Answer to Question #219904 in Mechanical Engineering for munthier

Question

In an air standard Otto cyclc the maximum and minimum tcmperatures arc 1400

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

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