Eng3901 - Problem Sets 1

1 Problem Set 1

1. (2-31 Moran & Shapiro, 6e) Warm air is contained in a piston-cylinder assembly oriented horizontallyas shown. The air cools slowly from an initial volume of 0:003m3 to a �nal volume of 0:002m3. Duringthe process, the spring exerts a force that varies linearly from an initial value of 900N to a �nal value ofzero. The atmospheric pressure is 100 kPa, and the are of the piston face is 0:018m2. Friction betweenthe piston and the cylinder wall can be neglected. For the air, determine the initial and �nal presures,in kPa, and the work, in kJ. (p1 = 150 kPa, p2 = 100 kPa, W12 = �0:125 kJ)

2. (2-33 Moran & Shapiro, 6e) Carbon monoxide gas (CO) contained within a piston-cylinder assemblyundergoes three processes in series:

� Process 1-2: Expansion from p1 = 5bar, V1 = 0:2m3, to V2 = 1m3, during which the pressure-volume relationship is pV = c, where c is a constant.

� Process 2-3: Constant-volume heating from state 2 to state 3, where p3 = 5bar.

� Process 3-1: Constant-pressure compression to the initial state.

Sketch the processes in series on p-V co-ordinates and evaluate the work for each process, in kJ.(W12 = 160:9 kJ, W23 = �400 kJ, W31 = 0kJ)

3. (2-66 Moran & Shapiro, 6e) Steam in a piston-cylinder assembly undergoes a polytropic process withn = 2, from an initial state where p1 = 500 lbf= in2, v1 = 1:701 ft

3= lb, u1 = 1363:3Btu= lb to a �nal statewhere u2 = 990:58Btu= lb. During the process, there is a heat transfer from the steam of 342:9Btu.The mass of steam is 1:2 lb. Neglecting changes in kinetic and potential energies, determine the work,in Btu, and the �nal speci�c volume, in ft3= lb. (W12 = 104:4Btu, v2 = 3:8 ft

3= lb)

4. (2-68 Moran & Shapiro, 6e) Air is contained in a vertical piston-cylinder assembly by a piston of mass50 kg and having a face area of 0:01m2. The mass of the air is 5 g, and initially the air occupies avolume of 5 l. The atmosphere exerts a pressure of 100 kPa on the top of the piston. The volume ofthe air slowly decreases to 0:002m3 as the speci�c internal energy of the air decreases by 260 kJ= kg.Neglecting friction between the piston and the cylinder wall, determine the heat transfer to the air, inkJ. (Q12 = �1:747 kJ)

5. (2-76 Moran & Shapiro, 6e) A gas within a piston-cylinder assembly undergoes a thermodynamic cycleconsisting of three processes:

� Process 1-2: Constant volume, V = 0:028m3, U2 � U1 = 26:4 kJ.� Process 2-3: Expansion with pV = const, U3 = U2.� Process 3-1: Constant pressure, p = 1:4 bar, W31 = �10:5 kJ.

There are no signi�cant changes in kinetic or potential energies.

(a) Sketch the cycle on a p-V diagram.

Eng3901 - Problem Sets 2

(b) Calculate the net work for the cycle, in kJ. (Wnet = 8:28 kJ)

(c) Calculate the heat transfer for process 2-3, in kJ. (Q23 = 18:78 kJ)

(d) Calculate the heat transfer for process 3-1, in kJ. (Q31 = �36:9 kJ)(e) Is this a power cycle or a refrigeration cycle? (Power)

2 Problem Set 2

1. (3-6 Moran & Shapiro, 6e) Determine the phase or phases in a system consisting of H2O at the followingconditions and sketch p-v and T -v diagrams showing the location of each state.

(a) p = 5bar, T = 151:9 �C. (Saturated liquid, or saturated vapour, or saturated liquid and vapour)

(b) p = 5bar, T = 200 �C. (Superheated vapour)

(c) p = 2:5MPa, T = 200 �C. (Compressed liquid)

(d) p = 4:8 bar, T = 160 �C. (Superheated vapour)

(e) p = 1bar, T = �12 �C. (Ice)

2. (3-24 Moran & Shapiro, 6e) Water is contained in a closed, rigid, 0:2m3 tank at an initial pressureof 5 bar and a quality of 50%. Heat transfer occurs until the tank contains only saturated vapour.Determine the �nal mass of vapour in the tank, in kg, and the �nal pressure, in bar. (m = 1:064 kg,p = 10:51 bar)

