In general chemistry, we tell our students that the second law of thermodynamics is all about maximizing entropy. What is entropy? It’s a nebulous thingamajig that we are seemingly “forced” to introduce to explain why certain physical processes take place. For example, gases seem to always expand into vacuum, and table salt always seems to dissolve in water at room temperature and pressure.
When I first started teaching, general chemistry textbooks characterized entropy qualitatively (e.g., disorder, freedom of movement, heat dissipation); and then quantified the change in entropy by relating it to the change in enthalpy per unit temperature. Students are puzzled by what this means. Then we thought it might be clearer if we smuggled in some physical chemistry concepts into general chemistry, and current textbook “teaches” students how to count microstates and group them into macrostates. This causes our students to focus on one particular view of entropy: counting the number of arrangements and assessing probabilities of different arrangements. It feels more scientific when you can quantify something, I suppose. And (while they shouldn’t), students feel more comfortable when there’s a formula you can plug things into.
What we often don’t tell them: Our characterization of entropy arises because we’re using a closed-system model of equilibrium thermodynamics. I’ve been trying to highlight the usefulness and limitations of models in my classes, more than usual this semester. I think subconsciously that’s because it feels like we’re all trapped in our little Zoom boxes on-screen. I can’t wait to get back to in-person classes and relish the freedom of being in a more “open” environment.
Perhaps a better and more general way to think about the second law is that it’s all about reducing gradients. We talk about gradients in chemistry, usually related to concentration gradients, and we allude to gradients when we use the dictum that “everything is trying to become more stable” – energetically. We talk about downhill chemical reactions being favorable. We use the example of a waterfall when we discuss potential gradients in electrochemistry, analogizing the flow of electrons in the latter to the flow of water molecules in the former. And of course, the zeroth law of thermodynamics is all about reducing temperature gradients – our epitome of a ‘spontaneous’ process.
In closed systems, gradients are reduced until they no longer exist. You’re done. You’re at equilibrium. You’ve maximized your entropy. This is an oddly static picture. We remind our students that things are actually at dynamic equilibrium – chemical reactions are still going back and forth but at the same rates so that macroscopically it looks like nothing’s changing. Students then get muddled when they encounter steady state flows in biochemistry. It vaguely looks similar, but seems different. That’s because we’re now in a non-equilibrium situation, and we’re no longer operating in a closed system. But we’re still trying to reduce a gradient – even though that gradient persists in an open system even as energy flows down the gradient to be dissipated. This wider lens view of thermodynamics is (I think) more useful because it helps us understand Schrodinger’s Paradox – why seemingly ordered life exists in conjunction with the second law of thermodynamics.
The authors of the book Into the Cool have something useful to say about this: “Classical thermodynamics heads towards maximum entropy, exhaustion. In Onsager’s realm [of near-equilibrium processes] we see another situation, systems that minimize their entropy production. Energy scientists often assign systems a certain quantity of entropy production. But a better measure is specific entropy production… per unit weight, per unit volume of flow, per unit surface area… Subjected to continuous flow of energy and matter, no system can come to equilibrium… it does the next best thing… goes to a state of minimum entropy production – that is, to a state as close to equilibrium as possible.”
How do living systems accomplish this? Interestingly, here’s where kinetics comes in. Below is a typical picture I show in my G-Chem classes. I remind them that we often treat thermodynamics and kinetics as being independent from each other (the “activation energy” is not connected to the thermodynamic gradient), but they are more subtly connected.
Imagine a mountain-top lake, such as those that feed the great rivers of planet Earth. Water flows down, often in more than one path. Gradients drive the flow, and the kinetic energy of liquid water cuts it way through the solid earth. The flows can change, cutting out new paths downhill, and sometimes they deepen the current flow path allowing a greater flux of water. Sometimes they spill over their banks in flooding devastation. What did we humans do? We sought to utilize the natural flow down the gradient. We built dams. These structures allow us to control the flow of water, converting the potential energy into other forms whereby we can do useful work. We’ve set up a barrier allowing us to control the kinetics of water flow. The downhill thermodynamic gradient is dammed by kinetics.
I’ll quote from Into the Cool once more: “We are continually threatened by a too-large entropy production that would destroy our delicate bodies. Activation energy… keeps our bodies from exploding in puffs of smoke… In life, the chemical tendency inherent in the second law for the hydrogen of bodies to react with the oxygen in the atmosphere does not happen as violently – as in rocket fuel – but is channeled through the complex chemical systems we recognize as metabolism. And so, with intricate feedback loops and controls, we slowly‘burn’, metabolizing rather than bursting into flames. But these chemical systems, like a waterwheel catching and redirecting a powerful stream to run a mill, can fail…”
Death lurks around the corner. We’re damned by thermodynamics. But life persists. Dammed by Kinetics. It’s an intricate dance. A dynamic steady state. A spiral of cycles. Let the music play on while the sun shines and maintains its energy gradient with us here on planet Earth.
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