Problem $2-$ Ideal Otto cycle with variable specific heats $(10$ pts$)$

An ideal Otto cycle has a compression ratio of $9\mathrm{.}5$ and is modeled using air. At the start of the compression process $P_1=95$kPa,$T_1=7C$ and $V_1=3$ liters. The maximum air temperature in the cylinder is $927C.$ Please answer the following questions.

Note: This problem is to be solved using variable specific heats. You will not receive credit for solutions that use constant specific heats.

a$.$ Sketch the cycle on P$-$v and T$-$s diagrams. Identify the states using numbers as shown in your textbook and indicate which processes transport heat.

b$.$ Compute the temperature and pressure at the end of the compression cycle.

c$.$ For each repetition of the cycle calculate the heat rejection and the net work production, in kJ$.$

d$.$ Calculate the thermal efficiency.

e$.$ Consider that the crank of the engine turns at $3000$ RPM$.$ Determine the power for one cycle. Hint: two revolutions of the crank represent one cycle.