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PS9 Solutions

# PS9 Solutions - MAE 105A Introduction to Engineering...

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Unformatted text preview: MAE 105A Introduction to Engineering Thermodynamics Winter 2008 Problem Set 9 Air enters an insulated turbine operating at steady state at 4.89 bar, 597°C and exits at 1 bar, 297°C. Neglecting kinetic and potential energy changes and assuming the ideal gas model, determine (a) the work developed, in kJ per kg of air ﬂowing through the turbine (b) whether the expansion is internally reversible, irreversible, or impossible. Air enters an insulated diffuser 'operating at steady state at 1 bar, —3°C, and 260 1n/s and exits with a velocity of 130 m/s. Employing the ideal gas model and ignoring potential energy, determine (a) the temperature of the air at the exit, in °C. (b) the maximum attainable exit pressure, in bar. [Problem 6.107 in Moran and Shapiro]. Air enters a compressor operating at steady state at 1 bar, 22°C with a volumetric ﬂow rate of l m3/niin and is compressed to 4 bar, 177°C. The power input is 3.5 kW. Employing the ideal gas model and ignoring kinetic and potential energy effects, obtain the following results: (a) For a control volume enclosing the compressor only, determine the heat transfer rate, in kW, and the change in speciﬁc entropy from inlet to exit, in kJ/kg—K. What additional information would be required to evaluate the rate of entropy production? (b) Calculate the rate of entropy production, in kW/K, for an enlarged control volume enclosing the compressor and a portion of its immediate surroundings so that heat transfer occurs at the ambient temperature, 22°C. Air enters a 3600—kW turbine operating at steady state with a mass ﬂow rate of i8 kg/s at 800°C, 3 bar and a velocity of 100 1111's. The air expands adiabatically through the turbine and exits at a velocity of 150 m/s. The air then enters a diffuser where it is decelerated isentropically to a velocity of 10 m/s and a pressure of 1 bar. Employing the ideal gas model, determine (a) the pressure and temperature of the air at the turbine exit, in bar and °C, respectively. (b) the rate of entropy production in the turbine, in kW/K. (c) Show the processes on a T—s diagram. Air enters an insulated compressor operating at steady state at 1.05 bar, 23°C with a mass flow rate of 1.8 kg/s and exits at 2.9 bar. Kinetic and potential energy effects are negligible. (a) Determine the minimum theoretical power input required, in kW, and the corresponding exit temperature, in °C. (b) If the exit temperature is 147°C, determine the power input, in kW, and the isentropic compressor efﬁciency. Three devices are operating at steady state conditions: a pump, a boiler, and a turbine. The water enters the pump at p1 : 1 bar, T; a 30°C; enters the boiler at p; = 8 bar; enters the turbine at p3 ~= 8 bar, X3 : l; and leaves the turbine at p4 : 1 bar. 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