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ME 104 Thermodynamics [F23]

Homework Assignment 11

[Due Mon 11/13]

Text: Thermodynamics: An Engineering Approach, Y. Çengel and M. Boles, McGraw-Hill, 10th Edition, 2024. The link to the book is provided on the course site.

Problem 1: [10–57E] An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 120°F and 14.7 psia at the beginning of the compression process and at 3200 R at the end of the heat-addition process. Accounting for the variation of specific heats with temperature, determine (a) the cutoff ratio, (b) the heat rejection per unit mass, and (c) the thermal efficiency.

Problem 2: [10–59] An ideal Diesel cycle has a maximum cycle temperature of 2000 °C. The state of the air at the beginning of the compression is P₁=95 kPa and T₁=15 °C. This cycle is executed in a four-stroke, eight-cylinder engine with a cylinder bore of 10 cm and a piston stroke of 12 cm. The minimum volume enclosed in the cylinder is 5 percent of the maximum cylinder volume. Determine the power produced by this engine when it is operated at 1600 rpm. Use constant specific heats at room temperature.

Problem 3: [10–94] Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 70 MW, assuming both the compressor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 85 percent. Assume constant specific heats at room temperature.

Problem 4 [10–100] A gas-turbine power plant operating on the simple Brayton cycle has a pressure ratio of 7. Air enters the compressor at 0°C and 100 kPa. The maximum cycle temperature is 1500 K. The compressor has an isentropic efficiency of 80 percent, and the turbine has an isentropic efficiency of 90 percent. Assume constant properties for air at 300 K with C_v = 0.718 kJ/kg·K, C_p = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, k=1.4.

(a) Sketch the T-s diagram for the cycle.

(b) If the net power output is 150 MW, determine the volume flow rate of the air into the compressor in m³/s.

(c) For a fixed compressor inlet velocity and flow area, explain the effect of increasing compressor inlet temperature (i.e., summertime operation versus wintertime operation) on the inlet mass flow rate and the net power output with all other parameters of the problem being the same.