This is the second in a series of posts prompted by Stephen Wolfram’s lengthy paper “How Did We Get Here? The Tangled History of the Second Law of Thermodynamics” (click here for it on ArXiv). The Second Law of Thermodynamics says, in brief, that the universe is Doomed, which leads to questions of how we can be so lucky as to not have reached Doom yet. Last week (click here for it) we discussed the Second Law in terms of jars of beads and kindergarteners in a room full of toys. To see how this idea extends to the very habitability of the universe requires knowing something about heat and temperature — thermodynamics.
Temperature is weird. Think of most measurements you know of. Can you have a length less than zero? No. And while we measure length in different units, like inches, centimeters, and light years, we know that zero inches equals zero centimeters equals zero light-years. Can you have less than zero time? No. And zero seconds equals zero hours equals zero years.
But temperature can be less than zero. And the two most commonly used temperature scales, Celsius/Centigrade and Fahrenheit, don’t even agree with each other on their zero point. Zero Celsius is not zero Fahrenheit. That is weird.
Since temperature in Celsius or Fahrenheit can be less than zero, apparently neither zero Fahrenheit nor zero Celsius represents true zero temperature. At the time these systems were created no one knew what zero temperature was. What is true zero temperature, then?
Look at a gas such as air. Air expands when its temperature is raised. Air contracts when its temperature is lowered. A “Ziploc” bag with air in it will be bigger when warmer and smaller when cooler. If you measure the bag’s volume and its temperature and plot volume vs. temperature you get a plot that looks like the left-hand plot below. This plot is linear. If you project backwards to see at what temperature the volume of the gas in the bag would be zero, as seen at below right, you get an answer of 460 degrees below zero. This works no matter what gas is in the bag — air, helium, natural gas, CO2, you name it. If you do the same experiment in Celsius temperature your answer comes out to 273 degrees below zero Celsius. This temperature of -460°F or -273°C is the true zero of temperature, otherwise known as absolute zero.

Temperature scales really should have their zero point at absolute zero. There are two “absolute” temperature scales that do — one called the Kelvin scale that has units based on the Celsius system, and one called the Rankine scale that has units based on the Fahrenheit system. In Fahrenheit, water boils at 212, freezes at 32, and absolute zero is at -460. In Rankine, everything is shifted by 460. Water boils at 672, freezes at 492, and absolute zero is 0. In Celsius/Centigrade, water boils at 100, freezes at 0, and absolute zero is at -273. In Kelvin, everything is shifted by 273. Water boils at 373, freezes at 273, and absolute zero is 0. Note that zero Kelvin equals zero Rankine, just like zero inches equals zero centimeters.
So what is temperature, then? And what is this absolute zero? Temperature is a measure of the microscopic-scale motions of atoms and molecules that comprise matter. The three common phases or states of matter are solids, liquids, and gasses. Each of these has certain microscopic characteristics which result in macroscopic properties which we can see easily.
The macroscopic properties of a solid (like salt, rock, and ice) are that it is rigid (it holds it own shape) and incompressible. That is because the molecules in a solid are held in fixed positions by elastic bonds between them. The molecules can vibrate around those fixed positions, much as if they were connected together by springs, but cannot move around among each other. The macroscopic properties of a liquid (like water or the metal mercury) are that it takes shape of its container, but has a defined top surface. A liquid flows and is incompressible. This comes from molecules that are bound together but able to move freely around one another, like magnetic marbles. The macroscopic properties of a gas (like oxygen, methane, or helium) are that it takes shape of its container completely — it has no defined surface. Gasses flow and are compressible. This is because the molecules in a gas are not bound together. They fly freely at high speed and only interact when they collide. They also collide with the walls of the gas’s container. All these collisions occur without loss of energy.

In each state, greater temperature corresponds to greater motion of molecules and more energy per molecule. In ice on a bitterly cold day, the molecules vibrate around their fixed positions less violently than in ice on a day that is just a few of degrees below freezing. When liquid water is very hot, but not boiling, the molecules move around one another more rapidly than when the liquid water is cool. And the molecules in steam fly around faster and collide more violently in steam that has been heated to hundreds of degrees above boiling than in steam whose temperature is just barely above boiling. Temperature is a measure of the motion energy of molecules in any substance. And when there is no motion you have absolute zero temperature.
The fact that greater temperature means greater violence of movement in molecules explains why most materials expand when heated. In the case of solids, the greater violence of vibration means that the molecules that make up the solid must “spread out” — one hundred people standing and shuffling their feet can be packed pretty close together. If those same people start dancing jigs they will have to spread out. The result is that solids expand when heated. The expansion is in all directions.
The connection between temperature and violence of movement in molecules also explains “evaporative cooling” and sweat. Evaporative cooling occurs because, while it is true that in a hot material molecules move more violently than in a cooler material, that is only true in the average. In fact, molecules in any material move in random directions, at random speeds. Some move faster and some move slower than the average for the whole. Even in a solid, some molecules vibrate more violently than others. Roughly speaking, most molecules in a material move near the average speed, with relatively few molecules moving at exceptionally high or low speeds. The profile of molecular speeds is known as the molecular speed distribution. Note that even in a hot material there will be some very slow-moving molecules, and even in a cold material there will be some very fast-moving molecules.
In a liquid, the faster-moving molecules are more likely to break free of the rest of the molecules and fly free, going into a gaseous state (evaporation). When the faster molecules leave, the slower ones are left behind and the average speed of molecules for the liquid is lowered. Since temperature depends on molecular speed, a lower average speed means a colder liquid.

