Термодинамикалық жүйелердегі тәртіпсіздіктің өлшемі

Measure of disorder within thermodynamic systems

In classical thermodynamics, entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid 19th century to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the system. 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 correspond to the macroscopic state (macrostate) of the system. He showed that the thermodynamic entropy is k ln Ω, where the factor k has since been known as the Boltzmann constant.

Differences in pressure, density, and temperature of a thermodynamic system tend to equalize over time. For example, in a room containing a glass of melting ice, the difference in temperature between the warm room and the cold glass of ice and water is equalized by energy flowing as heat from the room to the cooler ice and water mixture. Over time, the temperature of the glass and its contents and the temperature of the room achieve a 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 thermal equilibrium, the entropy change from the initial state is at its maximum. The entropy of the thermodynamic system is a measure of the progress of the equalization. Many irreversible processes result in an increase of entropy. 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.

Entropy values of important substances may be obtained from reference works or with commercial software in tabular form or as diagrams. One of the most common diagrams is the temperature entropy diagram (TS diagram). For example, Fig.2 shows the TS diagram of nitrogen, depicting the melting curve and saturated liquid and vapor values with isobars and isenthalps.

We now consider inhomogeneous systems in which internal transformations (processes) can take place. If we calculate the entropy S1 before and S2 after such an internal process the Second Law of Thermodynamics demands that S2 ≥ S1 where the equality sign holds if the process is reversible. The difference 1=Si = S2 − S1 is the entropy production due to the irreversible process. The Second law demands that the entropy of an isolated system cannot decrease. Suppose a system is thermally and mechanically isolated from the environment (isolated system). For example, consider an insulating rigid box divided by a movable partition into two volumes, each filled with gas. If the pressure of one gas is higher, it will expand by moving the partition, thus performing work on the other gas. Also, if the gases are at different temperatures, heat can flow from one gas to the other provided the partition allows heat conduction. Our above result indicates that the entropy of the system as a whole will increase during these processes. There exists a maximum amount of entropy the system may possess under the circumstances. This entropy corresponds to a state of stable equilibrium, since a transformation to any other equilibrium state would cause the entropy to decrease, which is forbidden. Once the system reaches this maximum entropy state, no part of the system can perform work on any other part. It is in this sense that entropy is a measure of the energy in a system that cannot be used to do work. An irreversible process degrades the performance of a thermodynamic system, designed to do work or produce cooling, and results in entropy production. The entropy generation during a reversible process is zero. Thus entropy production is a measure of the irreversibility and may be used to compare engineering processes and machines.