3. (3-28 Moran & Shapiro, 6e) Water vapour is heated in a closed rigid tank from saturated vapour at160 �C to a �nal temperature of 400 �C. Determine the initial and �nal pressures, in bar, and sketchthe process on T -v and p-v diagrams. (p1 = 6:178 bar, p2 = 9:99 bar)

4. (3-34 Moran & Shapiro, 6e) Ammonia in a piston-cylinder assembly undergoes a constant-pressureprocess at 2:5 bar from T1 = 30

�C to saturated vapour. Determine the work for the process, in kJ= kgof refrigerant. (w12 = �23:84 kJ= kg)

5. (3-38 Moran & Shapiro, 3e) Determine the speci�ed property data for H2O at the states indicated andlocate each state on carefully labelled p-v and T -v diagrams.

(a) At p = 1:5 bar, T = 280 �C, �nd v in m3= kg and u in kJ= kg. (v = 1:695m3= kg, u = 2778:6 kJ= kg)

(b) At p = 1:5 bar, v = 0:9m3= kg, �nd T in �C and u in kJ= kg. (T = 111:4 �C, u = 2059:9 kJ= kg)

(c) At p = 12bar, T = 400 �C, �nd v in m3= kg and h in kJ= kg. (v = 0:2652m3= kg,h = 3260:7 kJ= kg)

(d) At T = 320 �C, v = 0:3 m3= kg, �nd p in MPa and u in kJ= kg. (p = 0:9177MPa, u =2827:5 kJ= kg)

(e) At p = 32MPa, T = 400 �C, �nd v in m3= kg and h in kJ= kg. (v = 0:00236m3= kg, h =2055:9 kJ= kg)

(f) At T = 200 �C, x = 80%, �nd p in bar and v in m3= kg. (p = 15:54 bar, v = 0:1022m3= kg)

(g) At T = �10 �C, v = 1:0891 � 10�3m3= kg, �nd p in kPa and h in kJ= kg. (p = 0:2602 kPa,h = �354:09 kJ= kg)

(h) At p = 2:5MPa, T = 140 �C, �nd v in m3= kg and u in kJ= kg. (v = 1:0784 � 10�3m3= kg,u = 587:82 kJ= kg)

6. (3-51 Moran & Shapiro, 6e) Propane within a piston-cylinder assembly undergoes a constant-pressureprocess from saturated vapour at 400 kPa to a temperature of 40 �C. Kinetic and potential energye¤ects are negligible. For the propane:

(a) Show the process on a p-v diagram;

(b) Evaluate the work, in kJ= kg; and (w12 = 10:2 kJ= kg)

(c) Evaluate the heat transfer, in kJ= kg. (q12 = 80:3 kJ= kg)

Eng3901 - Problem Sets 3

3 Problem Set 3

1. (3-70 Moran & Shapiro, 6e) A two-phase mixture of H2O, initially at x = 30% and a pressure of100 kPa, is contained in a piston-cylinder assembly, as shown. The mass of the piston is 10 kg, and itsdiameter is 15 cm. The pressure of the surroundings is 100 kPa. As the water is heated, the pressureinside the cylinder remains constant until the piston hits the stops. Heat transfer to the water continuesat constant volume until the pressure is 150 kPa. Friction between the piston and the cylinder wall,and kinetic and potential energy e¤ects are negligible. For the overall process of the water, determinethe work and heat transfer, in kJ. (W13 = 0:106 kJ, Q13 = 1:43 kJ)

2. (3-81 Moran & Shapiro, 6e) A piston-cylinder assembly contains ammonia, initially at 0:8 bar and�10 �C. The ammonia is compressed to a pressure of 5:5 bar. During the process, the pressure andspeci�c volume are related by pv = const. For 20 kg of ammonia, determine the work and heat transfer,each in kJ. (W13 = �4884:3 kJ, Q13 = �4877:1 kJ)

3. (3-119 Moran & Shapiro, 6e) As shown below, a piston-cylinder assembly whose piston is resting on aset of stops contains 0:5 kg of helium gas, initially at 100 kPa and 25 �C. The mass of the piston and thee¤ect of the atmospheric pressure acting on the piston are such that a pressure of 500 kPa is required toraise it. How much energy must be transferred by heat to the helium, in kJ, before the piston startsrising? Assume ideal gas behaviour for the helium. (Q12 = 1857:1 kJ)

