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physics
thermodynamics

Thermodynamics for Engineers 1st edition Kenneth A. Kroos, Merle C. Potter - Solutions

A valve separates the 10-m3 insulated, evacuated tank of Fig. 4.67 from a pipe line that contains a gas at 2000 kPa and 300°C. The gas in the pipe is held at constant conditions after the valve is opened. Determine the final temperature and mass of the gas in the tank after the tank is
The evacuated tank in Problem 4.68 is not insulated. After a long period of time, the temperature is measured to be 347°C. Determine the heat transfer from the tank if the gas in the pipe line isa) Air,b) Steam,c) Nitrogen.Figure 4.67
The diffuser of Fig. 4.43 decreases the velocity of air from 180 m/s to 20 m/s. Estimate the temperature change of the air in the insulated section.(A) 10°C(B) 16°C(C) 24°C(D) 32°CFigure 4.43
An air line at 100 psi and 70°F is used to fill the 2800-in3 tire of a vehicle that contains air at only 5 psi and 70°F. Assuming negligible heat transfer from the rigid tire during filling, estimate the temperature of the air in the tire when the pressure reaches 35 psi. Also, estimate the added
After a long period of time, the volume of Problem 4.72 a will reach the temperature of the atmosphere. Estimate the final pressure in the volume if the initial pressure wasa) 2 MPa,b) 1200 kPa,c) 800 kPa.Figure 4.68
A 10-ft-diameter insulated spherical balloon contains air at 180 psia and 70°F. A special valve allows the air to leave at a constant rate of 0.4 lbm/s. Calculate the temperature and pressure after a) 8 minutes b) 15 minutes. Estimate the time needed for the temperature to reach - 20°F.
The refrigeration cycle of Fig. 4.70 operates with R134a. It is powered by an input of 30 kW to the compressor. Determine the cooling rate and the COP. The inlet pressure to the compressor isa) 120 kPa,b) 140 kPa,c) 180 kPa.Figure 4.70
Air, with a velocity of 40 m/s, enters a relatively short constant-diameter pipe section at 40°C and 120 kPa and leaves at 200°C with a velocity of 44 m/s. The heat transferred to the air in the 10-cm-diameter pipe is nearest: (A) 242 kJ/s (B) 187 kJ/s (C) 92 kJ/s (D) 67 kJ/s
If the high-temperature reservoir in Problem 5.9 is at 160°C, the low-temperature reservoir for a Carnot heat pump is at: (A) 65 °C (B) 55 °C (C) 45 °C (D) 35 °C
Show that a violation of the Kelvin-Planck statement of the second law implies a violation of the Clausius statement of the second law. This requires an argument similar to that used in Example 5.1.
A telemarketer advertises an emergency electric generator powered by a gasoline engine. The gasoline-powered engine supposedly produces 500 ft-lbf/s of mechanical power while the electric generator produces i) 600 W, ii) 800 W, iii) 1000 W of electric power. Which of these generators are possible?
The heat engine of Fig. 5.24 accepts 30 kJ/s of heat from a high-temperature reservoir and producesa) 10 hp,b) 15 hp,c) 20 hp. Determine the rejected heat and the efficiency of the engine.Figure 5.24
A power plant produces 20 MW of power by burning trash and rejects 14 × 107 kJ each hour from a cooling tower. Calculate the efficiency of the power plant and the amount of heat supplied by the trash burner every hour.
A gas turbine engine is used to propel a ship. It has a thermodynamic efficiency of 0.75. How much heat must be supplied to this engine for it to produce a) 4000 hp, b) 200 000 Btu/min, c) 3 300 000 ft-lbf/s?
An automobile engine produces 200 hp at an efficiency of 28%. What rate of heat transfer is required from the gasoline? How many kilograms of gasoline would be needed per hour if there are 50 MJ/kg of gasoline?
A power plant burns coal to deliver 80 MJ/s of heat to the steam. The plant turbines produce 15 000 hp. What is the rate of heat rejection from this plant, and what is its thermodynamic efficiency?
A heat engine is required to produce a) 120 hp, b) 70,000 ft-lbf/s, c) 100 Btu/s by accepting 500 000 Btu/hr from a heat source. How much heat is dumped to the low-temperature reservoir, and what is the efficiency of the engine?
