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titleDerivation


LaTeX Math Block
anchorcg1
alignmentleft
c = - \frac{1}{V} \frac{dV}{dp} = - \frac{d}{dp} \left( \ln V \right) \rightarrow \ln \frac{V}{V_0} = - \int_{p_0}^p c(p) dp


Substituting

LaTeX Math Inline
bodyV
from
LaTeX Math Block Reference
anchorZ
into
LaTeX Math Block Reference
anchorcg1
one arrives to
LaTeX Math Block Reference
anchorZ_c
.


The z Z-factor value is trending towards 

LaTeX Math Inline
bodyZ \rightarrow 1
 for incompressible fluids and 
LaTeX Math Inline
bodyZ \rightarrow a \cdot p
 for strongly compressible Fluids.



See also

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Natural Science / Physics /Thermodynamics 

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