Sunday, December 31, 2017

The Laws of Thermodynamics PART 1

The Laws of Thermodynamics

Thermodynamics is the branch of physics that explores how heat and temperature relate to the energy of a system and its ability to do work. Almost every field of science, especially those in chemistry and engineering, relies heavily on an understanding of the principles of thermodynamics. Words such as internal energy, heat, temperature and entropy signal that a thermodynamic process is being described. Every process in the universe is a thermodynamic process.

A Brief History

Even the ancient Egyptians were curious about heat. In their time, free from any scientific encumbrances, they thought of heat as one of four essential or basic elements of matter, fire, along with water, earth and air. Much later, in the 17th and 18th centuries, investigators began to wonder if heat was a kind of physical substance, something that flows such as phlogiston or caloric. They imagined that heat physically flowed from one substance or object into another. In the early and mid-1800's, scientists such as Joseph Black, Antoine Lavoisier and James Prescott Joule, utilized the rigour of the scientific method to study heat scientifically and quantitatively. The study of thermodynamics as a science took off when engineers used these new concepts about heat transfer to maximize the efficiency of the first steam engines.
The first steam engine, the Thomas Savory steam pump, patented in 1698, was a highly inefficient but inexpensive coal-chugging device designed to pump water out of coalmines. It wasn't elegant but in short order people realized that they could use the power of steam to manufacture machinery and transport goods and people. Besides leading to the first railway locomotives, the improved stationary piston steam engine revolutionized manufacturing in general. It was a crucial development that ushered in the Industrial Revolution across Europe and North America. The first stream engine, as we know it, had a piston that could generate and transfer power to a machine. It was invented in 1712 by Thomas Newcomen. James Watt later in 1781 revolutionized the steam engine into a rotary motion engine that could drive factory machinery. He also introduced a condenser, which greatly improved its efficiency.

About a century after Watt's revolutionary work (in 1894), another Scotsman, William Thomson (Lord Kelvin), came up with the first precise definition of this new field of steam-engine thermodynamics, as well as the word itself: "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."

If we look back on all the frenetic activity of the 18th and 19th centuries that contributed to numerous branches of thermodynamics we have today, the birth of thermodynamics as a modern science is actually best attributed to a less well-known man, Sadi Carnot. Thirty years prior to Lord Kelvin's work, he published "Reflections of the Motive Power of Fire," an examination of heat, power and engine efficiency. In this treatise, he introduced the concept of work along with its connection to thermal energy (which is thermodynamics in a nutshell). He abstracted the steam engine so that, as an engineer and physicist, he could focus it into an idealized heat engine. By doing so, he developed the first model thermodynamic system, a concept that is still widely used today, especially among engineers who need to understand the often-nuanced differences between a real mechanical engine and the simpler idealized theoretical model. Most physicists today consider Sadi Carnot to be the father of thermodynamics. Yet, sadly, almost no one paid attention to his book during his lifetime, cut short at the age of 36 by cholera. Because cholera is so contagious, all of his belongings and almost all of his writings were buried along with him when he died. Miraculously, the book survived and Lord Kelvin, with much effort, was able to get a copy of it to use as part of the basis for his own famous work.

In A Nutshell

So what exactly is thermodynamics? You could think of it as the puzzle that connects four concepts: heat, temperature, energy and work. The box the puzzle comes in is the thermodynamic system. There are four basic laws that tell us how the puzzle fits together: These are the zeroth law, the first law, the second law and the third law.

Physicist Lidia del Rio and co-authors recently wrote in the Journal of Physics A that "If physical theories were people, thermodynamics would be the village witch. The other theories find her somewhat odd, somehow different in nature from the rest, yet everyone comes to her for advice, and no one dares to contradict her."

What is a Thermodynamic System?

The concept of a thermodynamic system began with Sadi Carnot, who thought about the "working substance" in a heat engine. In his case, this working substance was a volume of water vapour. His working substance was, in essence, a thermodynamic system in itself. It was aptly named a "working" substance because, as a system, it can do work when heat is transferred into it. It can be put in contact with a piston or a boiler, for example. Below is a modern version of Carnot's engine diagram. It gives us an idea of how his working substance works in a simple heat engine.

