1. A rigid, uninsulated tank of volume 2.0 m3 is connected to a supply pipe that contains air at 150 kPa and 290 K. Initially, the tank is completely empty (evacuated). The tank valve is opened, and air flows from the supply pipe into the tank until the tank pressure reaches 150 kPa, at which point the valve is closed (sealing the tank). If the final temperature in the tank is 380 K, determine the total amount of heat removed from the tank during the process.
2. 0.10 kg of steam is contained in an uninsulated piston-cylinder assembly. The steam is initially at 200°C and 1.0 MPa. The system undergoes a process in which 70 kJ of heat is lost to the surroundings. The final pressure is 1.5 MPa and the final quality is 0.72.
a. Determine the final temperature.
b. Determine the extensive work performed during this process (and specify the direction "in" or "out").
3. Assume a nuclear power plant, with a thermal efficiency of 33%, operates on the ideal Rankine cycle. The nuclear reactor temperature is 500°C. The working fluid (water) absorbs 300 MW of heat in the boiler. The water enters the pump as a saturated liquid at 150 kPa at 100 kg/s. The waste heat is rejected to the atmosphere, which is at approximately 20°C.
a. Determine the net power output of the plant.
b. Determine the specific enthalpy at the turbine outlet.
c. Is it theoretically possible to design a heat engine with a thermal efficiency of 65% that operates between the heat source and sink described above? (Yes or No, and explain why or why not.)
4. Assume an engine is running on the ideal Diesel cycle with air as the working fluid, and a compression ratio of 15. The combustion process is modeled as a heat input of 600 kJ/kg. The exhaust and intake processes are modeled as a single heat rejection process whereby 250 kJ/kg is rejected from the system. At the beginning of the compression stroke, the air is at 100 kPa and 295 K.
a. Determine the thermal efficiency.
b. Estimate the temperature at the end of the compression stroke.
c. Estimate the temperature at the end of the expansion stroke (power stroke).