Hello, today we begin to explore the fundamentals of classical or macroscopic thermodynamics. You may ask why, when this is a set of courses about statistical thermodynamics, why we are studying classical thermodynamics. I hope the reason will become apparent relatively quickly. I think you will find that developing this understanding will make everything that follows much easier. This slide shows four of the most important figures in thermodynamics, Sadi Carnot, Rudolf Clausius, William Thompson also known as Lord Kelvin, and Max Planck. Sadi Carnot was a French military engineer. He is credited with discovering the second law of thermodynamics. Rudolf Clausius was a German physicist and mathematician. He restated Sadi Carnot's principles into the form we use today. William Thompson was an Irish-Scottish mathematical physicist. He worked on thermodynamics, bringing it into its modern form. He was ennobled as Baron Kelvin as an honor for his many achievements. Max Planck was a theoretical physicist, a German theoretical physicist. He is best known to engineers for the Planck Function of radiation, heat transfer. However his fame really comes as a founder of quantum mechanics, something he did not really believe in. As a classic engineering approach, he did a curve fit to the measurement of black body radiation, but to make what became known as the Planck Function work from a theoretical point of view, he had to postulate that light could have a particle nature. We will discuss this in more detail later. It is useful to discuss solving thermodynamic problems in terms of the fundamental problem. We will show that essentially all thermodynamic system problems can be cast in a similar form. Consider an isolated system, divide it into two subsystems by a piston. The question arises, what happens in the following situation. We start with a piston fixed impermeable and adiabatic. That means it cannot move, no mass can pass through it, and no heat transfer. What happens in that situation? Suppose then the piston becomes diathermal, in other words, heat transfer is allowed. Next, suppose the piston is now allowed to move, what will happen then? Finally, what if the piston becomes porous to one or more chemical species? This is a situation that is commonly used in chemical separations, osmosis, and processes of that type. We will now explore over the next few videos answering this question. To proceed it is necessary to introduce some rules. We call these rules postulates. The postulates we will use are those described by Callen, in Thermodynamics the 2nd edition, published by John Wiley & Sons in 1985. As Callen states, the postulates should be the simplest ones that will do the job. Of course well over 100 years of thermodynamic development should give a decent guide as how to choose the postulates. Nonetheless, they're postulates and they must be proved after the fact or a posteriori rather than a priori or from the beginning. If the Latin is unfamiliar, note the definitions in the slide. Moving along postulate one, there exists certain states, called equilibrium states of simple systems that macroscopically are characterized completely by the eternal energy U, the volume V, and the mole numbers of the chemical components, where r is the number of chemical components. Now, we could alternatively use mass rather than moles. It would essentially be the same thing. What are the implications of this postulate? One implication is that previous history plays no role in determining the final state. This goes along with the idea we've already discussed that when systems are in equilibrium, the property functions do not depend on any dynamic quantities. Another consequence or implication of this postulate is that all microscopic quantum states are allowed. This turns out actually not to be true except in a practical sense and will make more sense after we discuss quantum mechanics. There are violations of this postulate as shown in the slide. Note that it only applies to systems for which the beginning and the end states are in equilibrium. Next postulate two, there exists a function called entropy of the extensive parameters of any composite system defined for all equilibrium states and having the following property: The values assumed by the extensive parameters are those that maximize the entropy over the manifold of constrained equilibrium states. This postulate introduces the concept of entropy and essentially states the second law of thermodynamics, manifold of constrained equilibrium states. You perhaps studied in undergraduates, quasi-equilibrium processes. That is where even though a process is taking place which in principle would lead to non-equilibrium conditions, if you do it slowly enough, then at any particular point through the process the conditions of the mass in the control system is in equilibrium. This postulate introduces the terms extensive and intensive properties. You've probably been exposed to these before but we're taking much more care this time. Extensive properties are those that depend directly on the size of the system. For example, if you double the size of the system, then the internal energy will double. Other properties for which this holds are volume, mass, number of moles, entropy, and enthalpy. Intensive properties are those that do not directly depend on the size of the system. We shall see that these are temperature, pressure, and chemical potential. Then finally there are normalized properties and these are what you call the intensive properties, probably in your undergraduate thermodynamic class. These are extensive properties that have been normalized on the mass or number of moles or volume. In undergraduate thermo, you used lowercase letters for these. For example, lowercase u,h, and s for internal energy enthalpy and entropy. There are other consequences of the second postulate. It is important to remember that postulate two only applies for equilibrium states. Also, that it is the total entropy including all subsystems and surroundings that is maximized. A very important consequence is that we can solve the fundamental problem if we know the fundamental relation which functionally we can relate or we can write as S equals a function of U,V, and the N_i. Postulate three, the entropy of a composite system is additive over the constituents subsystems. The entropy is continuous and differentiable and is a monotonically increasing function of energy. These essentially provide some guidance to the mathematical character of the entropy. The consequences of Postulate three include the following: It simplifies the mathematics. The entropy of the overall system is the sum of the entropies of each subsystem. On our simple fundamental problem where we have a subsystem a and b, the total entropy would be S_a Plus S_b. Next, the entropy of each subsystem is a function only of the properties of that subsystem. Say, subsystem j would be a function of U_j, V_ j, and the N_i_j. Next, entropy is a first-order function of the extensive properties. This means that if we multiply each independent property by a common factor, say lambda as shown in the slide, the entropy is multiplied by the same amount. These make entropy a much simpler kind of function to deal with. The consequences of Postulate three also include that the partial derivative of entropy with energy is always positive. This means that entropy can be inverted with respect to energy in the fundamental equation. Finally, the extensive properties can be normalized as shown in the slide. Next, we have Postulate four. This is also called the Nernst postulate or third law of thermodynamics. It states, the entropy of any system vanishes in the state for which the partial derivative of the internal energy with entropy is zero. We shall see that this implies that the entropy goes to zero as T goes to zero. Finally, here are two examples for fundamental relations. The first is for a Van der Waals liquid. It applies throughout the domain of gaseous and liquid behavior. The second is for an ideal gas which only applies in the ideal gas domain. They're written in normalized form lowercase s is a function of lowercase volume and internal energy and we've assumed in both cases they're for a simple compressible substance. Then again, for an ideal gas as a function of u and v. And the other parameters are constants of these relationships. This ends the video. Thanks and have a great day.
