Gibbs' paradox for entropy of mixing

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

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Activities of Components in the Ca2MgSi2O7-CaSiO3Molten System

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19960837 ◽

1996 ◽

Vol 61 (6) ◽

pp. 837-843

Author(s):

Ladislav Kosa ◽

Ivan Nerád ◽

Katarína Adamkovičová ◽

Jozef Strečko ◽

Ivo Proks

Keyword(s):

Gibbs Energy ◽

Molar Mass ◽

Excess Entropy ◽

Enthalpy Of Mixing ◽

Real Particle ◽

Entropy Of Mixing ◽

Energy Of Mixing ◽

Gibbs Energy Of Mixing

Activities of the components, the Gibbs energy of mixing, and the excess entropy of mixing have been calculated for the Ca2MgSi2O7-CaSiO3 system. The mole fractions of the components were calculated assuming that in the point of the formal component Ca2MgSi2O7, the molar mass of the quasi-real particle in the melt corresponds to its formula molar mass, whereas in the point of the formal component CaSiO3 the molar mass of the quasi-real particle in the melt is 8.5 times higher than as corresponds to its formula. The fact that the enthalpy of mixing is zero whereas the excess entropy of mixing is non-zero suggests that Ca2MgSi2O7-CaSiO3 melts behave as athermal solutions.

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Mixing indistinguishable systems leads to a quantum Gibbs paradox

Nature Communications ◽

10.1038/s41467-021-21620-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Benjamin Yadin ◽

Benjamin Morris ◽

Gerardo Adesso

Keyword(s):

Statistical Mechanics ◽

Thought Experiment ◽

Entropy Change ◽

Ideal Gas ◽

Gibbs Paradox ◽

Quantum Case ◽

Entropy Increase ◽

Level Of Knowledge ◽

Different Gases ◽

As If

AbstractThe classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an “ignorant” observer, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.

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Mathematical solution of the Gibbs paradox

Mathematical Notes ◽

10.1134/s0001434611010329 ◽

2011 ◽

Vol 89 (1-2) ◽

pp. 266-276 ◽

Cited By ~ 5

Author(s):

V. P. Maslov

Keyword(s):

Gibbs Paradox ◽

Mathematical Solution

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