Laws of Thermodynamics: Definition, Equations & Examples

The perpetual pump is one of many perpetual motion machines that have been designed over the years, with the aim of producing continuous motion, and often, as a result, free energy. The design is quite straightforward: Water flows down from a raised platform over a water wheel, which is attached to gears, which in turn operate a pump that pulls water from the surface back up to the raised platform, where the process starts over again.

When you first hear about a design like this, you might think it’s possible and even a good idea. And scientists of the day agreed, until the laws of thermodynamics were discovered and dashed everybody’s hopes of perpetual motion in one swoop.

The laws of thermodynamics are some of the most important laws of physics. They aim to describe energy, including how it is transferred and conserved, along with the crucial concept of the ​entropy​ of a system, which is the part that kills all hope of perpetual motion. If you’re a student of physics, or you’re just looking to understand the many thermodynamic processes occurring all around you, learning the four laws of thermodynamics is a crucial step on your journey.

What Is Thermodynamics?

Thermodynamics is a branch of physics that studies ​heat energy and internal energy​ in thermodynamic systems. Heat energy is the energy passed through heat transfer, and internal energy can be thought of the sum of the kinetic energy and potential energy for all of the particles in a system.

By using kinetic theory as a tool – which explains the properties of the body of matter by studying the motions of its constituent particles – physicists have been able to derive many crucial relationships between important quantities. Of course, calculating the total energy of billions of atoms would be impractical, considering the effective randomness of their precise motions, so the processes used to derive the relationships were built around statistical mechanics and similar approaches.

Essentially, simplifying assumptions and a focus on the “average” behavior over a large number of molecules gave scientists the tools to analyze the system as a whole, without getting stuck in endless calculations for one of billions of atoms.

Important Quantities

To understand the laws of thermodynamics, you need to make sure you understand some of the most important terms. ​Temperature​ is a measure of the average kinetic energy per molecule in a substance – i.e. how much the molecules are moving around (in a liquid or gas) or vibrating in place (in a solid). The SI unit for temperature is Kelvin, where 0 Kelvin is known as “absolute zero,” which is the coldest possible temperature (unlike zero temperature in other systems), where all molecular motion ceases.

Internal energy​ is the total energy of the molecules in a system, meaning the sum of their kinetic energy and potential energy. A difference in temperature between two substances allows heat to flow, which is the ​thermal energy​ that transfers from one to the other. ​Thermodynamic work​ is mechanical work that is performed making use of heat energy, like in a heat engine (sometimes called a Carnot engine).

Entropy​ is a concept that’s difficult to define clearly in words, but mathematically it’s defined as the Boltzmann constant (​k​ = 1.381 × 1023 m2 kg s1 K1) multiplied by the natural logarithm of the number of microstates in a system. In words, it’s often referred to as the measure of “disorder,” but it can be thought of more accurately as the degree to which the state of a system is indistinguishable from a large number of other states when viewed at the macroscopic level.

For example, a tangled headphone wire has a large number of specific possible arrangements, but most of them look just as “tangled” as the others and so have higher entropy than a state where the wire is neatly coiled up with no tangling.

The Zeroth Law of Thermodynamics

The zeroth law of thermodynamics gets it’s number because the first, second and third laws are the most well-known and widely-taught, however, it’s just as important when it comes to understanding the interactions of thermodynamic systems. The zeroth law states that if thermal system A is in thermal equilibrium with thermal system B, and system B is in thermal equilibrium with system C, then system A must be in equilibrium with system C.

This is easy to remember if you think about what it means for one system to be in equilibrium with another. Thinking in terms of heat and temperature: Two systems are in equilibrium with each other when the heat has flowed as such to bring them to the same temperature, like the uniform warm temperature you get some time after pouring boiling water into a jug of colder water.

When they’re in equilibrium (i.e. at the same temperature), either no heat transfer occurs or any small amount of heat flow is quickly canceled out by a flow from the other system.

Thinking about this, it makes sense that if you bring a third system into this situation, it will shift toward equilibrium with the second system, and if it is in equilibrium, it will also be in equilibrium with the first system too.

