The p-V diagram of a petrol engine at maximum power output (full throttle) with a compression ratio of 10 and a gravimetric air/fuel ratio of 15 is analysed on the basis of an Otto cycle with the following modifications to approximate real conditions:

• for compression from state 1 to 2: $\gamma = 1.4$;
• for heat addition from state 2 to 3: $c_v = 0.880\ \mathrm{kJ/(kg\,K)}$;
• for expansion from state 3 to 4: $\gamma = 1.3$;
• $p_3$ is reduced by 20% to allow for incomplete combustion and heat-transfer losses;
• 15% of the work output is lost to friction and to driving essential auxiliaries (e.g. the water pump).

Estimate the brake thermal efficiency of the engine given $T_1 = 288\ \mathrm{K}$, calorific value of the fuel 43 710 kJ/kg and air gas constant $R = 0.287\ \mathrm{kJ/(kg\,K)}$.