How would you quantitatively evaluate the expected performance of a heat engine? (explain in narrative)

Derive the correction factor formula for conical nozzle i=-(1+ cosa) and calculate the nozzle angle correction factor for a nozzle whose divergence hal-fangle is 13 (hint: assume that all the mass flow originates at the apex of the cone.

Air inially occupying a volume of 1 m2 at 100 kpa, 27 c undergoes three internally reversible processes in series. process 1-2 compression to 500 kpa during which pv constant process 2-3 adiabatic expanslon to 100 kpa process 3-1: constant-pressure expansion to 100 kpa (a) calculate the change of entropy for each of the three processes. (b) calculate the heat and work involved in each process. (c) is this cycle a power cycle or refrigeration cycle?

Air enters a horizontal, constant-diameter heating duct operating at steady state at 290 k, 1 bar, with a volumetric flow rate of 0.25 m°/s, and exits at 325 k, 0.95 bar. the flow area is 0.04 m2. assuming the ideal gas model with k = 1.4 for the air, determine (a) the velocity at the inlet and exit, each in m/s, and (c) the rate of heat transfer, in kw flow rate, in kg/s, (b) the mass kg 0.3