1) A piston-cylinder device contains helium gas initially at 150 kPa, 20°C and 0.5 m³. The helium is now compressed in a polytropic process to 400 kPa and 140 C. Determine the heat loss or gain during this process.
2) A rigid tank containing 0.4 m³ of air at 400 kPa and 30°C is connected by a valve to a piston-cylinder device with zero clearance. The mass of the piston is such that a pressure of 200 kPa is required to raise the piston. The valve is now opened slightly, and air is allowed to flow into the cylinder until the pressure in the tank drops to 200 kPa. During the process, heat is exchanged with the surroundings such that the entire air remains at 30°C at all times. Determine the heat transfer for this process.
3) A piston-cylinder device initially contains steam at 200 kPa, 200°C and 0.5 m³. At this state, a linear spring (F ∝ x) is touching the piston but exerts no force on it. Heat is now slowly transferred to the steam, causing the pressure and volume to rise to 500 kPa and 0.6 m³, respectively. Show the process on a P-V diagram with respect to saturation lines and determine (a) final temperature, (b) the work done by the steam, (c) the total heat transferred.
4) A mass of 5 kg of saturated liquid-vapor mixture of water in a piston-cylinder device at 100 kPa. Initially, 2 kg of the water is in the liquid phase and the rest in the vapor phase. Heat is transferred to the water, and the piston, which is resting on the stops, starts moving when the pressure inside reaches 200 kPa. Heat transfer continues until the volume increases by 20%. Determine (a) the initial and final temperatures, (b) the mass of liquid when the piston starts moving, (c) the work, (d) the heat transfer.
5) In large gas turbine power plants, air is preheated by the exhaust gases in a heat exchanger called regenerator before it enters the combustion chamber. Air enters the regenerator at 1 MPa and 550 K at a mass flow rate of 800 kg/min. Heat is transferred to the air at a rate of 3200 kJ/s. Exhaust gases enter the regenerator at 140 kPa and 800 K and leave at 130 kPa and 600 K. Treating the exhaust gases as air, determine (a) the exit temperature of the air and (b) the mass flow rate of exhaust gases.
6) Steam enters a turbine steadily at 8 MPa and 550°C with a velocity of 50 m/s and leaves at 20 kPa with a quality of 95%. A heat loss of 30 kJ/kg occurs during the process. The inlet area of the turbine is 150 cm² and the exit area is 1400 cm². Determine (a) the mass flow rate of the steam, (b) the exit velocity, and (c) the power output in kW.
7) An insulated vertical piston-cylinder device initially contains 0.2 m³ of air at 200 kPa and 22°C. At this state, a linear spring touches the piston but exerts no force on it. The cylinder is connected by a valve to a line that supplies air at 800 kPa and 22°C. The valve is opened, and air from the high pressure line is allowed to enter the cylinder. The value is turned off when the pressure in the cylinder reaches 600 kPa. If the enclosed volume inside the cylinder doubles during this process, determine (a) the mass of air that entered the cylinder and (b) the final temperature of the air inside the cylinder.
8) A 5-L pressure cooker has an operating pressure of 200 kPa. Initially, 20% of the volume is occupied by liquid and the rest by vapor. The cooker is placed on a heating unit that supplies heat to the water inside at a rate of 400 W. Determine how long it will take for the liquid in the pressure cooker to be depleted (i.e., the cooker contains only saturated vapor at the final state).