An automobile engine uses gasoline at a rate of 1 ft3/hr. Gasoline has a density of 45 lbm/ft3 and a heating value of 21 000 Btu/lbm. If the engine has a thermodynamic efficiency of a) 30%, b) 25%, c) 20%, what is the horsepower produced by the engine?
An automobile has a gas mileage of 30 miles/gal when traveling at 60 mph on a flat road with no head wind. Gas contains about 21,000 Btu/lbm with a density of 45 lbm/ft3. Estimate the efficiency of the engine if it produces a) 17 hp, b) 14 hp, c) 12 hp under those conditions.
The engine of an automobile requires 20 hp to travel at 100 km/hr. If the engine's efficiency is 18%, determine the rate of fuel consumption, in L/km, assuming an energy content of 45 MJ/kg and a density of 720 kg/m3.
A power plant burns 50 000 kg of coal each hour. Coal contains about 26 MJ/kg of energy. If the efficiency of the plant is 34%, estimate the heat transfer each day to the nearby river used to receive the rejected energy.
The power plant of Fig. 5.25 providesa) 200 GJ/hr,b) 3000 MJ/min,c) 60 000 kJ/s from the boiler to the steam that flows through the plant. It rejects 120 GJ/hr to the environment, and the pump requires the power indicated. Calculate the horsepower output and the cycle efficiency. Is it necessary to
A refrigerator is advertised that will remove 10 kW from the refrigerator while dumping 15 kW of heat into the kitchen. How much horsepower is the compressor using to run this system?
The refrigeration cycle of Fig. 5.26 is intended to cool a space by supplyinga) 10 kJ/s,b) 15 kJ/s,c) 20 kJ/s of cooling. Determine the rate of heat transfer that is rejected from the condenser and the performance of the cycle.Figure 5.26
The refrigeration cycle of Fig. 5.26, which requires 5 hp by the compressor, as shown, is intended to heat a space. It has a COP of 5 when operating in the heating mode. Determine the rate of heat transfer that is provided to the space being heated and the rate of heat transfer accepted by the
The refrigeration cycle of Fig. 5.26 requires 5 hp by the compressor, as shown, and emits 72,000 Btu/hr by the condenser. Calculate the heat transfer rate to the evaporator and the COP if used as a heater.Figure 5.26
An air conditioner removes 25 000 Btu/min from a room. The compressor of Fig. 5.27 uses 7 hp to run the system. What is the rate of heat rejection to the outside environment? What is the coefficient of performance for this air conditioner?Figure 5.27
Seven thousand kJ/hr of heat is removed from the inside of a refrigerator while transferring 9000 kJ/hr of heat into a kitchen. What is the coefficient of performance of this refrigerator?
An air-conditioning system transfers 100 kJ/s of heat from the condenser. How much horsepower must the compressor supply if the COP is a) 8, b) 6, c) 4?
Show that the working fluid used in a Carnot cycle does not influence the efficiency of the cycle. Use an argument similar to that used in Example 5.5.
A Carnot engine operates between a heat source at 300°C and a heat sink at i) 100°C, ii) 20°C, iii) -30°C. What is the maximum possible efficiency of this engine for each heat sink?
A Carnot heat engine receives 1 MJ/s of heat from a source at 1000°C and rejects 0.4 MJ/s of heat to a sink of unknown temperature. Calculate the temperature of the heat sink and the efficiency of the engine.
An entrepreneur proposes a heat engine that presumably receives 360,000 Btu/hr from a heat source at 300°F and produces 23,000 ft-lbf/s of power while rejecting heat to a heat sink at 100°F. Determine whether or not this engine can possibly work.
The heat engine of Fig. 5.21 operates between the two reservoirs shown, producing 100 kW of power and 50 kJ/s of rejected heat. The engine's efficiency is nearest:(A) 33%(B) 50%(C) 67%(D) 80%Figure 5.21
A heat engine is proposed to operate between the two reservoirs shown in Fig. 5.31. It is proposed to produce 30 hp by transferring 4000 kJ/min from the high-temperature reservoir. Make an engineering analysis of the proposal.Figure 5.31
An engineer at a utility company suggests that a hot spring can provide 450 lbm/min to produce power. The average temperature of the spring is 200°F, and a 55°F stream can be used as a thermal sink. Estimate the maximum power that can be produced.