4. (3-124 Moran & Shapiro, 6e) Two kilograms of air, initially at 5 bar, 350K and 4 kg of carbon monoxide(CO) initially at 2 bar, 450K are con�ned to opposite sides of a rigid, well-insulated container by a

Eng3901 - Problem Sets 4

partition, as shown. The partition is free to move and allows conduction from one gas to the otherwithout energy storage in the partition itself. The air and CO each behave as ideal gases with constantspeci�c heat ratio, k = 1:395. Determine at equilibrium: (a) the temperature, in K; (b) the pressure,in bar; and (c) the volume occupied by each gas, in m3. (T = 417:4K, p = 239:2 bar, VAir = 1:002m3,VCO = 2:073m

3)

5. (3-135 Moran & Shapiro, 6e) A piston-cylinder assembly contains air modelled as an ideal gas with aconstant speci�c heat ratio, k = 1:4. The air undergoes a power cycle consisting of four processes inseries:

� Process 1-2: Constant-temperature expansion at 600K from p1 = 0:5MPa to p2 = 0:4MPa.

� Process 2-3: Polytropic expansion with n = k to p3 = 0:3MPa.� Process 3-4: Constant-pressure compression to V4 = V1.� Process 4-1: Constant-volume heating.

Sketch the cycle on a p-v diagram. Determine the work and heat transfer for each process, in kJ= kg,and the thermal e¢ ciency of the cycle. (w12 = 38:38 kJ= kg, w23 = 34:0 kJ= kg, w34 = �55:2 kJ= kg,w41 = 0kJ= kg, q12 = 38:38 kJ= kg, q23 = �0:54 kJ= kg, q34 = �193:27 kJ= kg, q41 = 172:61 kJ= kg,�th = 0:081)

4 Problem Set 4

1. (4-49 Moran & Shapiro, 6e) The intake to a hydraulic turbine installed in a �ood control dam is locatedat an elevation of 10m above the turbine exit. Water enters at 20 �C with negligible velocity andexits from the turbine at 10m= s. The water passes through the turbine with no signi�cant changes intemperature or pressure between the inlet and exit, and heat transfer is negligible. The acceleration ofgravity is constant at g = 9:81m= s2. If the power output at steady state is 500 kW, what is the mass�ow rate of the water, in kg= s? ( _m = 10; 395 kg= s)

2. (4-63 Moran & Shapiro, 6e) Air enters a water-jacketed air compressor operating at steady state witha volumetric �ow rate of 37m3=min at 136 kPa, 305K and exits with a pressure of 680 kPa and atemperature of 400K. The power input to the compressor is 155 kW. Energy transfer by heat fromthe compressed air to the cooling water circulating in the water jacket results in an increase in thetemperature of the cooling water from inlet to exit with no change in pressure. Heat transfer from theoutside of the jacket as well as all kinetic and potential energy e¤ects can be neglected. Determinethe temperature increase of the cooling water, in K, if the cooling water mass �ow rate is 82 kg=min.(�T = 11:1K)

3. (4-78 Moran & Shapiro, 6e) As shown below, a condenser using river water to condense steam with a mass�ow rate of 2� 105 kg=h from saturated vapour to saturated liquid at a pressure of 0:1 bar is proposedfor an inductrial plant. Measurements indicate that several hundred meters upstream of the plant, theriver has a volumetric �ow rate of 2� 105m3=h and a temperature of 15 �C. For operation at steadystate and ignoring changes in kinetic and potential energies, determine the river-water temperature rise,in �C, downstream of the plant traceable to use of such a condenser, and comment. (�T = 0:573 �C)

Eng3901 - Problem Sets 5

4. (4-95 Moran & Shapiro, 6e) The �gure below provides steady-state data for a throttling valve in serieswith a heat exchanger. Saturated liquid refrigerant 134a enters the valve at T1 = 36 �C with a mass�ow rate of 0:26 kg= s and is throttled to T2 = �8 �C. The refrigerant then enters the heat exchanger,exiting as saturated vapour with no signi�cant decrease in pressure. In a separate stream, liquid waterenters the heat exchnager at T4 = 20 �C and exits as a liquid at T5 = 10 �C. Stray heat transfer andkinetic and potential energy e¤ects can be ignored. Determine: (a) the pressure at state 2, in kPa; and(b) The mass �ow rate of the liquid water stream. (p2 = 217:04 kPa, _m4 = 0:882 kg= s)