Eric Gaba; Wikipedia
Thermal energy as transferred as heat from a hot furnace TH (left) through the fluid of a working substance such as water vapour (the circle) into a cold heat sink, TC (right). As the heat is transferred, it forces the working substance to do mechanical work on its surroundings (W). This work could be then be transferred to the cycles of expansion/contraction that turn a piston, for example.

This diagram is a simple theoretical thermodynamic system. Carnot thought of it as an isolated system. That means there would be no interaction whatsoever with the surrounding air, the walls of the containers used, etc. There would be no interactions that, in real life, make all thermodynamic systems, at least to some degree, open in terms of energy transfer. In a real steam engine, for example, there are numerous ways in which energy is lost to the surrounding materials and to the air, particularly as heat loss and as friction, a loss of usable work. In a real engine, there are always many ways in which energy that could theoretically do work is permanently lost instead and those losses are substantial. No real mechanical engine can be 100% efficient. Most are far from it. The latest gasoline fuel-injection combustion engine technology is up to about 35% efficiency. The latest stream turbine power generator technology is about 42% efficient which means that in both cases the majority of the energy generated is lost from the system and unavailable to do useful work.

Everything that has a temperature is a thermodynamic system, and in reality all such systems interact with other surrounding systems. The only truly isolated system is perhaps the universe itself (at least according to non-multiverse theories). These interactions mean that real thermodynamic systems are complicated, so when we want to study how a system works, we want to simplify it into a theoretically isolated system where we can limit its interactions with the world around it. We impose theoretical impermeable walls around it. "Isolated" is different from "closed." A closed thermodynamic system is one in which energy, but not matter, can be exchanged with its surroundings. In an open system both energy and matter can be exchanged.

A theoretical example of an isolated system is hot coffee enclosed in an impossibly perfectly insulated Thermos bottle. It is never going to cool off (there is no energy transfer) and you can't smell its aroma (there is no transfer of matter). An example of a closed system would be hot coffee in a very well sealed plastic container. It's going to cool off but you can't smell it. An example of an open system could be the hot coffee in an open mug. You can smell its aroma because its molecules are mixing into the air you are breathing. There is an exchange of matter. It is going to eventually reach room temperature because the cup is transferring heat to the countertop it rests on and to the air around it. As an open system, it is going to change until it reaches a state of equilibrium with the room around it. The hot coffee will warm the room it is in but the room is likely to be so large compared to the coffee that the change would be undetectable. The room with the coffee in it, taken as an approximately isolated system, will have the same total energy when the coffee is hot as when it has cooled to room temperature because the energy is conserved.

We have described the "state" of our coffee "system" as hot. The transfer of heat from the coffee to the air around it is an example of a thermodynamic process. The coffee eventually cools from hot to room temperature. A thermodynamic variable or property is also called a state function. A "state function" of this system is temperature. Internal energy, mass, pressure, volume, enthalpy and entropy (all concepts we will explore) are examples of state functions in thermodynamics.

The thermodynamic state of our coffee system is described by its properties such as temperature, volume, and pressure. As the coffee cools, its state changes. It will continue to cool until the coffee reaches a state of thermodynamic equilibrium with its surroundings. Equilibrium means that the system is in balance with its surroundings. The coffee eventually reaches the same temperature as the air and countertop upon which it sits. This is thermal equilibrium. A system will also spontaneously move toward other kinds of equilibrium as well, such as mechanical equilibrium (toward equal pressure for example) and chemical equilibrium (toward minimal Gibbs energy, a form of potential energy that is widely used in chemical thermodynamics). Thermodynamic equilibrium is a state of complete equilibrium where all these kinds of equilibrium are in place. If the coffee was sealed in a pressurized but heat-permeable container, it would eventually reach thermal equilibrium but not complete thermodynamic equilibrium because its pressure cannot equalize with the air around it. When a system is in complete thermodynamic equilibrium, it will not change spontaneously. It will remain in the same state indefinitely, unless work is done to it. It cannot do work because it does not have energy available to do work.

The description of our coffee is a classical thermodynamic description. It doesn't take into account the states of the molecules or atoms or subatomic particles in the coffee and it makes the assumption that the dynamic process (the change that occurs) is continuous or smooth. The coffee cools gradually, not in jumps, for example. If we want to look at the individual dynamics of the atoms in our coffee, we need to deal with quantum thermodynamics. This field of study explores the relationship between two independent theories: (classical) thermodynamics and quantum mechanics.

