Thermodynamics

Problem 1 – 25 points

A heat engine operating at steady state has a thermal efficiency of 35% and generates 100 MW of electricity while discharging energy by heat transfer to cooling water at an average temperature of 20°C. The average temperature of the steam passing through the boiler is 460°C.

(a) What is the rate at which energy is discharged to the cooling water (MW)?

(b) What is the minimum theoretical rate at which energy could be discharged to the cooling water (MW)?

Problem 2 – 25 points

Each of the parts below is a separate problem. calculate the appropriate quantity.

(a) Refrigerant-134a at T = 40°F and s = 0.22194 Btu/lbm·°R. Find u (Btu/lbm).

(b) Water at P = 5.0 MPa and T = 100°C. Find the exact value of s (kJ/kg·K).

(c) Refrigerant-134a at P = 80 psia and T = 50°F. Find s (Btu/lbm·°R).

(d) Nitrogen (ideal gas) at T = 250 K. Find (kJ/kmol·K).

(e) An inventor claims to have developed a refrigerator that maintains the refrigerated space at 40°F while operating in a room where the temperature is 85°F and that has a COP of 13.5. Is this claim reasonable?

Problem 3 – 25 points

A Carnot heat engine drives a Carnot refrigeration cycle as shown.

(a) How much work does the heat engine produce (in Btu)?

(b) What is T3 (in °R)?

(c) What is Q3 (in Btu)?

Problem 4 – 25 points

Steam at 1 MPa and 600°C enters a well-insulated turbine operating at steady state with a velocity of 50 m/s and exits at 0.01 MPa with a velocity of 100 m/s. The work developed per kg of steam flowing is claimed to be 1050 kJ/kg. Is this a valid claim?

(Clearly justify your answer). Assume negligible potential energy changes.

Problem 1 – 25 points

Steam enters an adiabatic turbine at 8 MPa and 500°C at a rate of 18 kg/s, and exits at 0.2 MPa and 300°C. Determine the rate of entropy generation (kW/K) in the turbine.

Problem 3 – 25 points

Steam enters an adiabatic turbine at 8 MPa and 500°C with a mass flow rate of 3 kg/s and leaves at 30 kPa. The isentropic efficiency of the turbine is 0.90. Determine the powerout-put (MW) of the turbine.

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