The rate of evaporation depends on things like temperature difference and surface area, but it also depends on other factors. For instance, our bodies cool themselves via evaporative cooling by sweating. Evaporation of water depends on the humidity level in the air. If we are doing strenuous activity on a hot day, we will sweat. If the air outside our bodies is hot and dry, evaporation occurs rapidly, our bodies cool themselves efficiently by sweating, the sweat goes away (evaporates), and we feel comfortable and dry. If the air outside our bodies is hot and very humid, evaporation does not occur rapidly, our bodies do not cool themselves efficiently by sweating, the sweat runs off our brows and noses and down our backs, soaking our clothes, and we feel hot and sweaty.
Yes, sweating is connected to Doom!
One way of stating the Second Law of Thermodynamics is to say that heat energy naturally flows from hotter objects to colder objects. Consider a hot object — “Object A” — like a lump of clay. Its molecules move rapidly on average, but some move faster than average; some move slower than average. Now think of a cool object that is otherwise identical to A — we’ll call this “Object B”, another lump of clay. Its molecules move slowly on average, but again some move even slower than average, and a very few move really fast.
The two lumps are then smashed together. Now there can be direct interaction between molecules. When that happens, the fast-moving molecules in A are on average going to smack the slow-moving molecules in B, transferring some energy from the “fasts” to the “slows”. The result is that the molecules in B will move more violently, and B’s temperature will increase, while the molecules in A will move less violently, and A’s temperature will decrease. Heat flows from Hot to Cold. Object A cools down and object B heats up until they reach the same temperature (that is, until they have the same average molecular motion), a state called thermal equilibrium.
This does not mean that occasionally one of B’s few fast-movers won’t happen to transfer energy to one of A’s few slow-movers. But the chances of that happening are very small. In order for heat to flow from Cold to Hot, it would require that all of B’s fast-movers just so happened to interact with all of A’s slow-movers. The chance of that occurring is ridiculously small, given the number of molecules in even as small an object as a grain of sand.
And so the flow of heat is like the beads in the jar in last week’s post. A hot object (A) and a cold object (B) are like the reds beads sitting atop the yellow beads: the fast-movers are generally in one place, the slow-movers in another. But allow nature to take its course, and things mix and become a homogeneous mess.
So what we learned this week, that the Second Law of Thermodynamics says that heat energy naturally flows from hotter objects to colder objects, and what we learned last week, that the Second Law of Thermodynamics says that things in nature tend toward disorder, are of a piece. That means that the universe is Doomed to eventually becoming a homogeneous mess — hot things must cool off, cool things must warm up, and eventually everything must reach the same temperature, or thermal equilibrium. No glowing stars warming the cool seas of their planets, providing energy for life. Instead, there will be just a universal darkness that lasts forever as its last bits of temperature difference approach equilibrium, asymptotically (remember that term from math class?).
This Doom can’t be stopped, because as we saw last week, undoing disorder requires effort. Where does effort come from? Ultimately from heat flow — the sun warms the Earth, plants grow, and we eat the plants and have energy to re-arrange the beads in the jar or clean up the room. The phrase sometimes used to describe this Doom of the universe is “heat death”.
But the Second Law means something else besides Doom. It means that things are always changing, and thus the universe has not always been the way it is now. Wolfram points to an 1852 paper by William Thomson (a pioneer in thermodynamics, who had the title of Lord Kelvin) titled “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” as evidence of the first time someone realized this. Thomson writes that at one time “the earth must have been… unfit for the habitation of man” and that in the future “the earth must again be” unfit.
Uh-oh. That’s a problem. How do we explain how we are here, in this happy moment of a habitable Earth in a universe Doomed to eternal lifelessness?
We will talk about that in two weeks (taking a break from this topic next week)!
CLICK HERE for all posts in this series.