A Glimpse Into The Future

Quantum thermodynamics attempts to describe thermodynamic changes that occur at the atomic scale. Analogous to how thermodynamics developed from trying to improve steam engine technology, quantum thermodynamics, a very young field, is growing out of our desire to shrink technologies into a variety of quantum machines. A significant challenge here is that classic concepts such as temperature and work need to find some kind of quantum counterpart. One breakthrough is that we can now equate a system's energy with its information, an idea that we will revisit later in this article. Internal energy doesn't equate to thermal energy in a system.

Changes at the quantum level are not continuous because particle properties are quantized. They come in discrete packets. If you recall the de Broglie matter wave, all matter at the atomic scale is both particle and wave in nature, and changes in energy are limited to specific jumps in energy levels. Subatomic behaviours belong to the realm of quantum mechanics. A quantum description of a system can give us an idea of how atoms behave but it can't tell us anything about the macroscopic system as a whole. We can't add up de Broglie waves to get a complete thermodynamic picture of the coffee in our earlier example. Technically, we can't study each individual particle in a system. In order to describe the internal energy of the coffee at the quantum level, we would need to know, at the same time, all the trajectories and kinetic energies, all particle masses, magnetic moments and angular momenta of billions of particles. Even if we could manage such a feat, we would still lack a complete thermodynamic description of the coffee because it also possesses emergent properties. These are properties that emerge when a collection of many atoms behave together in a macroscopic system, such as temperature, volume and even pressure, which cannot be described at the level of individual atoms. Even if we could know all the quantum information of every particle in the coffee, we still couldn't know what its temperature is, and how fast it is cooling.

Complicating our effort further, all quantum systems have uncertainty built into them. Quantum systems have a unique and intriguing property: you can't know both the energy and the position (or the momentum and the velocity) of any particle at the same time. This means that an atom, for example, cannot be treated like a tiny sphere of matter. It is more accurately a statistical cloud of where it might be and how fast it is going, which has uncertainty built into it.

This seemingly impossible problem does have a satisfactory solution however: we can use statistics. It is a mathematical bridge between quantum thermodynamics and classical thermodynamics. It deals with individual particles or atoms or molecules by taking averages of their dynamic properties, and using those average values to describe a system.

Thanks to advances in technology, even a system containing just a few molecules or even atoms can now be harnessed to do microscopic work. Last year three scientists won the Nobel Prize in chemistry for developing the world's tiniest machines, with motors smaller than the width of a human hair. Fraser Stoddart developed a molecular computer chip that can store 20 kB of memory. Bernard Feringa built a nanocar with four molecular motors as wheels. John-Pierre Sauvage inspired other researchers to develop machines such as microscopic robots that can grasp and collect amino acids. Work is underway to develop a fast-charging quantum battery in which energy can be stored and released on demand from a quantum system.

As the wave of new micro-technologies gains momentum, the field of thermodynamics needed to describe how they work is having trouble keeping up. How do concepts of heat and efficiency translate into this new realm of tiny machines? While statistics can bridge the gap between the quantum realm and classical realm of a (large) macroscopic system, how can it bridge the gap between quantum-scale process in a quantum-scale (tiny) system and a macroscopic-scale (large) observer? Statistics, so useful when describing processes and states of macroscopic systems, finds little use here. In quantum machines, every quantum bit of information has real meaning and cannot be treated as a statistical average. Is irreversible heat loss in a macroscopic system equivalent to quantum dissipation in a quantum system? There is a lot of heated debate about how to link quantum and macroscopic thermodynamic processes because all of these new technologies must obey the same thermodynamic principles as the original heat engine.

The Four Laws Of Thermodynamics

Zeroth Law

Though this law might not be familiar to a lot of us, its impact is quite enormous. It can be summed up in a simple statement: If two systems are in thermal equilibrium with a third system then they must also be in thermal equilibrium with each other. This implies that the sizes of the systems and what kinds of molecules they are composed of don't matter. As James Clerk Maxwell famously said, "all heat is of the same kind." It is a deceptively simple observation of equivalence, which underpins all the thermodynamic laws, and which establishes that temperature as a universal property of matter, as explained in this 4-minute video by The Royal Institution.