A Carnot engine undergoes the cycle of Fig. 5.32. The net work output is 200 kJ. Determine the required heat addition and T H if the cycle efficiency isa) 50%,b) 60%,c) 70%. Air is the working fluid.Figure 5.32
An inventor proposes to extract 100°C water from a hot spring and use it to power a heat engine. The atmosphere is at 20°C. The proposed engine would operate with a flow rate of 150 kg/min and produce 50 hp, according to the inventor. Comment as to the feasibility of the proposal using calculated
The Carnot engine of Fig. 5.33 operates with an efficiency of 60% by rejecting energy to a heat sink maintained ata) 30°C,b) 20°C,c) 10°C. If the rejected heat rate is 50 kJ/s, determine the power output, the heat rate from the heat source, and the temperature of the heat source.Figure
Three reservoirs are at temperatures T1, T2, and T3. A Carnot engine is positioned between T1 and T2, a second Carnot engine between T2 and T3, and a third Carnot engine between T1 and T3. Express the efficiency η3 of the third Carnot engine in terms of the efficiencies η1 and η2 of the other
The Carnot refrigeration cycle of Fig. 5.35 operates between two reservoirs maintained at 5°C and 23°C, respectively. If 400 kJ/s is transferred from the low-temperature reservoir, determine the horsepower required by the compressor and the rate of heat transfer to the high-temperature reservoir.
A refrigerator requires 5 hp to provide 24 000 kJ/h of cooling. The COP of the refrigerator is nearest: (A) 1.8 (B) 2.0 (C) 2.4 (D) 2.8
The Carnot refrigeration cycle of Fig. 5.35 is used as a heat pump to supply heat to the high-temperature reservoir. Determine the horsepower required by the compressor and the rate of heat transfer from the low-temperature reservoir if the heat supply rate isa) 200 kJ/s,b) 700 kJ/s,c) 2000
An inventor proposes an engine that utilizes the boiling water of a hot spring and suggests it can operate with an efficiency of 22% in an area where a local stream has an average temperature of 12°C. Such a proposal is: (A) Not possible (B) Very likely possible (C) Possible but improbable (D)
Steam at 500° C and 4 MPa enters a turbine with an isentropic efficiency of 86%. The exit pressure is 100 kPa. The exiting temperature of the steam is nearest: (A) 95° C (B) 107° C (C) 118° C (D) 126° C
Saturated R134a at 120 kPa enters an adiabatic compressor with an efficiency of 80%. The exit pressure is 1.6 MPa, as shown in the T-s diagram of Fig. 6.38. The exiting temperature of the refrigerant from the compressor is nearest:(A) 104° C(B) 99° C(C) 95° C(D) 89° CFigure 6.38
The exergy of the steam at state 1 is nearest:(A) 1340 kJ/kg(B) 17900 kJ/kg(C) 3030 kJ/kg(D) 4400 kJ/kgSteam enters a turbine (see Figures 6.39 and 6.40) at 4 MPa and 500° C and leaves as saturated steam at 40 kPa. Assume standard conditions for the dead state.Figure 6.39Figure 6.40
The second-law efficiency of the turbine is nearest:(A) 68%(B) 72%(C) 78%(D) 82%Steam enters a turbine (see Figures 6.39 and 6.40) at 4 MPa and 500° C and leaves as saturated steam at 40 kPa. Assume standard conditions for the dead state.Figure 6.39Figure 6.40
The isentropic efficiency of the turbine is nearest:(A) 80%(B) 75%(C) 70%(D) 67%Steam enters a turbine (see Figures 6.39 and 6.40) at 4 MPa and 500° C and leaves as saturated steam at 40 kPa. Assume standard conditions for the dead state.Figure 6.39Figure 6.40
The irreversibility of the process is nearest:(A) 529 kJ/kg(B) 389 kJ/kg(C) 319 kJ/kg(D) 229 kJ/kgSteam enters a turbine (see Figures 6.39 and 6.40) at 4 MPa and 500° C and leaves as saturated steam at 40 kPa. Assume standard conditions for the dead state.Figure 6.39Figure 6.40
The T-s diagram of a Carnot refrigeration cycle utilizing R134a is shown in Fig. 6.41. Heat transfer takes place in the condenser and evaporator at constant temperature. Verify the Clausius inequality using x2 = 1 and x3 = 0.Figure 6.41
The T- s diagram of a Carnot steam power cycle is shown in Fig. 6.42. Heat transfer takes place in the boiler and condenser only. Assume an isentropic turbine and pump. Determine the Clausius inequality numerical result for this cycle if x2 = 0 and x3 = 1 and PB isa) 2 MPa,b) 4 MPa,c) 6 MPa.Figure
A piston moves in a cylinder at constant temperature while heat transfer occurs. If the pressure doubles, determine entropy change in the air assuming constant specific heats from Table B-2.
