Question

A spark ignition engine working on ideal Otto cycle the compression ratio 6. The initial pressure and temperature of air are 1 bar and 37°C. The maximum pressure in the cycle is 30 bar. For unit mass flow, calculate

Answer 1

Process 1-2

$R= \frac{8.314}{28.97}=0.287 kJ/kgK\\ v_1=\frac{mRT_1}{P_1}=\frac{1*0.287*310.15}{100}=0.89 m^3/kg\\ \frac{P_2}{P_1}=(\frac{V_1}{V_2})^{\gamma} \implies P_2= 6^{1.4}=12286kPa\\ v_2=\frac{v_1}{\gamma}=\frac{0.89}{6}=0.1483 m^3/kg\\$

Process 2-3

$v_2=v_3=0.1483 m^3/kg\\ P_3=30 bar\\ \frac{P_3}{P_2}=\frac{T_3}{T_2} \implies T_3=635.08*\frac{30}{12.286}=1550.75 K\\$

Process 3-4

$v_4=v_1=0.9 m^3/kg\\ \frac{T_3}{T_4}=(\frac{v_4}{v_3})^{\gamma-1} =6^{1.4-1} \implies T_4 = \frac{1550.75}{6^{0.4}}=757.32 K\\ \frac{p_3}{p_4}=(\frac{v_4}{v_3})^{\gamma-1} =6^{1.4} \implies p_4 = \frac{30}{6^{0.4}}=2.441 bar\\$

Process 4-1

This has a constant volume where heat is rejected