Chemistry: Entropy & the 2nd Law of Thermodynamics

This lesson has not been reviewed.

Please purchase the lesson to review.

We know that the majority of spontaneous processes occur with the release of energy. In other words, if we go from a higher energy to a lower energy - in terms of a chemical reaction, we can talk about an enthalpy - that nature, in general, is always going to favor releasing energy in that process. But we also know that there are some processes that are spontaneous even when that doesn't happen. And a classic example of that is evaporation of water, that it costs us energy. We can measure the amount of energy it costs. The enthalpy is positive to evaporate the water. And yet, it still happens. So we want to focus now on this other influence in nature - this other driving force, almost we could say - entropy.
Now, to get a better idea of what entropy is and why it is, let's do a thought experiment. Let's suppose that we have two bulbs that are completely empty and they're connected by a valve and initially, I have the valve closed. And we'll introduce - as a thought experiment - one molecule of a gas. Now, I'm going to open that valve and I'm going to ask what is the probability, when I come back tomorrow, that this molecule will be in this side? Well, the answer is going to be 50 percent, right? Just like flipping a coin, I've got an equal probability of it being here or here, as long as my two volumes are the same, which they are, in this thought experiment.
So now, let me ask you another question. What if we introduced a second molecule of gas on this side - we opened our valve again, went away and came back tomorrow - what are the chances that both of those molecules are on the same side of the container? Well, now, the probability would be 50 percent for this one times 50 percent for this one - or 2.5 percent total probability that both molecules would be on this side. Well, what about putting in a third or a fourth or 10 or 20 or 100? We know now that the probability of having all of those molecules appear on one side, once we've opened that valve, gets vanishingly small as we get to more and more particles. Because It's not the probability of one particle anymore; it's the probability of one particle times the probability of this particle times the probability of the next particle and so on. So it's the probability to whatever power of particles we have. So if it was 4 particles, it would be .5^4 would describe the probability. But if it's 100 particles, then it would be .5^100. And if it's Avogadro's number of particles - a whole mole of particles - then it's going to be a number so huge that it would take us the rest of this CD just to write out the zeros for it.
So, it's not when we open this valve and we ask what's the possibility of all the molecules staying here and not expanding over into the empty space? The probability is not zero that they'll all stay here, but it's vanishingly small. It's whatever number the particle is times .5 to the number of particles that you have. And so, looking at that another way, if we kind of take our macroscopic view again and say, okay, we've got a mole of gas over here and I turn the valve, what's going to happen? Well, we know what's going to happen is that gas is going to expand into this other container. We don't need to talk about pressures. We don't need to talk about anything else. Forget all of that. Just simply on where the molecules are and what are the chances of the molecules being here versus here, we know that what's going to happen is that gas will expand. And it would be extremely unlikely if all of sudden - after having the gas equally spread out in those two containers - if all of a sudden, spontaneously, all the gas rushed back over into this container. We could calculate the probability of that happening, but we know it's next to zero.
So this is a sense of entropy. On a macroscopic level, we can say, "Oh, nature likes to go to more disorder." But another way to interpret that is through statistics, that it's not that nature has some special sense that it gets more disordered if it expands this gas; it's simply the statistical possibilities of all of the molecules randomly ending up over here are infinitesimally small. So really, that's all entropy is - it's statistics.
So, again, we can go to this notion of expanding a gas - the idea that we turn this valve, that gas expands. That is going to increase the entropy of the system when that happens, simply because the molecules now can experience a greater volume than before. When I take a drop of food coloring and I add it to this water, the food coloring expands, but not for any mystical reason - not for any reason of energy or anything else - but simply because the molecules can experience more volume - more statistical possibilities - if they leave that droplet and venture out into the rest of the volume of the water. In fact, I could calculate, if I had nothing else to do with my life, what the statistical chances are for all of those dye molecules to reassemble into one drop. I'd be able to calculate a real number. But it's not worth us doing, because the number is simply so small. But once again, it all has to do with statistics. That's what's behind entropy.
In a similar sense, we could talk about a chemical reaction - a chemical reaction involving two liquids, let's say, mixed together. And after the reaction is complete, we generate a mole of gas, let's suppose, as one of our products. Maybe we generate carbon dioxide or something like that. And what we find is that although there may be a strong chemical reason that this reaction may not occur - in other words, suppose that it's an endothermic reaction - well, there may be an entropic reason that it does occur. In other words, it might be that simply because of the statistical possibilities, to have the molecules up here in this volume - compared to down here, trapped next to other molecules - that there is just so much more randomness on this side of the equation than this side - or in this state of affairs than this - that the system would want to do this, even if it costs energy to do it - in terms of the enthalpy being endothermic. So the same exact idea, that it's possible to have a process that costs you energy yet still be spontaneous if the entropy increases.
