Problem $3-$ Ideal Diesel cycle with variable specific heats $(15$ pts$)$

A Diesel internal combustion engine operates with a compression ratio of $18$ and a cutoff ratio of $2.$ You are interested in performing an analysis of this heat power cycle using the airstandard method for an ideal compression$-$ignition engine using variable specific heats. At the beginning of the compression process the air is at $100$ kPa and $300$ K $.$ Please answer the following.

a$.$ Sketch the cycle on P$-$v and T$-$s diagrams, denote the states using the same numbers used in your textbook. Include the symbols for transport of heat on their corresponding processes.

b$.$ Compute the maximum temperature and the maximum pressure during this cycle.

c$.$ Evaluate the heat transfer per unit mass that represents the heat produced during the combustion process, in kJ$/$kg$.$

d$.$ Determine the thermal efficiency for the cycle.

e$.$ Compute the mean effective pressure, in kPa $.$