Question

In an air standard Otto cycle the maximum and minimum tcmperatures arc 1400°C and 15°C. The heat supplied per kg of air is 800 kJ. Calculate the compression ratio and the thermal eficiency. Calculale also the. ratio of maximum to minimum pressures in the cycle.

Answer 1

Compression ratio

$Q_{2-3}=C_v(T_3-T_2)\\ 800=0.718(1673-T_2)\\ T_2= 1673-\frac{800}{0.718}=558.8 K\\ \frac{T_2}{T_1}=(\frac{v_1}{v_2})^{\gamma-1}\\ \frac{v_1}{v_2}=(\frac{558.8}{288})^{\frac{1}{0.4}}= 5.243$

Thermal Efficiency

$η= 1-\frac{1}{r_c^{r-1}}=1-\frac{1}{5.243^{0.4}}=48.45 \%$

The ratio of maximum to minimum pressures

$\frac{T_2}{T_1}=(\frac{P_2}{P_1})^{\frac{\gamma-1}{\gamma}}\\ \frac{P_2}{P_1}=(\frac{558.8}{288})^{\frac{1.4}{0.4}}=10.174.............1\\ \frac{P_3}{P_2}=(\frac{T_3}{T_2})=\frac{1673}{558.8}=2.993............2\\ \therefore Eqn \space 1 \space *Eqn \space 2\\ \frac{P_3}{P_1}=10.174*2.993=30.45$