Now, does it always happen - is it always spontaneous - if it goes through an increase in entropy? Certainly, the answer to that is going to be no, that there are going to be certain processes - and we'll talk lots more about this - where the chemical price to pay - the energetic price, the enthalpic price - is just much to great to, even if you get the benefit of having more disorder. So, again, what we're going to find out is what determines how spontaneous a reaction is is this fine balance between the enthalpic cost or gain - how much heat needs to be absorbed or released - and the disorder - what the entropy of the system is.
Now, we talked about the idea of nature wanting to have greater disorder in terms of particles. Let's talk about something a little different. Let's talk about the notion of thermal energy - just random thermal energy, kinetic energy if you will - not talking just about translational kinetic energy but how molecules vibrate, how they spin, how they move - everything involving how they store energy.
Now, wouldn't it be wonderful if you could have a house and let's suppose you're in the middle of a Virginia winter and it's minus 20 outside and so it's darn cold. And you could be able to somehow summon in the heat. Now, remember, there is still thermal energy out at minus 20 degrees - plenty of random energy out there. It would be wonderful if you could somehow bring that heat into your house without costing any energy in the process. I mean there's plenty of thermal energy out there. It's just a matter of getting it to come into your house so you could keep your house at a nice, cozy 75 degrees when it's cold outside. And you know this is a pipe dream. This is not going to happen. You're going to need to spend a lot of energy, through your electrical bills or through a chemical reaction, like burning oil, to be able to get your temperature above the temperature of outside. And there's a good reason for that, that nature is not going to spontaneously have energy that's been spread out throughout the universe spontaneously assemble in one location. That would be the same idea as if you had a cow that spontaneously could fly simply because it absorbed enough energy from the surroundings. There's plenty of energy around for the cow to do this, but nature doesn't seem to cooperate in that way. We can't spontaneously assemble energy and draw energy into one point, or one small location. Nature spontaneously wants to go the other direction. If you have a fire outside a bonfire, that heat liberated from that chemical reaction is lost into the surroundings and we can't get that back.
So, there are processes involving taking heat - whether it's just from the sun - now I'm not talking about solar energy; I'm talking about just heat as a result of the sun - so not photons now, just thermal energy - and using that heat to, let's say, warm up a gas or create a gas from a liquid, a low-boiling liquid, run a turbine with the pressure of the gas and then dump off the heat, so that we can go back to a liquid again, and we turn that liquid and complete the cycle. This type of process does occur. In fact, one of the places this occurs is in geysers. You take advantage of the fact that the heat at the center of the Earth is much higher than out at the surface, and it boils water, turns to steam. We use that energy in power plants. Geothermal plants do that.
But what makes those processes happen is the fact that you can remove heat over here and transfer heat from higher temperatures to lower temperatures. But nature will not transfer heat spontaneously - thermal energy spontaneously - from two equal temperatures. Nor will it spontaneously ever transfer energy from a lower temperature to a higher temperature. So the idea of heating our house this way could never happen because it would require transferring energy from a lower temperature to a higher temperature. And that's not a spontaneous process.
So we've talked about particles. We've talked about energy. It's time to get to the second law of thermodynamics, which says:
"The total entropy for any spontaneous process must increase."
Now, that's very profound. That means that nature will always insist on - if it's going to be a spontaneous process - increasing the entropy of the universe. But wait a minute. This says nothing about energy at all. What happened to the idea of nature wanting to go to lower energy? Okay, let me ask you to think about this. If I take a beer out of the refrigerator on a hot Texas summer day and I set that beer out, it won't take very long for the beer to collect moisture from the surroundings on the surface of the beer bottle. And we see condensation of water - if it's a humid day, at least. Well, that, seemingly, violates the second law of thermodynamics, because gas molecules were spread throughout. They had maximum disorder and yet, in this process, they're being collected into the liquid phase. How is that possible? Doesn't that violate the second law of thermodynamics? And the answer is, no. This is talking about total entropy. Not just the entropy of the water molecules, but the entropy of the whole enchilada, of the world, of the universe. And in that sense, we haven't violated anything. Why? Because what happens when those water molecules come together? Well, they release heat when they condense. That heat is lost in the surroundings. That heat increases the entropy of the universe. So we raise the entropy of the universe at the expense of loosing some of the entropy of the water molecules, but overall, it's a net plus. We've increased entropy. We haven't violated the second law. We haven't violated the first law. That just says energy is saved - conserved - so we haven't violated anything in terms of that.
But now we understand why nature wants to go to lower energy in the first place. The only reason nature cares about going form high energy to low energy is that in doing so, the energy difference is released to the surroundings, and that increases the entropy of the universe. So you see, it's all about entropy. Everything in the world can be explained by the second law of thermodynamics and nature's desire to maximize disorder.
Thermodynamics
Entropy
Entropy and the Second Law of Thermodynamics Page [1 of 3]