ME 200 - HOMEWORK #5 – FALL 2014 Due: October 17, 2014 Problem 5.1 A piston-cylinder device contains 12 kg of saturated R-134a vapor at 3.2 bar. An electric source supplies 8 A current to a resistor within the cylinder for 4 minutes and there is heat transfer of 400 kJ to the system. During these energy interactions, the pressure is maintained constant in the cylinder. The refrigerant reaches a final temperature of 700C. Determine (a) The voltage of the source. (b) Show the expansion process for the R-134a on a P-v diagram. Label states, show property values, and indicate appropriate lines of constant pressure. Problem 5.2 An insulated rigid container is separated into two parts using a partition that is free to move and the partition allows heat transfer without any energy storage by itself. Initially 2 kg of air at 5 bar and 350 K is contained on one side of the partition while the other side contains 4 kg of carbon monoxide at 2 bar and 450 K. Heat transfer across the partition occurs and it moves until thermodynamic equilibrium is established inside the container. Consider variable specific heats for air and carbon monoxide. (a) Calculate the equilibrium temperature (K). (b) Find the equilibrium pressure (bar). (c) What is the volume (m3) occupied by each gas at equilibrium? Problem 5.3. A heat pump supplies 40 kW of heat to maintain the inside of a house at 250C in cold winter months when the ambient temperature is 00C. Power required to operate the heat pump cycle is provided by a heat engine cycle which receives 10 kW of heat from a reservoir at 5000C. The heat engine has thermal efficiency of 50%. The heat engine rejects heat to the ambient reservoir at 00C. (a) Calculate the coefficient of performance of the heat pump. (b) Determine the net rate of heat transfer (kW) for the ambient reservoir. Problem 5.4. Consider a 200 MW power plant consisting of an adiabatic steam turbine, a constant pressure condenser, an adiabatic pump, and a constant pressure boiler. Steam enters the turbine at 10 MPa with a specific enthalpy of 3526 kJ/kg (State 1) and expands to a pressure of 0.1 bar and v = 12 m3/kg (State 2). Steam leaving from the turbine rejects heat and saturated liquid water exits the condenser (State 3). Water is pumped back to the boiler pressure using the pump and exits the pump at 10 MPa and 500C (State 4). (a) Complete the following Table State Pressure (bar) Temperature (0C) Specific volume (m3/kg) 1 2 3 4 Specific enthalpy (kJ/kg) Phase Quality Sat. Liquid (b) Calculate the mass flow rate (kg/s) of steam. (c) What is the thermal efficiency (%) of the power plant? (d) Show the cycle on a T-v diagram. Label states, show property values, and indicate appropriate lines of constant pressure. Problem 5.5 A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series, beginning at State 1 where the pressure is 1 bar and the volume is 1.5 m3, as follows: Process 1-2: Compression with pV= constant, W12 = -104 kJ, U1 = 512 kJ, U2 = 690 kJ. Process 2-3: W23 = 0, Q23 = - 150 kJ. Process 3-1: W31 = +50 kJ. Neglecting changes in KE and PE, determine (a) Q12, Q31, and U3 in kJ. (b) Can this cycle be a power cycle? Explain. Problem 5.6 Refrigerant-134a is throttled from saturated liquid state at 7 bar to a pressure of 1.4 bar. Determine the temperature drop during this process and the final specific volume. Problem 5.7 In air-conditioning systems, streams of cold and warm air are mixed to get air with the right temperature. Consider a mixing chamber into which cold air enters at 80C and 100 kPa at a rate of 0.55 m3/s and warm air enters at 300C and 100 kPa. The ratio of mass flow rates of warm to cold air streams is 1.6. Using variable specific heats, determine the mixture temperature leaving the mixing chamber.