Entropy

Here is the seventieth episode of Quantum Foam, Entropy. This is the measure of a systems thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measurement of the molecular disorder or randomness of a system. The concept of entropy provides deep insight into the direction of spontaneous change for many everyday phenomena. There are a lot of examples that is relevant to this topic. Its introduction by Rudolf Clausius in 1850 is a highlight of nineteenth century physics. The idea of entropy provides a mathematical way to encode the intuitive notion of which processes are impossible even though they would not violate the fundamental law of conservation of energy. For example, a block of ice placed on a hot stove surely melts while the stove grows cooler. Such a process is called irreversible because no slight change will cause the melted water to turn back into ice while the stove grows hotter. In contrast, a block of ice placed in an ice water bath will either thaw a little more or freeze a little more depending on whether a small amount of heat is added to or subtracted from the system. Such a process is reversible because only an infinitesimal amount of heat is needed to change its direction from progressive freezing to progressive thawing. Similarly, compressed gas confined in a cylinder could either expand freely into the atmosphere if the valve were open, an irreversible process, or it could do useful work by pushing a movable piston against the force needed to confine the gas. This is the main idea involved with the concept of entropy.
The concept of entropy was first introduced in 1850 by Clausius as a precise mathematical of testing whether the second law of thermodynamics is violated by a particular process. The test begins with the definition that if an amount of heat Q flows into a heat reservoir at constant temperature T then its entropy S increases by delta S equals Q over T. The formula is delta S equals Q over T sub 2 minus Q over T sub 1. If T sub 1 equals T sub 2 then the reservoirs are in equilibrium and so delta S equals 0. We are interested in how this information describes the efficiency of heat engines. What is the connection between entropy and the second law? Heat at the molecular level is the random kinetic energy of motion of molecules and collisions between molecules. Because individual collisions are unchanged by reversing the direction of time, heat can flow just as well in 1 direction as the other. Thus, from the point of view of fundamental interactions, there is nothing to prevent a chance event in which a number of slow moving molecules happen to collect together in 1 place and form ice while the surrounding water becomes hotter. Such chance events could be expected to occur from time to time in a vessel containing only a few water molecules. The same chance events are never observed in a full glass of water. Not because they are impossible, but because they are exceedingly improbable. This is because a small glass of water an enormous number of interacting molecules, about 10 to the twenty-fourth molecules, making it highly unlikely that, in the course of their thermal motion a significant fraction of cold molecules will collect together in 1 place. This demonstrates the idea behind the very complicated topic of entropy.