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Thermodynamics Problems and Solutions

## Problem 1: Piston-Cylinder Assembly

Water, initially a saturated liquid at 160°C, is contained in a pistol-cylinder assembly. The water undergoes a process to the corresponding saturated vapor state, during which the piston moves freely in the cylinder. If the change of state is brought about by heating the water as it undergoes an internally reversible process at constant pressure and temperature, determine the work and heat transfer per unit mass in kJ/kg. [MO1]

2.Water initially at 155°C is contained in a piston-cylinder assembly. The water undergoes a process to the corresponding saturated vapor state, during which the piston moves freely in the cylinder. There is no heat transfer with the surroundings. If the change of state is brought about by the action of a paddle wheel, determine the net work per unit mass in kJ/kg and the amount of entropy produced per unit mass in kJ/kg. [MO2]

3.A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 25°C. The exterior air, which is at 9°C, serves as the source. Calculate the rate of entropy change of the two reservoirs and determine if this heat pump satisfies the second law of thermodynamics, according to the increase of entropy principle. [MO7]

4.A rigid tank is divided into two equal parts by a partition. One part of the tank contains 3.0 kg of compressed liquid water at 400 kPa and 50°C, while the other part is evacuated. The partition is now removed and the water expands to fill the entire tank. Determine the entropy change of the water during this process, if the pressure in the tank is 30 kPa. [MO2]

5.Water vapor enters a turbine at 6 MPa and 400°C, and leaves the turbine at 200 kPa with the same specific entropy as that at the inlet. Calculate the difference between the specific enthalpy of the water at the turbine inlet and exit. [MO3, MO5]

6.A 1.00 ft3 well insulated rigid can initially contains refrigerant 134a at 90 psia and 30°F. Now a crack develops in the can and the refrigerant starts to leak out slowly. Assuming the refrigerant remaining in the can has undergone a reversible, adiabatic process, determine the final mass in the can when the pressure drops to 15 psia. [MO1]

7.Steam enters a turbine at a flow rate of 7.5 kg/s at a temperature of 600°C and a pressure of 10 MPa. The steam exits at a pressure of 100 kPa. The isoentropic efficiency of the turbine is 0.80. Determine the power output from the turbine, assuming that it is insulated. [MO3, MO5, MO6]

8.Liquid water enters an adiabatic pump at 20°C and 100 kPa, at a flow rate of 3.5 kg/s. The water exits at 2000 kPa. The isentropic efficiency of the pump is 0.75. Determine the power consumed by the pump. [MO3, MO5, MO6]

9.Refrigerant 134a at p1 = 30 lbf/in2, T1 = 40oF enters a compressor at a steady state with a mass flow rate of 300 lb/h and exits as saturated vapor at p2 = 160 lbf/in2. Heat transfer occurs from the compressor to its surroundings, which are at T0 = 40oF. Changes in kinetic and potential energy can be ignored. The power input to the compressor is 3 hp. Determine the heat transfer rate for the compressor, in Btu/hr, and the entropy production rate for the compressor, in Btu/hr·oR. [MO3, MO7]

10.A stream turbine receives 25 kg/s of steam at 5.0 MPa and 500°C, and the steam exits at 150 kPa. The turbine is adiabatic. Plot the power produced, the entropy generation rate for isentropic efficiencies varying between 0.4 and 1.0. [MO3, MO4, MO5, MO7]