5. (4-105 Moran & Shapiro, 6e) separate streams of steam and air �ow through the turbine and heatexchanger arrangement shown below. Steady-state operating data are provided on the �gure. Heattransfer with the surroundings can be neglected, as can all kinetic and potential energy e¤ects. Deter-mine: (a) T3, in �C; and (b) the power output of the second turbine, _Wt2, in kW. (T3 = 849:3 �C,_Wt2 = 16; 190 kW)

Eng3901 - Problem Sets 6

5 Problem Set 5

1. A two-stage turbine with a moisture separator is used in a steam powerplant. Water enters the HPturbine at state 1 (p1 = 4MPa, T1 = 300 �C, _m1 = 40 kg= s). The water exits the the HP turbine atstate 2 (p2 = 500 kPa, x2 = 0:95). The moisture separator is a well-insulated device used to removethe liquid water from the steam that will enter the LP turbine. The process in the moisture separatoroccurs at a constant pressure. Saturated liquid exits the moisture separator at state 3 and saturatedvapour enters the LP turbine at state 4. Water exits the LP turbine at state 5 (p5 = 10 kPa, x5 = 0:9).State all assumptions when answering the following questions.

(a) What is the mass �ow rate of the steam entering the LP turbine? ( _m4 = 38 kg= s)

(b) What is the total power output of the two-stage turbine? ( _W = 27:9MW)

2. Two well-insulated air compressors and a mixing chamber are shown below. Air enters the LP compressorat state 1 ( _m1 = 5kg= s, p1 = 100 kPa, T1 = 300K). The LP compressor requires a power input of572:45 kW. The air exits the LP compressor at state 2 (p2 = 500 kPa) and enters an adiabatic mixingchamber where it mixes with a second air stream at state 3 ( _m3 = 2kg= s, p3 = 500 kPa, T3 = 300K)in a constant pressure process. The mixed air stream then exits the mixing chamber at state 4 andenters the HP compressor. The air exits the HP compressor at 2MPa. Assume the processes in bothcompressors are polytropic, with the same exponent n. Use the air properties given below, and state allassumptions when answering the following questions.

(a) What is the polytropic exponent n for the processes in the compressors? (n = 1:25)

Eng3901 - Problem Sets 7

(b) What is the required power input to the HP compressor? (��� _WHP

��� = 857:6 kW)Air properties: cp = 1:005 kJ= kg � K, R = 0:287 kJ= kg � K

3. A simple steam power plant consists of a boiler, turbine condenser and pump. Steam enters the turbineat state 1 ( _m1 = 109 kg= s, p1 = 100 bar, T1 = 520 �C) and exits at state 2 (p2 = 0:08 bar, x2 = 0:9). Itthen eneters the condenser and exits at state 3 (p3 = 0:08 bar, saturated liquid). The pressure of thewater is increased in a pump to state 4 (p4 = 100 bar, T4 = 43 �C) and then enters the boiler. The liquidcooling water enters the turbine at state i , Ti = 20 �C, and exits at state e, Te = 35 �C. Determine:(a) the thermal e¢ ciency, �th; and (b) the mass �ow rate of the cooling water through the condenser,_mi, in kg= s. See the �gure on the solutions page. (�th = 0:332, _mi = 3758:7 kg= s)

4. A simple steam power plant consists of a boiler, a turbine, a condenser, an open feedwater heater, andtwo pumps as shown below. The steam enters the turbine at state 1 ( _m1 = 10 kg= s, p1 = 3MPa,T1 = 400 �C). Some of the steam is bled from the turbine at state 2 (p2 = 500 kPa, T2 = 180 �C) tobe used in the open feedwater heater. The remaining steam exits the turbine at state 3 (p3 = 10 kPa,x3 = 0:95) and enters the condenser. The water exits the condenser at state 4 (p4 = 10 kPa), ispressurized by the low pressure pump, and enters the open feedwater heater at state 5 (p5 = 500 kPa,T5 = 36

�C). The preheated water exits the feedwater heater at state 6 (p6 = 500 kPa), is pressurized tostate 7 (p7 = 3MPa) in the high pressure pump and enters the boiler. Heat is rejected by the steam atthe rate of j _QC j = 19:215MW in the condenser. The power requirements of the low and high pressurepumps are j _WLP j = 5kW and j _WHP j = 30 kW, respectively. Determine the thermal e¢ ciency of thepower plant. (�th = 0:268)

