Related papers: Redefining the Phase Space for Ideal Gas Systems R…
Molecular collision within an ideal gas originates from an intrinsic short-range repulsive interaction. The collision reduces the average accessible physical space for a single molecule and this has a direct consequence on the entropy of…
The article reveals the error that in classical thermodynamics leads to the Gibbs paradox. The essence of the error lies in the fact that the entropy of an ideal gas is attributed to additive quantities, but it is not correct. The value of…
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…
The formulas for the entropy of ideal gases mixture and the entropy change in mixing of ideal gases on the basis of the third law of thermodynamics were obtained. It is shown that when using these formulas, the Gibbs paradox within the…
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
We present a fully quantum solution to the Gibbs paradox (GP) with an illustration based on a gedanken experiment with two particles trapped in an infinite potential well. The well is divided into two cells by a solid wall, which could be…
The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
We prove a proposition that the entropy of the system composed of finite $N$ molecules of ideal gas is the $q$-entropy or Havrda-Charv\'at-Tsallis entropy, which is also known as Tsallis entropy, with the entropic index…
This article presents the results of research into the causes of the Gibbs paradox in the formulation discussed by J. W. Gibbs himself. In this formulation, we are talking about an inexplicable (paradoxical) jump in the entropy of mixing of…
The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them. This is an unphysical feature of the theory since every material in…
The 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,…
We point out that a special case of an ideal gas exhibits concentration of the volume of its phase space, which is a sphere, around its equator in the thermodynamic limit. The rate of approach to the thermodynamic limit is determined. Our…
The thermodynamics of an ideal gas enclosed in a box of volume a1 x a2 x a3 at temperature T is considered. The canonical partition function of the system is expressed in terms of complete elliptic integrals of the first kind, whose…
We provide an $N/V$-limit for the infinite particle, infinite volume stochastic dynamics associated with Gibbs states in continuous particle systems on $\mathbb R^d$, $d \ge 1$. Starting point is an $N$-particle stochastic dynamic with…
We show in this note that Gibbs paradox arises not due to application of thermodynamic principles, whether classical or statistical or even quantum mechanical, but due to incorrect application of mathematics to the process of mixing of…
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered…
There is the Gibbs theorem in thermodynamics, according to which the entropy of the mixture of ideal gases is equal to the sum of the entropies of the components of the mixture. J. W. Gibbs proved this by a mathematical derivation from the…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them. This is an unphysical feature since every material absorbs and…