# Ratio of Specific Heats

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From Brunt et al1:

• Gamma (γ) is the ratio of specific heats. A low value of gamma produces heat release value that is too high and a heat release rate that is negative after the completion of combustion.
• A temperature dependent equation for gamma is produced from experimental data:
gamma=1.338-60*10^(-5)T+1.0*10^(-8)T^2 (Equation 1)
• Gamma is also dependent on equivalence ratio, Φ. The effect of ignoring this term is an error of up to ±0.015 in gamma (0.8<Φ<1.2)

Hayes et al2 and Rocco3 present Zucrow and Hoffman's equations of gamma:

gamma=(bar C_p)/(bar C_p - bar R) (Equation 2)

for T < 1000K

bar C_p=(3.6359-(1.33736T)/1000+(3.29421T^2)/(1*10^6)-(1.91142T^3)/(1*10^9)+(0.275462T^4)/(1*10^12))bar R (Equation 3)

for T > 1000K

bar C_p=(3.04473-(1.33805T)/1000-(0.488256T^2)/(1*10^6)+(0.0855475T^3)/(1*10^9)-(0.00570132T^4)/(1*10^12))bar R (Equation 4)

The main advantage of temperature dependent gamma is that it adjusts to different engine operating conditions - higher values of gamma would be used at low engine load.

catool Implementation: See Return_Gamma_Data() in analysis.c

References:
1. Brunt, M. F. J., Rai, H., Emtage, A. L., "The Calculation of Heat Release Energy from Engine Cylinder Pressure Data," SAE Paper 981052, 1998.
2. Hayes, T. K., Savage, L.D., "Cylinder Pressure Data Acquisition and Heat Release Analysis on a Personal Computer," SAE Paper 860029, 1986.
3. Rocco, V., "D.I. Diesel Engine In-Cylinder Pressure Data Analysis Under T.D.C. Setting Error," SAE Paper 930595, 1993.