By being able to define temperature, we can measure the thermal energy in any system. We can use the scale of Fahrenheit, Celsius or Kelvin, but the Kelvin scale is the thermodynamic scale used by scientists. It starts at absolute zero, where there is no thermal energy in a system. A thermometer can be used to verify that systems in thermal equilibrium are at the same temperature.

If we define the barrier between two systems as a kind of wall permeable only to heat transfer, such as the wall of a coffee cup between hot coffee and our hands, we realize that only energy is transferred between the two systems, not matter. The zeroth law, though simple, shuts the door on earlier theories that treated heat as a physical entity, such as phlogiston or caloric, as types of matter thought to flow between objects.

Thermal Energy and Internal Energy

Temperature is the measure of the thermal energy of a system. As a statistical measurement, it measures an average of all the individual kinetic energies of the atoms and molecules in the system, which cannot be individually measured. Individual molecules do not have thermal energy or a temperature. They have only kinetic energy from which thermal energy emerges at the macroscopic scale. Temperature offers us a hint of what is happening at the molecular scale. Every molecule in a system, such as our coffee, has three physical degrees of freedom. It can move in three dimensions in space, and each degree of freedom has kinetic energy associated with it, which varies from molecule to molecule within the system. Some kinds of molecules (such as binary-shaped oxygen, O2) also have rotational motion about an axis (an additional degree of freedom). Thermal energy is the result of all of these molecular motions within a system. It is measured as temperature, which is their average kinetic energy. We might think of kinetic energy as unidirectional, such as an object rolling downhill gaining kinetic energy. Here, the important distinction is that the kinetic energies of the molecules are random and in all directions. There are cases where thermal energy cannot be measured as a temperature change, for example, during a phase change, which we will explore.

Work and Heat

Every thermodynamic system also has internal energy, which is a more encompassing form of energy, and which can be used to do work. Work, conversely, can also be done on a system to increase its internal energy. Unlike thermal energy, internal energy cannot be directly measured. It is the sum of the system's thermal energy plus its potential energy. The internal energy of a system, the sum of the kinetic and potential energies of the molecules and atoms, does not include energy due to the motion or location of the system as a whole relative to its surroundings. The system's gravitational potential energy or its motion through space is not included in other words. However, chemical bond energy, magnetic moment, internal electrical field, nuclear potential energy, and internal stress can all be included as contributions to the internal energy of a system. The internal energy of a system can also be changed by adding or subtracting matter from the system, transferring heat into or out of the system, or by doing work on the system or by the system itself dong work. The internal energy of a system also changes if thermal energy is added or removed.

Work performed by a system is energy transferred by the system to its surroundings. Unlike internal energy or thermal energy, which are properties of a system, work is energy-in-transit. A system doesn't contain work; it is a process of energy transfer. Likewise, heat (though we commonly say that an object contains heat or an object is hot) is not a property of a system. It is better understood, like work, as energy in transit. The kinetic motion of molecules in a system can be the source of, and the effect of, the transfer of heat from another system. The term "latent heat" (which we will explore) is also not a property of a system. It is best understood as internal energy released from, or absorbed into, a system, as internal energy transferred without a change in temperature.

We can't measure internal energy directly but we can get an idea of the change in internal energy in a system by using the concept of enthalpy. As described nicely in Wikipedia, enthalpy describes the internal energy of a system plus the energy "needed to make room for it," which is measured as pressure and volume. Like internal energy, we can't measure enthalpy directly but we can measure the change in enthalpy in a system. The concept of enthalpy is a convenient way to link internal energy (thermal energy plus potential energy) with work in a system. Enthalpy (H) is essentially (internal energy (U)) + ("work" energy, or pressure x volume). It is useful for reactions that involve gases, where changes in pressure and/or volume tend to be significant and easy to measure. For reactions that only involve liquids or solids, the change in enthalpy will pretty much equal the change in internal energy because there will be hardly, if any, change in volume or pressure in the system. Solids and liquids resist compression and expansion.

This brings us the first law of thermodynamics, which establishes the existence of internal energy in a system, next.

The Laws of Thermodynamics PART 2 CLICK HERE

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