A piston moves in a cylinder at constant pressure while heat is added. If the volume doubles, determine entropy change in the air assuming constant specific heats from Table B-2.
Air at 200° C and 300 kPa is compressed to 400 8 C and 800 kPa. Calculate the change in entropy and the specific volume for this process. Assume constant specific heats from Table B-2.
Nitrogen at 500 psia and 200° F is allowed to expand in an insulated control volume until the temperature is 30° F and the specific volume is increased by 90%. Calculate the change in entropy for this process. What is the final pressure? What work is required? Assume constant specific heats from
Four kilograms of an ideal gas are initially at 25° C and 150 kPa in the rigid container of Fig. 6.43. Heat is added until the pressure reaches 900 kPa. Determine the entropy change of gas if it isa) Air,b) Nitrogen,c) Carbon dioxide,d) Hydrogen. Assume constant specific heats from Table
An ideal gas is initially at 120 kPa and 20° C when contained in a 5-m3 volume. If it experiences an entropy increase of 4 kJ/K as the temperature is raised to 100° C, what is its final volume if the gas is a) Air, b) Nitrogen, c) Carbon dioxide, d) Hydrogen? Assume constant specific heats from
The ideal gasa) Air,b) Nitrogen,c) Carbon dioxide,d) Argon is compressed from 125° C and 100 kPa to 500 kPa in an isentropic process, as displayed in Fig. 6.44. Calculate the final temperature. How much work occurs during this process? Assume constant specific heats from Table B-2.Figure 6.44
The ideal gas a) Air, b) Nitrogen, c) Carbon dioxide, d) Argon is allowed to triple its volume in an isentropic process. If the final temperature is 20° F, what is the initial temperature and what work is produced? Assume constant specific heats from Table B-2E.
Two thousand kilojoules of heat are added to 10 kg of air contained in a rigid container. Calculate the final temperature and the entropy change of the air if the initial temperature and pressure are, respectively, a) 200° C and 200 kPa, b) 100° C and 400 kPa, c) 400° C and 100 kPa. Assume
The frictionless piston/cylinder arrangement of Fig. 6.45 contains 2 kg of nitrogen at 40° C and 200 kPa. If the pressure is held constant, calculate the final temperature and the entropy change if a paddle wheel inserted in the insulated cylinder addsa) 100 kJ of work,b) 200 kJ of work,c) 400
Heat is added to a volume that contains 2 kg of air, initially at 80° C and 200 kPa. Determine the work, the heat transfer, and the entropy change if the temperature is held constant while the volume is expanded to a) 2 m3, b) 3 m3, c) 4 m3. Assume constant specific heats from Table B-2.
Air is compressed in an isentropic process from 20ºC and 100 kPa until the final volume is a) Six times the initial volume, b) Eight times the initial volume, c) Ten times the initial volume,. Calculate the final pressure and temperature assuming constant specific heats from Table B-2.
Assume ideal conditions for each component of the refrigeration cycle of Fig. 6.33 (with T-s diagram in Fig. 6.34) and find ˆ®Î´q/T. R134a is the refrigerant. (Remember, q H is negative and q L is positive.)(A) - 0.062 kJ/kg ˆ™ K(B) - 0.085 kJ/kg ˆ™ K(C) -
Four hundred kilojoules of heat are transferred to 2 kg of air in a piston/cylinder arrangement that is maintained at constant pressure. Calculate the final temperature and the entropy change if the initial temperature is a) 100° C, b) 200° C, c) 400° C. Assume constant specific heats from Table
An electric heater provides 800 kJ of heat to nitrogen in a rigid 2-m3 volume. If the initial temperature is 100° C, determine the entropy increase if the initial pressure is a) 100 kPa, b) 400 kPa, c) 1000 kPa. Assume constant specific heats from Table B-2.
