Exercise $4.$ A four$-$cylinder, four$-$stroke, spark$-$ignition engine has a displacement volume of $300$ cc per cylinder. The compression ratio of the engine is $10,$ and it operates at a speed of $3000re\frac{v}{m}in.$ The engine is required to develop an output of $40$ kW at this speed. Assume that the engine operates on the Otto cycle and that the pressure and temperature at the inlet conditions are $1$ bar and $27C,$ respectively. Calculate:

The cycle efficiency.

The necessary rate of heat addition.

The mean effective pressure.

The maximum temperature of the cycle.

If the above engine is a compression$-$ignition engine operating on the Diesel cycle and receiving heat at the same rate, calculate:

The efficiency.

The maximum temperature of the cycle.

The cycle efficiency.

The power output.

The mean effective pressure.

Take $C_v=0\mathrm{.}717k\frac{J}{k}gK$ and $=1\mathrm{.}4.$