Claude is the author of the Sibyllic Statement: “The energy of the universe is constant; The entropy of the universe tends to a maximum. The goals of continuum thermomechanics are far from explaining “the universe,” but in this theory we can easily derive an explicit statement that is somewhat reminiscent of Clausius, but refers only to a modest object: an isolated body of finite size. The expression expressed above as a derivative with respect to E and the sum over Y gives the expression: In addition, a reversible heat engine operating between temperatures T1 and T3 must have the same efficiency as an engine composed of two cycles, one between T1 and another (intermediate) temperature T2 and the second between T2 and T3. This can only be the case if the second part of the second law states that the change in entropy of a system undergoing a reversible process is given by: The above shows an important point: The second law of thermodynamics is statistical in nature. It has no meaning at the level of individual molecules, whereas the law becomes essentially precise to describe a large number of interacting molecules. In contrast, the first law of thermodynamics, which expresses the conservation of energy, remains exactly true even at the molecular level. The example of ice melting in a glass of hot water also shows the other meaning of the term entropy, such as an increase in randomness and a parallel loss of information. First, all thermal energy is divided so that all slow (cold) molecules are in ice and all fast (hot) molecules are in water (or water vapor). Once the ice has melted and the system has reached thermal equilibrium, the thermal energy is evenly distributed throughout the system. The statistical approach provides much valuable information about the importance of the second law of thermodynamics, but from the point of view of applications, the microscopic structure of matter becomes irrelevant. The great beauty and strength of classical thermodynamics is that its predictions are completely independent of the microscopic structure of matter.
Question 2: What does the second law of thermodynamics imply? It is difficult to convert all the heat emitted by a heated body into work. The working material of a heat engine absorbs heat from a hot body, converts part of it into work and returns the rest to the cold body. No motor can convert all the heat from the source to work without wasting heat. This indicates that a sink is needed to maintain continuous work. In school textbooks, it is almost common to speak of the “Kelvin-Planck declaration” of the law, as for example in the text of ter Haar and Wergeland. [42] This version, also known as the explanation of the heat engine, of the second law indicates that there have been almost as many formulations of the second law as there have been discussions about it. While the first law of thermodynamics gives information about the amount of energy transfer as a process, it gives no insight into the direction of energy transfer and energy quality. The first law cannot indicate whether a metal rod with a uniform temperature can spontaneously become warmer at one end and colder at another. All the law can say is that there will always be an energy balance when the process takes place.
It is the second law of thermodynamics that provides the feasibility criterion of each process. A process can only take place if it satisfies both the first and second laws of thermodynamics. where Q is the heat, T is the temperature, and N is the “equivalence” of all uncompensated transformations involved in a cyclic process. Later, in 1865, Clausius defined the “equivalence value” as entropy. Following this definition, the most famous version of the second law was published the same year at a conference at the Philosophische Gesellschaft Zürich on September 24. Clausius concludes at the end of his lecture: The law according to which entropy always increases occupies, in my opinion, the highest position among the laws of nature. If someone points out that your favorite theory of the universe doesn`t agree with Maxwell`s equations, too bad for Maxwell`s equations. If it is determined that it is refuted by observation – well, these experimenters sometimes mess things up. But if it turns out that your theory violates the second law of thermodynamics, I cannot give you hope; There is nothing but to collapse in the deepest humiliation.
Although it is almost common in textbooks to say that the principle of Carathéodory expresses the second law and to treat it as equivalent to the statements of Clausius or Kelvin-Planck, this is not the case. To obtain the complete content of the second law, Carathéodory`s principle must be supplemented by Planck`s principle according to which isochoric work always increases the internal energy of a closed system that was originally in its own internal thermodynamic equilibrium. [17] [50] [51] [52] [clarification needed] We can imagine thermodynamic processes that save energy but never occur in nature. For example, when we put a hot object in contact with a cold object, we observe that the hot object cools and the cold object warms up until equilibrium is reached. The heat transfer goes from the hot object to the cold object. However, we can imagine a system in which heat is transferred from the cold object to the hot object instead, and such a system does not violate the first law of thermodynamics. The cold object becomes colder and the hot object becomes hotter, but the energy is preserved. Obviously, we do not encounter such a system in nature, and to explain these and similar observations, thermodynamicists have proposed a second law of thermodynamics. Clasius, Kelvin and Carnot proposed different forms of the second law to describe the specific physical problem each studied. The description of the second law on this slide comes from Halliday and Resnick`s textbook “Physics.” It starts by defining a new state variable called entropy.
Entropy has a variety of physical interpretations, including the statistical disorder of the system, but for our purposes, we consider entropy as another property of the system, such as enthalpy or temperature. So what exactly is the connection between entropy and the second law? Recall that at the molecular level, heat is the random kinetic kinetic energy of molecules, and collisions between molecules provide the microscopic mechanism for transporting thermal energy from one place to another. Since individual collisions remain unchanged by reversing the direction of time, heat can flow in either direction. Thus, from the point of view of fundamental interactions, nothing stands in the way of a random event in which several slow (cold) molecules gather in the same place and ice forms while the surrounding water becomes warmer. Such random events can be expected from time to time in a container containing only a few molecules of water. However, the same random events are never observed in a large glass of water, not because they are impossible, but because they are extremely unlikely. Indeed, even a small glass of water contains a huge number of interacting molecules (about 1024), making it highly unlikely that a significant portion of cold molecules will gather in the same place during their random thermal motion. Although such a spontaneous violation of the second law of thermodynamics is not impossible, an extremely patient physicist would have to wait several times for the age of the universe to see it.
This expression, along with the associated reference state, allows a designer working at the macroscopic scale (above the thermodynamic limit) to use the second law without directly measuring or accounting for the change in entropy in a completely isolated system. (See also Process Engineer). These changes have already been taken into account on the assumption that the system in question can achieve equilibrium with the reference state without changing the reference state. An efficiency for a process or set of processes that compares it to the reversible ideal can also be found (see effectiveness of the second law). The second law of thermodynamics can be expressed in many specific ways,[24] the most important classical statements[25] are the statement of Rudolf Clausius (1854), the declaration of Lord Kelvin (1851) and the statement in axiomatic thermodynamics of Constantin Carathéodory (1909). These statements represent the law in general physical terms by citing the impossibility of certain processes. Clausius` and Kelvin`s statements proved to be equivalent. [26] The theory of classical or equilibrium thermodynamics is idealized.