To approximate an actual spark-ignition engine consider an air-standard Otto cycle that has a heat addition of 1800 kJ/kg of air, a compression ratio of 7, and a pressure and temperature at the beginning of the compression process of 90 kPa, 10°C. Assuming constant specific heat, with the value

Question

To approximate an actual spark-ignition engine consider an air-standard Otto cycle that has a heat addition of 1800 kJ/kg of air, a compression ratio of 7, and a pressure and temperature at the beginning of the compression process of 90 kPa, 10°C. Assuming constant specific heat, with the value from Table A.5, determine the maximum pressure and temperature of the cycle, the thermal efficiency of the cycle and the mean effective pressure.

Accepted Answer

Compression: Reversible and adiabatic so constant s from Eq.8.33-34

[latex]\begin{aligned}& P _2= P _1\left( v _1 / v _2 ight)^{ k }=90(7)^{1.4}=1372 \,kPa \& T _2= T _1\left( v _1 / v _2 ight)^{ k -1}=283.2 imes(7)^{0.4}=616.6 \,K\end{aligned}[/latex]

Combustion: constant volume

[latex]\begin{aligned}& T _3= T _2+ q _{ H } / C _{ V 0}=616.6+1800 / 0.717= 3 1 2 7 \,K \& P _3= P _2 T _3 / T _2=1372 imes 3127 / 616.6= 6 9 5 8 \,k P a\end{aligned}[/latex]

Efficiency and net work

[latex]\begin{aligned}& \eta_{ TH }=1- T _1 / T _2=1-283.2 / 616.5= 0 . 5 4 1 \& w _{ ext {net }}=\eta_{ TH } imes q _{ H }=0.541 imes 1800=973.8 \,kJ / kg\end{aligned}[/latex]

Displacement and [latex]P_{ ext {meff }}[/latex]

[latex]\begin{aligned}& v _1= RT _1 / P _1=(0.287 imes 283.2) / 90=0.9029 \,m ^3 / kg \& v _2=(1 / 7) v _1=0.1290 \,m ^3 / kg \& P _{ ext {meff }}=\frac{ w _{ NET }}{ v _1- v _2}=\frac{973.8}{0.9029-0.129}= 1 2 5 8 \,k P a\end{aligned}[/latex]

Question 12.CSGP.67: To approximate an actual spark-ignition engine consider an a......

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