![]() ![]() The answers you may find even in the SE sites just mirror this state of things. Unfortunately, there is an embarrassing confusion, even in the scientific literature on such an issue. Your concern about the too many definitions of entropy is well-founded. I can understand the "cup of coffee" example of course, or the "your room gets messy over time" example. I'm stuck at this very fundamental philosophical definition. Mode => Again, before the big bang, or even in early epochs of the universe we had uniform states that were the most abundant possible states.But we need billions of billions of lines of descriptions to be able to describe the universe. Information => we can describe the universe before the Big Bang in one simple sentence: an energy point, X degrees kelvin.Now the universe is a repetition of energy density and void. Energy distribution => then why Big Bang happened at all? As they say, universe was one tiny point of energy equally distributed.Disorder => how about a snowflake? What is disorder? How do we agree on what is ordered and what is disordered? Because to me a snowflake is a perfect example of order.Now, I have these contrary examples in my mind: Entropy = statistical mode, and the system tends to go to a microscopic state that is one of the most abundant possible states it can possess.Entropy = information needed to describe the system, and systems tend to be described in less lines.Entropy = energy distribution, and systems tend to the most possible energy distribution.Entropy = disorder, and systems tend to the most possible disorder.Many definitions are presented, among which I can formulate three (please correct me if any definition is wrong): In this context, a the change in entropy can be described as the heat added per unit temperature and has the units of Joules/Kelvin (J/K) or eV/K.In many places over the Internet, I have tried to understand entropy. For the case of an isothermal process it can be evaluated simply by ΔS = Q/T. ![]() It can be integrated to calculate the change in entropy during a part of an engine cycle. This is often a sufficient definition of entropy if you don't need to know about the microscopic details. The relationship which was originally used to define entropy S is dS = dQ/T This is a way of stating the second law of thermodynamics. As a large system approaches equilibrium, its multiplicity (entropy) tends to increase. ![]() You can with confidence expect that the system at equilibrium will be found in the state of highest multiplicity since fluctuations from that state will usually be too small to measure. The multiplicity for ordinary collections of matter is inconveniently large, on the order of Avogadro's number, so using the logarithm of the multiplicity as entropy is convenient.įor a system of a large number of particles, like a mole of atoms, the most probable state will be overwhelmingly probable. The fact that the logarithm of the product of two multiplicities is the sum of their individual logarithms gives the proper kind of combination of entropies. The entropy of the combined systems will be the sum of their entropies, but the multiplicity will be the product of their multiplicities. It also gives the right kind of behavior for combining two systems. The logarithm is used to make the defined entropy of reasonable size. This is Boltzmann's expression for entropy, and in fact S = klnΩ is carved onto his tombstone! (Actually, S = klnW is there, but the Ω is typically used in current texts (see Wikipedia)).The k is included as part of the historical definition of entropy and gives the units joule/kelvin in the SI system of units. One way to define the quantity "entropy" is to do it in terms of the multiplicity. ![]() The multiplicity for seven dots showing is six, because there are six arrangements of the dice which will show a total of seven dots. The multiplicity for two dots showing is just one, because there is only one arrangement of the dice which will give that state. In throwing a pair of dice, that measurable property is the sum of the number of dots facing up. Here a "state" is defined by some measurable property which would allow you to distinguish it from other states. That is to say, it is proportional to the number of ways you can produce that state. The probability of finding a system in a given state depends upon the multiplicity of that state. Entropy Entropy as a Measure of the Multiplicity of a System ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |