{sys}}$ for each process: (a) Alcohol evap- orates. $(b)$ A solid explosive converts to a gas. $(c)$ Perfume vapors diffuse through a room.

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Video Transcript

Chapter 20 Problem 14 is asking us to predict the sign of entropy for various processes. So it's first review. What entropy is injury is about the freedom of particle motion or the dispersion of energy, The greater the entropy. And we do know entropy by s. So the greater the change of entropy. In this case, that means there's a greater freedom of particle motion or greater dispersion of inch of energy. And this happens as we move from the solid to the liquid to the gas phase. So we must make this an arrow. The gas phase has more entropy than the liquid phase, and the local face has more in the solid face. And this is because in the gas phase, particles has a great have a grated freedom of particle motion, and the energy is dispersed throughout the entire system. So we're considering various processes. We want to see if there is a change between the phase and how that changes to determine whether or not the entropy. The side of the interview will be positive or negative. When it comes to the sign and the change of entropy. Entropy is a state function. That means We're looking at the final state of interpret minus the initial. So doesn't matter how it went from a solid to a liquid or liquid to a gas. All that matters is where it wasn't beginning verse where it was in the end. So it's first consider alcohol evaporating. When we begin, alcohol is in the liquid state, and then that changes and becomes in the gas state. So our initial state for alcohol evaporating is going to be the liquid, and our final state is going to be the gas. So that will be gas minus the liquid are gas. Here it has a greater entropy is this is a positive value and the liquid is a small entropy. So it's a lower values. When we do, our gas minus are liquid. We're gonna end up with a positive son. Let's consider Ah, foul explosive turning into a gas. Well, clearly, we're starting off with a solid, which is our initial state. So it's gonna be on this side of the negative and we're ending up with the gas, which is our final state. So the gas has a greater entropy, minus a smaller interview value. We still end up with a positive side. And lastly, let's consider if we have perfume vapors dispersing throughout the room. So in this case, the perfume vapors initially began as a gas, and it finally begins. It ends up as a gas because it's staying in the same state and dispersing throughout the room. However, when the vapors begin their one part of the room and then at the end there spread throughout the entire rooms of the dispersion of energy has increased and the freedom of particle motion has increased. So since that space is increasing and that freedom of motion is increasing, we're finishing off in a state that has a greater freedom of particle motion. Then, where initially began, still has a gas, but within a smaller space, and therefore we're going from a larger space, a larger guess. So I put large here to a state where the gas is taking up a Somali space. It has a smaller degree. They're a smaller freedom, a particle motion in a small dispersion of energy. Going from a large minus, a smaller number again is going to give us a positive sign. So when you're thinking about entropy once again, think about as it progresses from one face to another when is progressing. If there's an increase in interview, that means there's also increased in the freedom of particle motion, and there's increase in the dispersion of the energy of those particles.