Problem $4-$ Diesel cycle with irreversibility $(15$ pts$)$

A Diesel cycle is modeled with air. The compression ratio and cutoff ratio are $16$ and $1\mathrm{.}6,$ respectively. The adiabatic compression process has an isentropic efficiency equal to $90\%,$ and the adiabatic expansion process has an isentropic efficiency equal to $85\%.$ Using the method of the cold$-$air standard when at the start of the compression the pressure and temperature are $100$ kPa and $27C,$ respectively, please answer the following.

a$.$ Sketch the cycle on a P$-$v and T$-$s diagram.

b$.$ Determine the maximum temperature of the air inside the cylinder.

c$.$ Determine the heat supplied per unit mass of air during the constant pressure process.

d$.$ Compute the net work for one cycle in $k\frac{J}{k}g.$

e$.$ Compute the thermal efficiency for the cycle.

f$.$ Now you want to estimate the amount of fuel consumption per cycle, in kg$.$ Consider that the diesel fuel has a heating value equal to $42000k\frac{J}{k}g$ and the combustion efficiency is $90\%.$ For your computations consider volume at the bottom dead center is equal to $4$ liters.