Example 2.2
Four kilograms of a certain gas is contained within a piston–cylinder assembly. The gas undergoes a process for which the pressure–volume relationship is The initial pressure is 3 bar, the initial volume is 0.1 m3 , and the final volume is 0.2 m3 . The change in specific internal energy of the gas in the process is u2 u1 4.6 kJ/kg. There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process, in kJ.
Example 2.3
Air is contained in a vertical piston–cylinder assembly fitted with an electrical resistor. The atmosphere exerts a pressure of 1 bar on the top of the piston, which has a mass of 45 kg and a face area of .09 m2 . Electric current passes through the resistor, and the volume of the air slowly increases by .045 m3 while its pressure remains constant. The mass of the air is .27 kg, and its specific internal energy increases by 42 kJ/kg. The air and piston are at rest initially and finally. The piston–cylinder material is a ceramic composite and thus a good insulator. Friction between the piston and cylinder wall can be ignored, and the local acceleration of gravity is g 9.81 m/s2 . Determine the heat transfer from the resistor to the air, in kJ, for a system consisting of (a) the air alone, (b) the air and the piston.
Example 2.4
During steady-state operation, a gearbox receives 60 kW through the input shaft and delivers power through the output shaft. For the gearbox as the system, the rate of energy transfer by convection is where h 0.171 kW/m2 K is the heat transfer coefficient, A 1.0 m2 is the outer surface area of the gearbox, Tb 300 K (27C) is the temperature at the outer surface, and Tf 293 K (20C) is the temperature of the surrounding air away from the immediate vicinity of the gearbox. For the gearbox, evaluate the heat transfer rate and the power delivered through the output shaft, each in kW.
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