I. (20%) Answer the following True (T) or False (F). If false, explain why for full credit. Both the Kelvin and Fahrenheit scales are absolute temperature scales. Specific volume, v, is an intensive property, whereas volume, V, and mass, m, are extensive properties. A closed system cannot be at steady state. If a system s temperature increases, it must have experienced heat transfer. The energy of an isolated system can only increase. The coefficient of performance of a heat pump must be greater than one. For any cycle, the net amounts of energy transfer by heat and work must be equal in value. A process that is adiabatic must be at constant temperature. The pressures listed in thermodynamic tables are absolute pressures, not gage pressures. As pressure increases toward the critical pressure, the values of hf and hg approach each other. For a substance modeled as an incompressible substance, the specific volume (and density) are taken as constant and the specific internal energy and enthalpy are functions of temperature only. A polytropic process described by pv n = constant must be an ideal gas.
I. (Continued) For an ideal gas, the specific heat cv must be less than the specific heat cp. For a one-inlet, one-exit steady-state control volume, the inlet volumetric flow rate must equal the exit volumetric flow rate. A rigid tank containing air develops a leak, and air flows out. Mass and energy rate balances do not apply to this process. When a flowing stream of matter is normal to the boundary at locations where mass enters or exits a control volume, and if all intensive property values are taken as uniform with position over the respective inlet or exit area, the flow is said to be one dimensional. Entropy is a property that can be assigned a value at any state of a pure substance for which pressure and temperature are known. The maximum theoretical thermal efficiency of any power cycle operating between thermal reservoirs at 100 o C and 500 o C is 80%. The entropy of a control volume can only increase with time. If an ideal gas undergoes a process at constant temperature for which the pressure decreases, the specific entropy must increase.
II. (20%) Five kg of Refrigerant 134a undergoes a polytropic process in a piston-cylinder assembly from 10 bar, 60 o C to a final pressure of 4 bar. The process follows pv 1.154 = constant. Kinetic and potential energy effects can be neglected. Show the process on a properly-labeled T-s diagram, and determine (a) the final volume, in m 3. (b) the work, in kj. (c) the amount of energy transfer by heat, in kj.
III. (25%) Air enters a compressor operating at steady state at 27 o C, 1 bar, with a mass flow rate of 0.16 kg/s and is compressed to 530 K, 12 bar. The compressor power input is 50 kw. Heat transfer occurs at a location on the boundary of the compressor where the temperature is Tb = 400 K. Neglecting kinetic and potential energy effects, and assuming ideal gas behavior for the air, determine (a) the volumetric flow rate at the inlet, in m 3 /s. (b) the rate of heat transfer, in kw. (c) the rate of entropy production for the control volume enclosing the compressor, in kw/k. T1 = 27 o C p2 = 1 bar (1) mሶ 1 = 0.16 kg/s air compressor Qሶ cv Wሶcv = 50 kw (2) T2 = 530 K p2 = 12 bar Tb = 400 K
IV. (35%) A vapor power plant operating at steady state has regeneration as shown on the accompanying sketch. Water is the working fluid. Data at various locations are shown in the table and on the figure below. The total power developed by the turbine stages is 205 MW. State p (bar) T ( o C) h (kj/kg) s (kj/kg K) Comments 1 120 400 3051.3 6.0747 2 10 200 2827.9 6.6940 3 0.04 ηt2 = 78% 4 0.04 121.46 0.4226 Sat. liquid 5 10 122.71 0.4267 6 10 762.81 2.1387 Sat. liquid 7 120 ηp2 = 83% (a) Fill in the missing specific enthalpies in the table, and show the cycle on a T-s diagram. (b) Determine the fraction of the total flow into the first turbine stage that is extracted at 2. (c) Determine the thermal efficiency of the cycle. (d) Determine the rate of entropy production in the open feedwater heater, in kw/k. T s
(1) Turb 1 Turb 2 (2) (3) Steam Generator (7) (6) Open Feedwater Heater (5) Condenser Pump 2 Pump 1 (4)