Eng3901 - Problem Sets 8

6 Problem Set 6

1. (4-106 Moran & Shapiro, 6e (modi�ed)) A tiny hole develops in the wall of a rigid tank of volume 0:5m3,and air from the surroundings at 1 bar, 21 �C leaks in. Eventually, the pressure in the tank reaches1 bar. The process occurs slowly enough that heat transfer between the tank and the surroundingskeeps the temperature of the air inside the tank constant at 21 �C. Determine the amount of heattransfer, in kJ, if initially the tank:

(a) is evacuated; or (Q12 = �50 kJ)(b) contains air at 0:4 bar and 21 �C. (Q12 = �30 kJ)

2. (4-110 Moran & Shapiro, 6e) The rigid tank shown below has a volume of 0:06m3 and initially containsa two-phase liquid-vapour mixture of H2O at a pressure of 15 bar and a quality of 20%. As the tankcontents are heated, a pressure-regulating valve keeps the pressure constant in the tank by allowingsaturated vapour to escape. Neglecting kinetic and potential energy e¤ects, determine the total massof H2O left in the tank, in kg, and the amount of heat transfer, in kJ, if heating continues until the�nal quality is x = 0:5. (m2 = 0:903 kg, Q12 = 2546:5 kJ)

Eng3901 - Problem Sets 9

3. (4-118 Moran & Shapiro, 6e) A well-insulated tank contains 25 kg of refrigerant R-134a, initially at300 kPa with a quality of 0.8. The pressure is maintained by N2 gas acting against a �exible bladder, asshown. The valve is opened between the tank and a supply line carrying R-134a at 1MPa and 120 �C.The pressure regulator allows the pressure in the tank to remain at 300 kPa as the bladder expands.The valve between the supply line and the tank is closed at the instant when all the liquid has vaporized.Determine the amount of refrigerant admitted to the tank, in kg. (mi = 9:03 kg)

4. (4-119 Moran & Shapiro, 6e) A well-insulated piston-cylinder assembly is connected by a valve to anair supply line at 8 bar and 300K, as shown. Initially, the air inside the cylinder is at 1 bar, 300K, andthe piston is located 0:5m above the bottom of the cylinder. The atmospheric pressure is 1 bar, and thediameter of the piston face is 0:3m. The valve is opened and air is admitted slowly until the volume ofthe air inside the cylinder has doubled. The weight of the piston and the friction between the pistonand cylinder wall can be ignored. Determine the �nal temperature, in K, and the �nal mass, in kg, ofthe air inside the cylinder. Try this problem assuming constant speci�c heats and table A-22 for airproperties. (T2 = 300K, m2 = 0:0821 kg using Table A-22)

Eng3901 - Problem Sets 10

7 Problem Set 7

1. (5-18 Moran & Shapiro, 6e) A power cycle receives energy QH by heat transfer from a hot reservoirat TH = 1500 �R and rejects energy QC to a cold reservoir at TC = 500 �R. For each of the followingcases, determine whether the cycle operates reversibly, operates irreversibly, or is impossible.

(a) QH = 900Btu, Wcycle = 450Btu (Irreversible)

(b) QH = 900Btu, QC = �300Btu (Reversible)(c) QC = �400Btu, Wcycle = 600Btu (Irreversible)

(d) �th = 0:7 (Impossible)

2. (5-37 Moran & Shapiro, 6e) A power cycle operating at steady state receives energy by heat transfer fromthe combustion of fuel at an average temperature of 1000K. Owing to environmental considerations,the cycle discharges energy by heat transfer to the atmosphere at 300K at a rate no greater than 60MW.Based on the cost of fuel, the cost to supply the heat transfer is $4.50/GW. The power developed bythe cycle is valued at $0.08/ kW � h. For 8000 hours of operation annually, determine:

(a) the maximum value of the power generated; and

(b) the minimum fuel cost. (Note: I used the new math in my solution where 1 � 0:3 = 0:67, so mynumbers are wrong, but the method is OK.)

