In a closed system with constant composition, if there is a slight reversible change, according to the first law of thermodynamics, the change of internal energy in the system is

dU = δQ + δW

According to the principle of statistical thermodynamics, the internal energy of an independent particle system is U = ∈ Ni ∈ I. When the closed system changes reversibly, the internal energy changes as follows

(6-74)

The first term ∈ idni on the right side of the above formula indicates the change value of internal energy due to the change of energy level distribution number when the energy level distribution number is fixed, and the second term ∈ NID ∈ i indicates the increase of internal energy due to the change of energy level when the energy level distribution number is fixed. According to the principle of classical mechanics, the change of internal energy can only be reflected by the heat and work exchange between the system and the environment for a closed system with constant composition.

Second, the nature of the second law of thermodynamics

From the thermodynamic definition of entropy and formula (6-78), it can be concluded that

(6-79)

The above formula is the expression of the second law of thermodynamics, which shows that the entropy change of reversible process is related to the change of energy level distribution number. However, the change of the distribution number of energy levels means that the micro-state number of the system has changed.

Entropy change is related to the change of micro-state number or thermodynamic probability ω of the system. There is a formula:

s = klnω+C(6-83)

Where c is an integer constant. If ω = 1 and S=0, the above formula becomes

S = klnΩ

This is the mathematical expression of Boltzmann theorem. As can be seen from the formula, entropy is a measure of the micro-state number of the system. A state with a small number of microscopic states ω corresponds to a more ordered state, while a state with a large ω value corresponds to a more disordered state. Therefore, the micro-state number ω reflects the degree of system order, that is, entropy is a measure of the degree of system order or chaos. When ω = 1, there is only one microscopic state, and the system is the most orderly, with zero degree of chaos and zero entropy. Based on the above discussion, we can make the following statement: in an isolated system, the direction of spontaneous change always changes from a more ordered state to a more disordered state, that is, from a state with fewer microscopic States to a state with more microscopic States, and from a state with a small entropy value to a state with a large entropy value, which is the essence of the second law of thermodynamics.

Third, the essence of the third law of thermodynamics

When T→0, all particles are in the ground state energy level, at this time ω 0 = 1, that is, there is only one way to put all particles in one energy level, and the system has only one microscopic state. Therefore, from Pozmann's theorem, that is, formula (6-25), it can be concluded that the entropy value of matter is zero at 0K, that is,

s0 = klnω0 = kln 1 = 0

The above formula can be regarded as the statistical expression of the third law of thermodynamics, which is consistent with the conclusion that the entropy value of any perfect crystal of pure matter is zero at 0 K.