What is Gibbs paradox and how is this paradox resolved?

What is Gibbs paradox and how is this paradox resolved?

This is the Gibbs paradox. The paradox is resolved by postulating that the gas particles are in fact indistinguishable. This means that all states that differ only by a permutation of particles should be considered as the same state.

What is Gibbs paradox explain?

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 difference, but vanishes for identical gases.

What do you mean by microcanonical ensemble?

Classical Statistical Mechanics The microcanonical ensemble is defined as a collection of systems with exactly the same number of particles and with the same volume. According to the Second Law of Thermodynamics, the system would respond by seeking the condition of maximum entropy of the system.

What is a microcanonical ensemble obtain Equipartition Theorem?

The general equipartition theorem holds in both the microcanonical ensemble, when the total energy of the system is constant, and also in the canonical ensemble, when the system is coupled to a heat bath with which it can exchange energy. Derivations of the general formula are given later in the article.

Does Gibbs paradox exist?

There are in fact two distinct paradoxes that go under the heading of the Gibbs paradox. The original one was formulated by Josiah Willard Gibbs in 1875 [1]. It addresses the mixing of two quantities of ideal gas, and the entropy change that occurs as a result of the mixing process.

Which of the following may be regarded as applying the principle of entropy?

Which of the following may be regarded as applying the principle of entropy? Explanation: These are some general applications of entropy principle. Explanation: (T1+T2)/2 is when no work is done, and sqrt(T1*T2) is the temperature with maximum work distribution. 9.

What is meant by ensemble in statistical mechanics?

In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in.

What is Gibbs ensemble?

The main idea of statistical mechanics, as formulated by Boltzmann and Gibbs, is to describe the microscopic state of equilibrium systems in terms of the probability of an ensemble of configurations compatible with the thermodynamic variables of the macroscopic state.

What do you understand from equipartition of energy for thermodynamic system?

equipartition of energy, law of statistical mechanics stating that in a system in thermal equilibrium, on the average, an equal amount of energy will be associated with each degree of freedom. (A particle moving through space has three degrees of freedom because three coordinates are needed to describe its position.)

What is the entropy of an ideal gas?

It is known [1] that the entropy change for a monatomic ideal gas is given by DS = nRln(Tf /Ti)-nRln(Pf/Pi), where R is the molar gas constant and n is the amount of substance. This formula, which was obtained by recurring to a reversible process between the states (Ti ,Pi) and (Tf,Pf), gives DS = -8.000 J K-1.

What is Gibbs paradox in chemistry?

The Gibbs paradox involves the contrast between mixing two quantities of (ideal) gases of a different kind and that of mixing two quantities of the same gas. In the case of different gases, mixing is accompanied by an entropy increase∆S =2R log2; in the case of same gases there is no entropy change:∆S =0.

What is the problem of ideal gas entropy?

Gibbs himself considered the following problem that arises if the ideal gas entropy is not extensive. Two identical containers of an ideal gas sit side-by-side. The gas in container #1 is identical in every respect to the gas in container #2 (i.e. in volume, mass, temperature, pressure, etc).

What is the significance of the entropy paradox?

The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the ” mixing paradox “. If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, the paradox is averted.

What is the mixing paradox in chemistry?

The mixing paradox. If gas A and B are different gases, there is an entropy that arises once the gases are mixed. If the gases are the same, no additional entropy is calculated. The additional entropy from mixing does not depend on the character of the gases; it only depends on the fact that the gases are different.