Entropy (classical thermodynamics)

Entropy is a property of thermodynamical systems. The term entropy was introduced by Rudolf Clausius who named it from the Greek word τρoπή, 'transformation'. He considered transfers of energy as heat and work between bodies of matter, taking temperature into account. Bodies of radiation are also covered by the same kind of reasoning. Entropy is a property of thermodynamical systems. The term entropy was introduced by Rudolf Clausius who named it from the Greek word τρoπή, 'transformation'. He considered transfers of energy as heat and work between bodies of matter, taking temperature into account. Bodies of radiation are also covered by the same kind of reasoning. More recently, it has been recognized that the quantity 'entropy' can be derived by considering the actually possible thermodynamic processes simply from the point of view of their irreversibility, not relying on temperature for the reasoning. Ludwig Boltzmann explained the entropy as a measure of the number of possible microscopic configurations Ω of the individual atoms and molecules of the system (microstates) which comply with the macroscopic state (macrostate) of the system. Boltzmann then went on to show that k ln Ω was equal to the thermodynamic entropy. The factor k has since been known as Boltzmann's constant. In a thermodynamic system, differences in pressure, density, and temperature all tend to equalize over time. For example, consider a room containing a glass of melting ice as one system. The difference in temperature between the warm room and the cold glass of ice and water is equalized as heat from the room is transferred to the cooler ice and water mixture. Over time the temperature of the glass and its contents and the temperature of the room achieve balance. The entropy of the room has decreased. However, the entropy of the glass of ice and water has increased more than the entropy of the room has decreased. In an isolated system, such as the room and ice water taken together, the dispersal of energy from warmer to cooler regions always results in a net increase in entropy. Thus, when the system of the room and ice water system has reached temperature equilibrium, the entropy change from the initial state is at its maximum. The entropy of the thermodynamic system is a measure of how far the equalization has progressed. There are many irreversible processes that result in an increase of the entropy. See: Entropy production. One of them is mixing of two or more different substances, occasioned by bringing them together by removing a wall that separates them, keeping the temperature and pressure constant. The mixing is accompanied by the entropy of mixing. In the important case of mixing of ideal gases, the combined system does not change its internal energy by work or heat transfer; the entropy increase is then entirely due to the spreading of the different substances into their new common volume. From a macroscopic perspective, in classical thermodynamics, the entropy is a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. Entropy is a key ingredient of the Second law of thermodynamics, which has important consequences e.g. for the performance of heat engines, refrigerators, and heat pumps. According to the Clausius equality, for a closed homogeneous system, in which only reversible processes take place,