3. (5-39 Moran & Shapiro, 6e) At steady state, a power cycle receives energy by heat transfer at an averagetemperature of 865 �F and discharges energy by heat transfer to a river. Upstream of the power plantthe river has volumetric �ow rate of 2512 ft3= s and a temperature of 68 �F. From environmentalconsiderations, the temperature of the river downstream of the the plant can be no more than 72 �F.Determine the maximum theoretical power that can be developed, in MW, subject to this constraint.( _Wmax = 990MW)

4. (5-43 Moran & Shapiro, 6e) A refrigeration cycle operating between two reservoirs receives energy QCfrom a cold reservoir at TC = 280K and rejects energy QH to a hot reservoir at TH = 320K. Foreach of the following cases, determine whether the cycle operates reversibly, operates irreversibly, or isimpossible.

(a) QC = 1500 kJ, Wcycle = �150 kJ (Impossible)(b) QC = 1400 kJ, QH = �1600 kJ (Reversible)(c) QH = �1600 kJ, Wcycle = �400 kJ (Irreversible)(d) � = 5 (Irreversible)

5. (5-56 Moran & Shapiro, 6e) For each kW of power input to an ice maker at steady state, determine themaximum rate that ice can be produced, in kg=h, from liquid water at 0 �C. Assume that 333 kJ= kgof energy must be removed by heat transfer to freeze water at 0 �C, and that the surroundings are at20 �C. ( _mice = 147:6 kg=h)

6. (5-66 Moran & Shapiro, 6e) A heat pump with a coe¢ cient of performance of 3.8 provides energy atan average rate of 75; 000 kJ=h to maintain a building at 21 �C on a day when the outside temperatureis 0 �C. If electricity costs 8 cents per kW � h:

(a) determine the actual operating cost and the minimum theoretical cost, each in $/day; and($10.53/day, $5.11/day)

(b) compare the results of part (a) with the cost of electrical-resistance heating. ($40/day)

Eng3901 - Problem Sets 11

8 Problem Set 8

1. (6-52 Moran & Shapiro, 6e) Two kilograms of refrigerant R-134a initially at 1:4 bar, 60 �C are com-pressed to saturated vapour at 60 �C. During this process, the temperature of the refrigerant departs byno more than 0:01 �C from 60 �C. Determine the minimum theoretical heat transfer from the refrigerantduring the process, in kJ.

2. (6-59 Moran & Shapiro, 6e) An electric motor operating at steady state draws a current of 10A witha voltage of 220V. The ouptut shaft rotates at 1000 rpm with a torque of 16N � m applied to anexternal load. The rate of the heat transfer from the motor to its surroundings is related to the surfacetemperature, Tb, and the ambient air temperature, To, by hA (Tb � To), where h = 100W=m2 � �C,A = 0:195m2, and To = 293K.

(a) Determine the temperature Tb, in K.

(b) For the motor as the system, determine the rate of entropy production, in kW=K.

(c) If the system boundary is located to take in enough of the nearby surroundings for heat transfer totake place at temperature To, determine the rate of entropy production, in kW=K, for the enlargedsystem.

3. (6-118 Moran & Shapiro, 4e) Air enters a compressor at steady state at 100 kPa, 20 �C with volumetric�ow rate of 9m3=min and exits at 500 kPa, 160 �C. Cooling water is circulated through a water jacketenclosing the compressor at a rate of 8:6 kg=min, entering at 17 �C and exiting at 25 �C with a negligiblechange in pressure. There is no signi�cant heat transfer from the outer surface of the water jacket, andall kinetic and potential energy e¤ects are negligible. For the water jacketed compressor as a controlvolume, determine the power required, and the rate of entropy production.

4. (6-98 Moran & Shapiro, 6e) The �gure below shows the steady-state test data for a well-insulatedcontrol volume in which two entering streams of air mix to form a single exiting stream. A hard-to-readphotocopy of the data sheet indicates that the pressure of the exiting stream is either 1:0 or 1:8MPa.Assuming the ideal gas model for air, with cp = 1:02 kJ= kg � K, determine if either or both of thesepressure values can be correct.

5. (6-146 Moran & Shapiro, 6e) As shown below, a steam turbine with an isentropic e¢ ciency of 90%drives an air compressor having an isentropic compressor e¢ ciency of 85%. Steady-state operating dataare provided in the �gure. Assume the ideal gas model for air.

(a) Determine the mass �ow rate of the steam entering the turbine, in kg of steam per kg of air exitingthe compressor.

(b) Repeat part (a) if �t = �c = 100%.

Eng3901 - Problem Sets 12