Thermodynamics MOC

Entropy

Entropy is a somewhat obscure quantity relating to the exchange of heat. The change in entropy for a quasistatic process is defined by¹

Statistical thermodynamics reveals

where is the Shannon entropy expressed in for the Distribution of microstates at equilibrium.

Entropy is a quantity which increases during any Irreversible process. For a real process

Thermodynamic entropy postulates

In thermodynamics, the following properties are postulated:

1. The entropy is a well-defined quantity for equilibrium states as a function of the extensive parameters of a system, e.g. .
2. The entropy of a composite system is the sum of the entropies of its subsystems, i.e. entropy is an extensive parameter.
3. In an infinitesimal quasistatic process the change in entropy is .
4. Entropy maximum principle:^[Essentially the Second law of thermodynamics] For an isolated system, the entropy can never decrease, moreover if an internal constraint is removed, the final equilibrium state is that which maximizes entropy.

As a thermodynamic potential

Entropy is the naural Thermodynamic potential for a closed thermodynamic system. Applying the ^Quasistatic,

whence

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Footnotes

1. There is an implicit claim that is an exact differential and hence the quantity is well-defined for an equilibrium state. For example, see Entropy of an ideal gas. ↩