Air undergoes a polytropic process in a piston–cylinder assembly from p1 = 1 bar, T1 = 295 K to p2 = 3 bar. The air is modeled as an ideal gas and kinetic and potential energy effects are negligible. For a polytropic exponent of 1.4, determine the work and heat transfer, each in kJ per kg of air, (1) assuming constant cv evaluated at 300 K. (2) assuming variable specific heats.

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