![]() ![]() However, after sufficient time has passed, the system reaches a uniform color, a state much easier to describe and explain.īoltzmann formulated a simple relationship between entropy and the number of possible microstates of a system, which is denoted by the symbol Ω. The use of reservoirs is redundant, since no extra information. The dye diffuses in a complicated manner, which is difficult to precisely predict. Equations (5) imply that dQ TdS -TndSn and dW -PdV PndVn, and the process is reversible. However, this description is relatively simple only when the system is in a state of equilibrium.Įquilibrium may be illustrated with a simple example of a drop of food coloring falling into a glass of water. Therefore, the system can be described as a whole by only a few macroscopic parameters, called the thermodynamic variables: the total energy E, volume V, pressure P, temperature T, and so forth. The ensemble of microstates comprises a statistical distribution of probability for each microstate, and the group of most probable configurations accounts for the macroscopic state. ![]() The large number of particles of the gas provides an infinite number of possible microstates for the sample, but collectively they exhibit a well-defined average of configuration, which is exhibited as the macrostate of the system, to which each individual microstate contribution is negligibly small. The collisions with the walls produce the macroscopic pressure of the gas, which illustrates the connection between microscopic and macroscopic phenomena.Ī microstate of the system is a description of the positions and momenta of all its particles. At a microscopic level, the gas consists of a vast number of freely moving atoms or molecules, which randomly collide with one another and with the walls of the container. When considering whether reactions have an increase or decrease in entropy, two factors are important: The number of moles created and states of the reactants. The easily measurable parameters volume, pressure, and temperature of the gas describe its macroscopic condition ( state). reservoir has no change in temperature and volume. A useful illustration is the example of a sample of gas contained in a container. A related quantity, the cross entropy CE(pk, qk), satisfies the equation CE(pk, qk) H(pk) + D(pkqk) and can also be calculated with the formula CE. ![]() Ludwig Boltzmann defined entropy as a measure of the number of possible microscopic states ( microstates) of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties, which constitute the macrostate of the system. Starting from the first law of thermodynamics and the relationship of enthalpy H to internal energy U: U qrev +wrev H U+ (PV) qrev + wrev + (P V) where: qrev and wrev are the most efficient (reversible) heat flow and work, respectively. Main article: Boltzmann's entropy formula ![]()
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