The Laws of Thermodynamics

As the name says, these are laws related to heat (thermo) and work (dynamics). Thermodynamics was developed in the early 1800's, particularly for the study of steam engines. It has since become one of the most fundamental branches of physics.

Originally, there were two laws of thermodynamics, the 1st and the 2nd. Later, more were added. Not all are universally accepted as "laws". I'll describe them in the order of most to least fundamental, though this has no bearing on their history or acceptance.

But before we start, let's define a few terms.

Thermodynamic System

In thermodynamics, it's often useful to separate the universe into "systems" that can be studied individually. For example, consider a block of ice melting in a room. In order to study this, it might be useful to consider the ice as a thermodynamic system, interacting with another thermodynamic system (the room). This allows us to understand how energy and matter moves between systems. The system's boundaries may be real (surface of the ice) or imaginary. Depending on the flow of energy, thermodynamic systems may be:

Thermodynamic processes can be described as:

Thermodynamic Equilibrium

A thermodynamic system is at equilibrium with its environment when its thermodynamic properties (those properties which measure its thermodynamic state, that is, its energy and mass, such as temperature, pressure, volume, etc.) do not change over time. Note that we are talking about macroscopic properties (temperature, pressure, volume, etc.). There will always be microscopic fluctuations, but the key is that over a period of time, there is no net flow of energy between the systems.

Thermodynamic Cycle

Many interesting thermodynamic processes (such as those that relate to heat engines) are cyclic. So it's often convenient to apply the laws of thermodynamics not to an individual thermodynamic process, but to the cycle as a whole. A thermodynamic cycle is simply a set or sequence of thermodynamic processes, which return the thermodynamic system back to its original state. By "original state" I mean the macroscopic thermodynamic parameters (temperature, pressure, volume, etc.) are the same at the end of the cycle as they were at the beginning.

With these definitions out of the way, here are the laws of thermodynamics.

Zeroth Law of Thermodynamics

This states that if two thermodynamic systems are in equilibrium with a third system, then they are also in thermodynamic equilibrium with each other. That is, all three share some thermodynamic state which does not allow a net energy flow between these systems. This state can be utilized conceptually to understand the idea of "temperature".

First Law of Thermodynamics

This is also known as the law of conservation of energy, and in the broadest sense it simply says that in any thermodynamic process, the total energy of the universe remains the same. Applying this law to a specific thermodynamic process, we can restate it as: the increase in energy for a thermodynamic system equals the amount of energy added (such as by heating the system) minus the energy lost as a result of the work done by the system on its surroundings. For a full thermodynamic cycle, the sum of net heat applied to the system and the net work done by the system equals zero.

Second Law of Thermodynamics

This law is stated in multiple ways, depending on the context. One common way to state this law is: the entropy of an isolated system not in equilibrium will tend to increase over time until it reaches equilibrium. In other words, the entropy of such a system will never decrease.

This statement may seem weird, but it makes sense when we consider that "equilibrium" here doesn't mean "equilibrium between two systems", but rather internal equilibrium. An isolated system can't exchange heat/work/energy with the outside, but on the inside it might have energy concentrated in parts of it. For example, consider the thermos flask half full of hot coffee. The thermos is an isolated system, but internally the coffee part of it has a lot more heat stored in it than the air part. The second law says that the entropy of the system as a whole will increase over time, until it reaches internal equilibrium, that is, when the heat is distributed evenly throughout the system.

Here's a more understandable version of the second law: in an isolated system, a process can only occur if it increases the total entropy of the system. Again, the system is isolated, meaning no exchange of heat/work/matter can occur with the outside. The heat content within the system cannot increase, nor can the matter. It's not doing work on the outside, and the outside isn't doing work on it. In such a system, the only processes that can occur are those which increase the total entropy of the system. For example, if there are pockets of hot and cold within the system, they can even out. If there are pockets of high and low pressure, they can even out. These processes all increase the entropy.

Another way to state the law is: heat can't spontaneously flow from a colder system to a warmer system. This is because the flow of heat from hot to cold increases entropy (evening out the differences) and therefore can occur spontaneously, but a flow from cold to hot would exaggerate the differences (decreasing entropy), which cannot spontaneously occur.

In a thermodynamic sense, entropy is a measure of energy dispersal, specifically dispersal of energy that can do work. Differences in temperature, pressure, or density can all be used to do useful work -- therefore, such differences are decreased, the energy is dispersed, increasing the entropy. When the system reaches maximum energy dispersal, it is at equilibrium within itself. No more net flow of energy will happen inside it, because it has reached maximum entropy. At this point, the system is no longer capable of doing work. This does NOT mean that the energy of the system is zero. It could be boiling hot, but because the heat has spread evenly through the system, it can no longer do any work. In order for this system to be used to do work, we must break its isolation, allow it to interact with something outside it. In that case, it may be possible to extract work from it again, but only because entropy is now increasing in the outside.

Third Law of Thermodynamics

This leads us directly to the next question. If, as in the previous example, you could have a thermos (an isolated system) at internal equilibrium (all parts of the system have the same energy density) it would have its maximum entropy. Since no further net movement of energy is possible within the system, this system can no longer do work.

But this system still has some definite heat content, even though the heat may be evenly dispersed. Suppose the temperature of this system is 100 degrees Centigrade. Obviously, there's a lot of heat in it. What happens to the entropy if all else remained the same, but the temperature was 0 degrees Centigrade instead of 100? This is answered by the Third Law: as the temperature of a system approaches absolute zero, the entropy approaches a constant minimum.

This tells us a couple of things: first, there is an absolute relationship between temperature and entropy. The lower the temperature, the lower the entropy. Second, it tells us that in order to reach absolute zero and zero entropy, the material must have a unique ground state. The ground state is simply the lowest energy configuration possible for a material. Most materials do not have a unique ground state, they have multiple ground states. For example, elements such as hydrogen which contain half-integer spins will have more than one ground state (having more than a single ground state is called degeneracy).

If there is degeneracy, the material even at absolute zero would still have some positive entropy. Only in the rare case of perfectly crystalline materials with a single ground state can you even theoretically have a temperature of absolute zero with zero entropy.