## The Principle of Increase of Entropy

written by: Haresh Khemani โข edited by: Lamar Stonecypher โข updated: 8/16/2008

The entropy of the system never reduces. In the ideal process it can remain remain constant, but in actual process the entropy of system and universe always increases. Let us why the entropy of the universe always increases and its relation to second law of thermodynamics.

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### Introduction

In the previous article on what is entropy, we saw the causes of increase in entropy of the sysem. Let us repeat them here once again.

In actual practice the reversible isentropic process never really occurs, it is only an ideal process. In actual practice whenever there is change in the state of the system the entropy of the system increases. Here are the various causes of the increase in entropy of the closed system are:

1) Due to external interaction: In closed system the mass of the system remains constant but it can exchange the heat with surroundings. Any change in the heat content of the system leads to disturbance in the system, which tends to increase the entropy of the system.

2) Internal changes in the system: Due to internal changes in the movements of the molecules of the system there is further disturbance inside the system. This causes irreversiblities inside the system and an increase in its entropy.

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### The Principle of Increase of Entropy

The entropy of the isolated system is the measure of the irreversibility undergone by the system. More is the irreversibility more increase is the entropy of the system. As such the reversible process is an ideal process and it never really occurs. This means the certain amount of the irreversibility is always there in the system, this also means that the entropy of the isolated system always goes on increasing, it never reduces. Here let us keep in mind that isolated system can always be formed by including any system and surroundings within a single boundary.

In his book Engineering Thermodynamics, the author P K Nag says, โAn irreversible process always tends to take the isolated system to a state of greater disorder. An isolated system always tends to a state of greater entropy. So there is link between entropy and disorder. It may be roughly said that the entropy of a system is a measure of degree of molecular disorder existing in the system. When the heat is imparted to a system, the disorderly motion of the molecules increases and so the entropy of the system increases. The reverse occurs when the heat is removed from the system."

Summarizing the first and second law of thermodynamics, Clausius made two statements:

1) The energy of the world (universe) is constant.

2) The entropy of the world tends towards a maximum.

Thus the entropy of the isolated system tends to go on increasing and reaches maximum value at the state of equilibrium. When the system reaches equilibrium the increase in entropy becomes zero.

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### Entropy and Second Law of Thermodynamics

As per second law of thermodynamics, all the spontaneous processes occur in the nature from higher to lower potential. It requires external work to carry out the process against the nature that is from lower to higher potential. Thus all the spontaneous processes are irreversible and they lead to increase in entropy of the universe. Further, since the entropy of the isolated system always tends to increase, it implies that in nature only those processes are possible that would lead to the increase in entropy of the universe, which comprises of the system and the surroundings.

If the potential gradient between the two states of the system is infinitesimally small (almost equal to zero) the process is said to be isentropic process, which means the entropy change during this process is zero. The change in entropy tends to zero when the potential gradient becomes zero. The value of entropy becomes maximum when system reaches equilibrium position.

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### Reference

Book: Engineering Thermodynamics by P K Nag