A $4-$stroke petrol engine with $4$ cylinders works according to the ideal Otto cycle with a compression

ratio of$11$and a displacement volume $4-$waa $-$vm$,$ from$0\mathrm{.}45$liters per cylinder. The air has a pressure of

$90$ kPaand a temperature of$50$ at the beginning of the compression process. For each cylinder, each

cycle$|1,5$ J added to energy. The motor runs at $3000$ rpm$.$ You may assume that the heat capacity of

the air is constant throughout the cycle. Name the state at the beginning of the compression

process 'state $1\text{'},$ just after the compression 'state $2\text{'},$ and so on$.$

a$)$ In which state will the pressure and temperature be greatest? Determine this maximum pressure

and temperature of the air during the cycle.

b$)$Determine the net work per cylinder per Otto cycle

c$)$Determine the thermal efficiency of the cycle

d$)$Determine the total power of the motor

e$)$Determine the initial.velocity of the gas with which the air flows out of the cylinder when

the exhaust valve opens. The opening is circular with a diameter of$3$and the pressure

outside the cylinder is$1.$Take into account a minor loss factor of$0\mathrm{.}3.$