# The 2nd Law of Thermodynamics

#### Prerequisites

The First Law of Thermodynamics restricts the set of processes that are allowed to happen in our world. Whenever a process that violates the First Law has been observed in the history of science, a new form of energy has been found that restores it (so far). We are on pretty sound footing when we state that we expect that no processes can or ever will violate the principle of energy conservation that the full form of the law expresses.

Does that mean we are done with our story of Thermodynamics?  We can ask:

If energy is conserved, why do we have to conserve energy?

You already know from your chemistry class that not all forms of energy are equivalent and the utility of energy may depend on the context. Understanding the limitations on what can be done with energy, and when, is critical for understanding the flow of energy (and information!) in biological systems.

The examples that follow will hopefully convince you that to fully account for what we actually observe in nature, we need to introduce at least one more Law about energy and the world. It will turn out that this additional law, the Second Law of Thermodynamics, is one of the most powerful and important statements in all of science. From your everyday experience, you already know a lot of results that are an expression of the Second Law. Let's review them in a few thought experiments.

### Thought Experiment 1.  The Hot Object and the Cold Object.

Suppose I place a hot object in contact with a cold object. What happens? As you would imagine, the hot object gets cooler and the cold object gets warmer. Heat is transferred from the hot object to the cold object, and the hot object's temperature decreases while the cold object's temperature increases.

Question:  Why do we never spontaneously observe the reverse process?  (The key word here is "spontaneously". We can do it if we put energy in — for example, a refrigerator moves heat out of a cold object and dumps it in warmer air. But it doesn't work if you don't plug it in!)

Why does the heat transfer in this example not go from the cold object toward the hot object, so that the temperature of the hot object increases and the temperature of the cold object decreases? Why doesn't the hot coffee get hotter and cool the air around it? As silly as such a scenario might sound, that result in no way violates the First Law of Thermodynamics. According to the principle of energy conservation, there is no reason why heat cannot transfer from a cold object to a hot object! And yet, as we all know, that just does not seem to ever spontaneously happen. Why not?

### Thought Experiment 2.  The Sliding Chair.

Suppose we push a chair across a classroom floor.  The moving chair (our system) has kinetic energy, but as we all have observed many times that chair quickly comes to rest.

Question: If energy is conserved, where did the kinetic energy of the moving chair go?

The answer is that the chair's kinetic energy is transferred to the incoherent kinetic and potential energies of the molecules comprising the floor — thermal energy. As the chair slides across the floor, its legs bump and jostle the floor molecules, causing them to oscillate randomly around their equilibrium positions. If we had a sensitive thermometer, we would measure that in fact the floor gets a little bit hotter! The kinetic energy of the chair has thus been transferred to motion of randomly oscillating floor molecules, causing the chair to stop moving and the floor to be at a slightly higher temperature.

Why do we never spontaneously observe the reverse process? Why do we never see the floor spontaneously cool a little bit, transferring some of its molecular kinetic energy to a resting chair so that the chair begins to slide across the room?

The important point to note here is that the First Law of Thermodynamics allows such a reverse process to occur. Nothing about the reverse process (the process by which the resting chair gathers energy from the floor it sits on and spontaneously begins to move) violates the First Law! Energy conservation alone tells us that both processes, the chair sliding to a stop and the chair absorbing energy from the floor and beginning to move, are allowed. So why do we only observe one of the two processes to occur spontaneously?

### Thought Experiment 3.  The Smoke-filled Room.

Suppose someone is smoking a cigarette in the corner of a room. As anyone standing in the opposite corner of the room will report, the smoke gradually spreads out to fill the room. Eventually the smoke is fairly uniformly distributed around the room.

Question:  Why do we never spontaneously observe the reverse process?  Why does the smoke in a smoke-filled room never spontaneously coalesce in the corner where the smoker is standing?

Although the application of the First Law of Thermodynamics to this situation may not seem as obvious as it does in some of the previous examples, there is nothing about the reverse process that smells like a First Law violation. Whatever collisions occur between the particles of smoke and the air molecules in the room, it would seem that those individual collisions — like collisions between billiard balls — could equally well occur in "forward" or "reverse" directions. Why then does smoke always spread out to fill the room?

All three of our examples speak to a common observation about the world:  while no processes are ever observed to violate the First Law of Thermodynamics, some processes simply are not observed to spontaneously occur ... even when the First Law permits them to. How then do we account for this? How do we make sense of a world in which only some processes occur and others don't?  It turns out that we will be able to explain all of these asymmetries by means of the Second Law of Thermodynamics.

Ben Geller 11/8/11 and Joe Redish 12/6/11

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