Page 69 - 48Fundamentals of Compressible Fluid Mechanics
P. 69
3.4. SPEED OF SOUND IN REAL GAS 31
From thermodynamics, it can be shown 4
(3.23)
and thus
The specific volumetric is the inverse of the density as
(3.24)
Substitute the equation (3.24) into equation (3.23) results
"
(3.25)
"!
!
!
Simplifying equation (3.25) to became #
(3.26)
Utilizing Gibbs equation (3.20)
$
(3.27)
Letting
for isentropic process results in
%
(3.28)
Equation (3.28) can be integrated by parts. However, it is more convenient to
express
in terms of and as following
(3.29)
4 See Van Wylen p. 372 SI version, perhaps to insert the discussion here.
'&
)(
