# Math Solution of Second Law Of Thermodynamics

The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium—the state of maximum entropy. Equivalently, perpetual motion machines of the second kind are impossible.

The second law is an empirically validated postulate of thermodynamics, but it can be understood and explained using the underlying quantum statistical mechanics, together with the assumption of low-entropy initial conditions in the distant past (possibly at the beginning of the universe). In the language of statistical mechanics, entropy is a measure of the number of microscopic configurations corresponding to a macroscopic state. Because equilibrium corresponds to a vastly greater number of microscopic configurations than any non-equilibrium state, it has the maximum entropy, and the second law follows because random chance alone practically guarantees that the system will evolve towards equilibrium.

## Math Solution of Second Law Of Thermodynamics

### Math Solution of Second Law Of Thermodynamics

Math Solution of Second Law Of Thermodynamics

*To Download Math Solution of Second Law Of Thermodynamics Click Here*

**Math Solution of Second Law Of Thermodynamics**

Math Solution of Second Law Of Thermodynamics

*Math Solution of Second Law Of Thermodynamics*

Math Solution of Second Law Of Thermodynamics

*To Download Math Solution of Second Law Of Thermodynamics Click Here*

Math Solution of Second Law Of Thermodynamics

Math Solution of Second Law Of Thermodynamics

The second law of thermodynamics states that the entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium—the state of maximum entropy. Equivalently, perpetual motion machines of the second kind are impossible.

The second law is an empirically validated postulate of thermodynamics, but it can be understood and explained using the underlying quantum statistical mechanics, together with the assumption of low-entropy initial conditions in the distant past (possibly at the beginning of the universe). In the language of statistical mechanics, entropy is a measure of the number of microscopic configurations corresponding to a macroscopic state. Because equilibrium corresponds to a vastly greater number of microscopic configurations than any non-equilibrium state, it has the maximum entropy, and the second law follows because random chance alone practically guarantees that the system will evolve towards equilibrium.

It is an expression of the fact that over time, differences in temperature, pressure, and chemical potential decrease in an isolated non-gravitational physical system, leading eventually to a state of thermodynamic equilibrium.

The second law may be expressed in many specific ways, but the first formulation is credited to the French scientist Sadi Carnot in 1824 (see Timeline of thermodynamics).

The second law has been shown to be equivalent to the internal energy U being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, …)