The First Law of Thermodynamics

The first law of thermodynamics states that the change in internal energy for a system (∆​U​) is equal to the heat transferred to the system (​Q​) minus the work done by the system (​W​). In symbols, this is:

∆U = Q - W

This is essentially a statement of the law of conservation of energy. The system gains energy if heat is transferred to it and loses it if it does work on another system, and the energy flow is reversed in the opposite situations. Remembering that heat is a form of energy transfer, and work is the transferring of mechanical energy, it’s easy to see that this law simply re-states the conservation of energy.

The Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of a closed system (i.e. an isolated system) never decreases, but it can increase or (theoretically) stay the same.

This is often interpreted as meaning that the “disorder” of any isolated system increases over time, but as discussed above this isn’t a strictly accurate way to look at the concept, although it is broadly right. The second law of thermodynamics essentially states that random processes lead to “disorder” in the strict mathematical sense of the term.

Another common source of misconception about the second law of thermodynamics is the meaning of a “closed system.” This should be thought of as a system isolated from the outside world, but without this isolation, entropy ​can​ decrease. For example, a messy bedroom left on its own will never get tidier, but it ​can​ switch to a lower-entropy more organized state if somebody enters and does work on it (i.e. cleans it).

The Third Law of Thermodynamics

The third law of thermodynamics states that as the temperature of a system approaches absolute zero, the entropy of the system approaches a constant. In other words, the second law leaves open the possibility that the entropy of a system can remain constant, but the third law clarifies that this only occurs at ​absolute zero​.

The third law also implies that (and is sometimes stated as) it’s impossible to reduce the temperature of a system to absolute zero with any finite number of operations. In other words, it’s essentially impossible to actually reach absolute zero, although it is possible to get very close to it and minimize the increase in entropy for the system.

When systems get very close to absolute zero, unusual behavior can result. For example, at close to absolute zero, many materials lose all resistance to the flow of electric current, shifting to a state called superconductivity. This is because resistance to current is created by the randomness of the motion of the nuclei of the atoms in the conductor – close to absolute zero, they barely move, and so the resistance is minimized.

Perpetual Motion Machines

The laws of thermodynamics and the law of the conservation of energy explain why perpetual motion machines are not possible. There will always be some “waste” energy created in the process for whatever design you might choose, in accordance with the second law of thermodynamics: The entropy of the system will increase.

The law of conservation of energy shows that any energy in the machine must come from somewhere, and the tendency toward entropy shows why the machine won’t perfectly transmit energy from one form to the other.

Using the water wheel and pump example from the introduction, the water wheel has to have moving parts (for example, the axle and its connection to the wheel, and the gears that transmit the energy to the pump), and these will create friction, losing some energy as heat.

This might seem like a small problem, but even with a small dip in energy output, the pump won’t be able to get ​all​ of the water back up onto the raised surface, thus reducing the energy available for the next attempt. Then, next time, there will be yet more wasted energy and more water unable to be pumped up, and so on. In addition to this, there will also be energy loss from the mechanisms of the pump.

The Entropy of the Universe and You

When thinking about the second law of thermodynamics, you might wonder: If the entropy of an isolated system increases, how could it possibly be that such a highly “ordered” system like a human being came to be? How does my body take disordered input in the form of food and transform it into carefully-designed cells and organs? Don’t these points conflict with the second law of thermodynamics?

These arguments both make the same mistake: Human beings are not a “closed system” (i.e. isolated system) in the strict sense of the world because you interact with and can take energy from the surrounding universe.

When life first emerged on Earth, although the matter transformed from a higher-entropy to a lower-entropy state, there was an energy input into the system from the sun, and this energy enables a system to become lower entropy over time. Note that in thermodynamics, the “universe” is often taken to mean the environment surrounding a state, rather than the whole cosmic universe.

For the example of the human body creating order in the process of making cells, organs and even other humans, the answer is the same: You take in energy from outside, and this enables you to do some things that appear to defy the second law of thermodynamics.

If you were completely cut off from other sources of energy, and you used up all of your body’s stored energy, it would indeed be true that you couldn’t produce cells or perform any of the range of activities that keep you functioning. Without your apparent defiance of the second law of thermodynamics, you would die.

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