[[eta].sub.C,norm] - Normalized compressor isentropic efficiency [gamma] - Ratio of specific heats
While perhaps somewhat intimidating at first glance, this equation only requires knowledge of the inlet and outlet pressures, the inlet temperature, the ratio of specific heats
k, and the loss factor Kloss.
This result, however, could not be reconciled with the experimentally obtained value [Gamma] = 1.408 for the ratio of specific heats: the theorem implied that the ratio [Beta] of total kinetic energy to translatory energy had to be [Beta] = [E.sub.kin]/[E.sub.trans] = 2, whereas from the value [Gamma] =1.408 it followed that this ratio was 1.634, in agreement with Clausius's results.
[Beta] has a constant average value, depending on the nature of the molecules, which can be calculated from the ratio of specific heats. It is remarkable that nowhere in the article he mentioned that one could also derive the value of [Beta] theoretically with the help of the equipartition theorem.
Having introduced the treatment of molecular motion in terms of degrees of freedom and having restated the theorem of equipartition (which Boltzmann had meanwhile proved and extended to a theorem of complete equipartition over all degrees of freedom), Maxwell obtained a general expression for the ratio of specific heats:
In 1871 Boltzmann returned to the anomaly.(24) He proved the theorem of complete equipartition and, having accepted the diatomic nature of most gas molecules, he derived the theoretical value [Gamma] = 1.33 for the ratio of specific heats. The anomalous experimental value [Gamma] 1.41, Boltzmann suggested, might be explained by interaction of molecules with the ether (Maxwell , p.232, later refuted this hypothesis).
When discussing future powertrains and the requirement for high efficiency, it is worth remarking that, on a fundamental level, the only two factors that influence the ultimate efficiency of an engine operating on the Otto-cycle are the compression ratio and the ratio of specific heats of the working fluid ([gamma]) .
The increase ]in efficiency once MBT phasing was reached is attributed to the improvement in the charge's ratio of specific heats and improved combustion efficiency, as has been demonstrated in previous publications.
A new correlation for [gamma], the ratio of specific heats was used for all heat release calculations presented here.
[gamma] here is defined as the ratio of specific heats of the combustion gases, this differs from the definition of [gamma] in the development of the ignition delay correlation discussed previously.
Many different methods for calculating the ratio of specific heats for use in HRR calculations exist in the literature including [1,30,31,32,33,34].