MAE 320 HW 7B. 1e. For an isolated system, please circle the parameter which will change with time. (a) Total energy;

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1 MAE 320 HW 7B his comprehensive homework is due Monday, December 5 th, 206. Each problem is worth the points indicated. Copying of the solution from another is not acceptable. Multi-choice, multi-answer question (6 oints) a. For ideal gas, please circle the property parameters which are functions of temperature only? (a) Specific internal energy u (b) Specific entropy s (c) Specific internal energy of ideal gas at ambient pressure: s (d) Relative pressure r (e) Relative specific volume v r b. lease circle the items which are not state properties: (a) otal Internal Energy; (b) Heat ransfer; (c) Boundary work; (d) Entropy; (e) Entropy Generation; c. he transfer of entropy is usually associated with (a) he transfer of mechanical work such as shaft work; (b) he transfer of electrical work; (c) he transfer of heat; (d) he transfer of mass; (f) All above d. lease circle the cases satisfying the conservation of energy. (a) Closed system; (b) Isolated system; (c) Control volume system under steady operation; (d) Control volume under unsteady operation; (e) Any system and any process; o e. For an isolated system, please circle the parameter which will change with time. (a) otal energy;

2 (b) otal mass; (c) otal entropy; (d) Entropy Generation; f. A heat engine cycle features with < 0 operates between a hot reservoir at 000 K and a Heat Engine cool reservoir at 300K. he efficiency of this heat engine? (a) 00%; (b) 70%; (b) >70%; (c) <70%; (d) Cannot be decided with information provided; g. A heat engine cycle features with = 0 operates between two thermal reservoirs. he Heat Engine statement the thermal efficiency of this actual engine is 00% violates: (a) st law; (b) he Kelvin-lank Statement; (c) he Clausius Statement; (c) he Carnot rinciple; (d) he Increase of Entropy rinciple; (e) Cannot be decided with information provided; h. For an actual cycle, please circle the valid equations (a) ds = 0 ; (b) > 0 (c) = 0 ; (d) < 0 ; (e) S gen < 0; (f) S gen > 0 ; (g) S = 0 ; gen 2. Short answer questions (24 oints) 2a. List all statements and principles associated with the 2 nd law of thermodynamics. (2 points) 2b. lease list at least three approaches capable increasing the entropy of a closed system. (3 points) 2

3 k k 2c. For ideal gas, please drive equation = C using isentropic process equation: v k = C. (3 points) 2d. he quality of energy is evaluated by the maximum percentage potential of such an energy to be converted to mechanical work. It is evident that the quality of energy is not affected by the quantity of energy. lease list the following energy in the order of high quality to low one. (4 points): (a) 000 kj electrical energy; (b) 5000 kj of thermal energy from hot reservoir at 600K; (c) 00 kj of thermal energy at 000 K; (d) million kj of thermal energy at 300 K. If you need the temperature of the cool reservoir for the estimation of the maximum potential for thermal energy to mechanical energy conversion, you can assume the temperature of cool reservoir is 300 K. 2e Find specific entropy of water at the following conditions and have them presented in the attached -S diagram in next page: (6 points) (a) (b) (c) = 0bar, = 400 C ; = 600 C, h = 3600kJ / kg ; = 40bar, x = f. Water enters an adiabatic turbine at 00 bar and 700 C (state ) and then exit at 00 ka and 250 C (state 2). lease mark state and 2, 2s in the -s diagram attached in next page and find the isentropic efficiency of this turbine. (6 oints) 3

