Mumbai University > Mechanical Engineering > Sem 5 > IC Engines

Marks: 10M

Year: Dec 2015

In an Otto engine pressure and temperature at the beginning of compression are 1 bar and 37oC respectively. Calculate the theoretical thermal efficiency of the cycle, if the pressure at the end of adiabatic compression is 15 bars. Peak temperature during the cycle is 2000K. Calculate the heat supplied per kg of air, work done per kg of air and the pressure at the end of adiabatic expansion. Take Cv=0.717 KJ/KgK and adiabatic index=1.4

${P_1} = 1bar,$, ${T_1} = 37 = 273 + 37 = 310K$, ${P_2} = 15bars$, ${T_3} = 2000K,$ ${C_v} = 0.717KJ/KgK$, $\gamma = 1.4$ $${p_1}{v_1} = mR{T_1}$$$$1 \times 10 \times {v_1} = 1 \times 287 \times 310$$$${v_1} = 0.8897{m^3}$$$${p_2} \times v_2^\gamma = {p_1} \times v_1^\gamma $$$$15 \times v_2^\gamma = 1 \times {0.8897^{1.4}}$$$${v_2} = 0.1286{m^3}$$$$\frac{{{p_1}{v_1}}}{{{T_1}}} = \frac{{{p_2}{v_2}}}{{{T_2}}}$$$$\frac{{1 \times 0.8897}}{{310}} = \frac{{15 \times 0.1286}}{{{T_2}}}$$$${T_2} = 672.12K$$$$\frac{{{P_2}}}{{{T_2}}} = \frac{{{P_3}}}{{{T_3}}}$$$${P_3} = \frac{{15}}{{672.12}}2000 = 44.63bar$$$${p_4}v_4^\gamma = {p_3}v_3^\gamma $$$${p_4} = \frac{{44.63 \times {{0.1286}^\gamma }}}{{{{0.8897}^\gamma }}}$$$${p_4} = 2.976bar$$$${T_4} = \frac{{{p_4}}}{{{p_1}}}{T_1} = \frac{{2.97}}{1}310 = 920.7K$$$${Q_s} = {C_v}({T_3} - {T_2}) = 0.717(2000 - 672.12)$$$${Q_s} = 952.1Kj/kg$$$${Q_r} = {C_v}({T_4} - {T_1}) = 0.717(920.7 - 310) = 437.872K$$$$Work{\text{ done = 952}}{\text{.1 - 437}}{\text{.872 = 514}}{\text{.228Kj/Kg}}$$$$\eta = \frac{{Work{\text{ done}}}}{{heat{\text{ supply}}}} = \frac{{514.228}}{{952.1}}$$$$\eta = 0.5400 = 54\% $$