# catoolRT

#### Mean Gas Temperature

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The mean gas temperature is required for the calculation of heat release.

For a polytropic process1:

p V_n = constant (Equation 1)

T_2/T_1=(V_1/V_2)^(n-1)=(p_2/p_1)^((n-1)/n) (Equation 2)

hence:

T_2=T_1(V_1/V_2)^(n-1)=T_1(p_2/p_1)^((n-1)/n) (Equation 3)

for a known reference location, such as inlet valve closure:

p_(ref) V_(ref) = n R T_(ref) (Equation 4)

rearranging gives:

T_(ref)/(p_(ref) V_(ref))=1/(n R) (Equation 5)

to calculate the temperature at an arbitrary position between inlet valve closure and exhaust valve opening:

T_(calc)=p_(calc) V_(calc) 1/(n R) (Equation 6)

assuming n and R remain constant, equation 5 can be substituted into equation 6:

T_(calc)=p_(calc) V_(calc) T_(ref)/(p_(ref) V_(ref)) (Equation 7)

catool Implementation: See Return_Temperature_Data() in analysis.c

References:

1. Wray, A. P., Ibrahim, S. S., Carrotte, J. F., "Engineering Thermodynamics," Departmental Publication No. 18, AAE Department, Loughborough University, 1997.