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- In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the thermodynamic operation of removal of impermeable partition(s) between them, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new unpartitioned closed system. In general, the mixing may be constrained to occur under various prescribed conditions. In the customarily prescribed conditions, the materials are each initially at a common temperature and pressure, and the new system may change its volume, while being maintained at that same constant temperature, pressure, and chemical component masses. The volume available for each material to explore is increased, from that of its initially separate compartment, to the total common final volume. The final volume need not be the sum of the initially separate volumes, so that work can be done on or by the new closed system during the process of mixing, as well as heat being transferred to or from the surroundings, because of the maintenance of constant pressure and temperature. The internal energy of the new closed system is equal to the sum of the internal energies of the initially separate systems. The reference values for the internal energies should be specified in a way that is constrained to make this so, maintaining also that the internal energies are respectively proportional to the masses of the systems. For concision in this article, the term 'ideal material' is used to refer to either an ideal gas (mixture) or an ideal solution. In the special case of mixing ideal materials, the final common volume is in fact the sum of the initial separate compartment volumes. There is no heat transfer and no work is done. The entropy of mixing is entirely accounted for by the diffusive expansion of each material into a final volume not initially accessible to it. In the general case of mixing non-ideal materials, however, the total final common volume may be different from the sum of the separate initial volumes, and there may occur transfer of work or heat, to or from the surroundings; also there may be a departure of the entropy of mixing from that of the corresponding ideal case. That departure is the main reason for interest in entropy of mixing. These energy and entropy variables and their temperature dependences provide valuable information about the properties of the materials. On a molecular level, the entropy of mixing is of interest because it is a macroscopic variable that provides information about constitutive molecular properties. In ideal materials, intermolecular forces are the same between every pair of molecular kinds, so that a molecule feels no difference between other molecules of its own kind and of those of the other kind. In non-ideal materials, there may be differences of intermolecular forces or specific molecular effects between different species, even though they are chemically non-reacting. The entropy of mixing provides information about constitutive differences of intermolecular forces or specific molecular effects in the materials. The statistical concept of randomness is used for statistical mechanical explanation of the entropy of mixing. Mixing of ideal materials is regarded as random at a molecular level, and, correspondingly, mixing of non-ideal materials may be non-random. (en)
- Le théorème de Gibbs permet de calculer l'entropie d'un mélange de gaz parfaits. Il s'énonce ainsi : « L'entropie d'un mélange idéal de gaz parfaits est égale à la somme des entropies de ses constituants supposés séparés, à la température du mélange, et sous des pressions égales aux pressions partielles qu'ils exercent dans le mélange. » Le théorème de Gibbs montre qu'un mélange de gaz parfaits est une solution idéale. (fr)
- Dalam termodinamika, entropi campuran adalah peningkatan total entropi ketika beberapa sistem pada awalnya memisahkan susunan yang berbeda, yang masing-masing dalam suatu tingkatan kesetimbangan internal termodinamika, dicampur tanpa reaksi kimia dengan pengangkatan partisi kedap di antara mereka, dengan diikuti oleh waktu untuk pembentukan keadaan termodinamika baru dari keseimbangan internal dalam sistem tertutup tanpa partisi baru. (in)
- Ентропія змішування — приріст ентропії при змішуванні двох термодинамічних систем, що складаються із частинок різного типу. При змішуванні частинок двох типів, кількість яких і , де , — стала Больцмана. Ентропія змішування не виникає при змішуванні однакових частинок. Це породжує цікаве питання про суб'єктивність визначення ентропії, оскільки обчислюваний вираз залежить від того, знаємо ми про відмінність між частинками, чи ні. Детальніше дивіться в статті Парадокс Гібса. (uk)
- 设在一密闭容器的两边分别装有服从理想气体假设的两种气体1和2，其温度及压力均相同，中间以一隔板隔开。当隔板抽去之后，1 和2两种气体分别扩散至整个容器空间，直至分布均匀为止。设和分别为气体1和气体2在混合气体中所占摩尔分数。混合熵为： 其中为气体常数, 为气体的摩尔数。 (zh)
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- Le théorème de Gibbs permet de calculer l'entropie d'un mélange de gaz parfaits. Il s'énonce ainsi : « L'entropie d'un mélange idéal de gaz parfaits est égale à la somme des entropies de ses constituants supposés séparés, à la température du mélange, et sous des pressions égales aux pressions partielles qu'ils exercent dans le mélange. » Le théorème de Gibbs montre qu'un mélange de gaz parfaits est une solution idéale. (fr)
- Dalam termodinamika, entropi campuran adalah peningkatan total entropi ketika beberapa sistem pada awalnya memisahkan susunan yang berbeda, yang masing-masing dalam suatu tingkatan kesetimbangan internal termodinamika, dicampur tanpa reaksi kimia dengan pengangkatan partisi kedap di antara mereka, dengan diikuti oleh waktu untuk pembentukan keadaan termodinamika baru dari keseimbangan internal dalam sistem tertutup tanpa partisi baru. (in)
- Ентропія змішування — приріст ентропії при змішуванні двох термодинамічних систем, що складаються із частинок різного типу. При змішуванні частинок двох типів, кількість яких і , де , — стала Больцмана. Ентропія змішування не виникає при змішуванні однакових частинок. Це породжує цікаве питання про суб'єктивність визначення ентропії, оскільки обчислюваний вираз залежить від того, знаємо ми про відмінність між частинками, чи ні. Детальніше дивіться в статті Парадокс Гібса. (uk)
- 设在一密闭容器的两边分别装有服从理想气体假设的两种气体1和2，其温度及压力均相同，中间以一隔板隔开。当隔板抽去之后，1 和2两种气体分别扩散至整个容器空间，直至分布均匀为止。设和分别为气体1和气体2在混合气体中所占摩尔分数。混合熵为： 其中为气体常数, 为气体的摩尔数。 (zh)
- In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the thermodynamic operation of removal of impermeable partition(s) between them, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new unpartitioned closed system. For concision in this article, the term 'ideal material' is used to refer to either an ideal gas (mixture) or an ideal solution. (en)
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