3.5. SUMMARY OF THERMODYNAMIC THEORY 37
new second-order thermodynamic coecients for water could be obtained from the complex
t of the equation of state provided by the International Association of the Properties of
Water and Steam (IAPWS) in Ref. 44.
Finally, it is dicult say how the second-order thermodynamic relations, such as
Eq. (3.29), would impact our theoretical results of the second-order acoustic phenomena,
such as the radiation force and streaming ow. In experiments the energy density in the
channel is calibrated through observations of particle motion due to the radiation force and
streaming-induced drag force. Consequently, it is not possible to make a comparison of
theory and experiments for the magnitude of one of these forces independent of the other.
To give a specic example, the comparison of the drag-force-dominated particle motion
in Ref. 11 Appendix B rely on the assumption that the theoretical expression for the
radiation force is correct, as this is used for the calibration of the energy density based on
radiation-force-dominated particle motion.
This ends the discussion of the possible inconsistency in the combination of rst-order
thermodynamics and second-order acoustics. The use of second-order thermodynamic
relations are left as a suggestion for future work, or at least to explain why this is not
necessary.
3.5 Summary of thermodynamic theory
In this chapter we have derived the governing equations for the conservation of mass,
momentum and energy in a compressible Newtonian uid. The governing equations were
rewritten using linear thermodynamic relations and expanded using second-order perturbation
theory. Through dimensional analysis, we discussed the relative orders of magnitude of
the rst-order acoustic elds, the adiabatic approximation, and the magnitude of the acoustic
streaming. As an outlook for future work, the possible ambiguity of the combination
of linear thermodynamic relations and second-order perturbation theory was discussed.