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5 (3) A piston cylinder system initially contains 0 kg air at 40 bar and 800 K (state ). After an isentropic expansion process V k = C, the temperature drops to 600 K (state 2). lease determine: (2 oints) (a) Find the average specific heat under constant volume and average specific heat ratio; (b) Find the boundary work boundary work and heat transfer during this expansion process; (c) he change in the total entropy of air from state and state 2; (d) he pressure of air at state 2 using equation k (e) he pressure of air at state 2 using equation equations identical?); k = C. You assume k=.358. s2 s = s s R ln o or 2 = r 2 r (are these two (4). A rigid tank initially contains 5 kg air at 200 ka and 27 o C (state ). he air is gradually heated to 527 o C using thermal energy from hot reservoir at 000 K (state 2). he blander installed in this tank consumed 400 kj of mechanical work in maintaining the homogeneous temperature of the air within this tank. During this process, a heat loss of 600 kj from this tank to ambient air occurs at boundary temperature 27 C. lease determine (2 points) (a) he pressure of air at state 2; (b) he change in total entropy of air during this process; (c) he entropy generation; (d) Based on your answer to (c), is this process reversible, irreversible or impossible? (5) R34a enters an insulated throttling valve of an industry cooling unit as saturated liquid at 8 bar and exits at 80 ka. he mass flow rate of this R-34a is 0 kg/s. lease find (2 points) (a) he possible lowest temperature of refrigeration room for this industry cooling unit to work properly? (b) he rate of entropy generation in this throttling valve. (6). A steadily operated, insulated steam turbine is designed to produce 2626 kw of power. Water enters this turbine at 6 Ma, 600 o C (state ) and leaves at 0 ka (state 2). he mass flow rate of water is 2 kg/s. You can ignore the changes in the kinetic and the potential energy, please determine (2 points) (a) he specific enthalpy, quality and specific entropy of water at exit (actual case); (b) he rate of entropy generation within the turbine; (c) he isentropic efficiency of the turbine; (d) resent both the actual and isentropic processes in the -s diagram attached in next page and have the initial state (), the actual final state (2a), and the ideal final state (2s) clearly marked. (e) Draw a schematic h-s diagram with both actual and the isentropic processes presented. 5

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7 (7) A piston cylinder system initially contains 0 kg of saturated liquid water at 200 ka. he water was slowly heated under constant pressure until all of the liquid water was vaporized and became saturated vapor. During this process, the heat loss from the piston-cylinder system to ambient air is 5000 kj, which occurs at its boundary with ambient air at 300 K. lease determine (2 oints): a) he amount of heat transferred into the system during this process; b) he total entropy generated if the heat needed to heat this system was provided by a hot reservoir with a temperature of 600 K; c) he total entropy generated if the heat was provided by a resister heater with the consumption of electricity; d) Explain why more entropy was generated when the heat was provided by a resister heater? ractice Questions. he solutions to these questions will be posted with other questions. You are encouraged to solve these questions although your answers to these two questions will not be graded. () A resister heater installed in a hot water tank is used to steadily heat water from 0 C to 60 C at a mass flow rate of 2 kg/min. he heat loss from water tank to ambient air is 20 kw, which occurs at boundary temperature of 7 C. You can assume the operation pressure is 00 ka, and ignore the changes in both kinetic energy and potential energy. he specific enthalpy of compressed liquid water can be calculated using equation h p, = h lease find the power of the resister heater and rate of entropy generation in this hot water tank. (2) A well insulated compressor operated under steady state. he CO 2 enters this compressor at 00 ka and 25 o C with a mass flow rate of 0 kg/s and exits at 5 bar and 450 K. he rate of heat loss from compressor to ambient air is 30 kw occurring at 300 K. he changes in kinetic and potential energy can be neglected. lease determine (a) he actual work input of this compressor; (b) he rate of entropy generation in this compressor; (c) Based on your answer to (b), is this compression process internally reversible, irreversible or impossible; (d) he exit temperature of CO 2 if compressed to 5 bar following an isentropic process; (e) he isentropic efficiency of this compressor; 7

5/6/ :41 PM. Chapter 6. Using Entropy. Dr. Mohammad Abuhaiba, PE

5/6/ :41 PM. Chapter 6. Using Entropy. Dr. Mohammad Abuhaiba, PE Chapter 6 Using Entropy 1 2 Chapter Objective Means are introduced for analyzing systems from the 2 nd law perspective as they undergo processes that are not necessarily cycles. Objective: introduce entropy