# The Second Law of Thermodynamics

It may be that compressible processes must be tested for reversibility by means of the Second Law of Thermodynamics. For completeness, we show this here in the form of the entropy-rate inequality. In differential form, the Second Law of Thermodynamics is:

dS, (3.11)

where S is the system entropy and T is the (absolute) temperature. S can be written in terms of the corresponding intensive property, s (entropy per unit mass) as:

S = J s dm = JJJ psdV.

system

volume

Then, the required rate equation form for the Second Law of Thermodynamics is:

— > Q (3.13)

dt T

Additional Physical Laws

The “laws” describing the physics of fluid motion in rate form usually must be supplemented by additional information so that a complete mathematical representation is achieved. Important supplementary physical relationships may come from thermodynamics, chemistry, heat transfer, or additional mechanical models to fully describe the fluid medium. For example, in Chapter 2, supplementary physical relationships are introduced in the form of the equation of state (see Eq. 2.1) and Newton’s Law of Viscosity (Eq. 2.4). These laws are incorporated as needed to fully describe any given situation.

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