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dQ
dS  (2.12.5)
T
And thus equation (2.12.4) becomes

dS  0 (2.12.6)

The SI unit for entropy is J
K
Definition of entropy was developed by Rudolf Clausius ( German
physicist and mathematician (1822-1888)) Clausius wrote that he
"intentionally formed the word Entropy as similar as possible to the word

Energy", basing the term on the Greek ἡ τροπή [tropé], transformation
The change in entropy between any two states 1(initial) and 2 (final) is
equal to

2 2 dQ
S  S 2  S 1  dS   (2.12.7)

1 1 T

There are such properties of the entropy of closed systems:
1. The entropy does not change for reversible processes: S  0

2.The entropy increases for irreversible processes: S  0

All processes in the nature occur in the direction of the entropy
increasing. The concept of the entropy permits to formulate the second law
of thermodynamics in another form:

The entropy of the closed system cannot decrease S  0

2.13 Entropy and Probability

Entropy is a macroscopic variable, associated with the overall state of a
system and calculable from the macroscopic quantities associated with its
overall state. We could see that all macroscopic variables in

thermodynamics have a corresponding microscopic quantity (such as
temperature, a macroscopic quantity, and mean molecular kinetic energy,
a microscopic quantity). If we make certain assumptions about the

microscopic properties of the system, we can usually find a way to relate
the macroscopic and microscopic quantities. In the case of the tem-
perature of a gas, these assumptions include a mechanical model of the
molecules and their interactions, along with a statistical distribution of

the molecular energies. We would, therefore, like to consider the

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