A frictionless piston compresses 0.2 kg of air in the insulated cylinder of Fig. 6.46 from the initial conditions shown. Estimate the final temperature and the work required if the final pressure isa) 800 kPa,b) 1400 kPa,c) 2 MPa. Assume constant specific heats from Table B-2.Figure 6.46
The gases that closely resemble air after combustion in an automobile cylinder are expanded such that the volume increases by a factor of 8. If the initial pressure is 275 psia, estimate the final temperature and the work produced if the initial temperature is a) 800° F, b) 1100° F, c) 1400° F.
A torque of 50 Nˆ™m is required to rotate the paddle wheel shown in Fig. 6.47 at 60 rad/s. If it rotates for 2 minutes during which time 200 kJ of heat is transferred to the air from a reservoir, calculate the final temperature in this rigid volume and the entropy increase in the air.
Two kilograms of air at 40° C and 200 kPa are contained in half of the insulated volume shown in Fig. 6.48. The partition is suddenly ruptured, and the air fills the entire volume. Determine the final pressure and the entropy change for this processFigure 6.48
The engine in Fig. 6.49 delivers 50 kJ by operating between two reservoirs at 900° C and 40° C. Its efficiency is 40%. Determine the entropy change of each reservoirFigure 6.49
A 4-lbm copper slab at 200° F is brought into contact with a 10-lbm aluminum slab at 60 ° F. Insulation allows the two slabs to arrive at the same temperature with no heat transfer to the surroundings. Determine the entropy generated by this process. Assume constant specific heats from Table B-4E.
Two kilograms of ice at -10° C are mixed in the insulated container of Fig. 6.50 with 12 kg of water at 25° C. Estimate the final temperature of the mixture and the net entropy change.Figure 6.50
Twenty kilograms of copper at 80° C are submerged in a container that holds water at 24° C. Two hundred kilojoules of heat is transferred from the water to the 25° C surroundings. Calculate the eventual temperature of the copper, the entropy change of the water plus the copper, and the entropy
Air is heated from 20° C to 800° C at constant pressure of 200 kPa in a cylinder with an initial volume of 4000 cm3. The entropy change, assuming an ideal gas with constant specific heats, is nearest: (A) 0.0123 kJ/K (B) 0.0972 kJ/K (C) 0.563 kJ/K (D) 3.11 kJ/K
Refrigerant 134a undergoes a process from 400 kPa and 400° C to a pressure of a) 400 kPa, b) 800 kPa, c) 1200 kPa in a rigid container. Calculate the heat transfer and the change in specific entropy.
Ten pounds of water at 14.7 psia and 40° F are heated to a) 280 ° F, b) 320° F, c) 500° F in a constant-pressure process. Calculate the change in entropy for this process.
Four kilograms of saturated steam are being condensed at a constant pressure of 120 kPa in the cylinder of Fig. 6.51 by transferring heat to the 25° C surroundings. Calculate the entropy generated by this process ifa) x2 = 0.6,b) x2 = 0.2,c) T2 = 40° C.Figure 6.51
Two kilograms of steam are contained in a 40-L rigid container originally at 120 kPa. If 2 MJ of heat are transferred from a 400° C reservoir, estimate the entropy generated.
Superheated steam is in a 10-ft3 rigid container at 200 psia and 800° F. The container is cooled until the pressure reaches 20 psia. Determine the necessary heat transfer and the entropy change of the universe if the heat is transferred to a 70° F atmosphere.
Steam at 200° C is compressed reversibly in an insulated cylinder from 100 kPa to a) 500 kPa, b) 800 kPa, c) 1200 kPa. Calculate the final temperature and the work requirement.
Determine the work output when 4 kg of steam, contained in a 0.4-m3 cylinder at 600° C and 8000 kPa, are expanded isentropically until the pressure is a) 1200 kPa, b) 800 kPa, c) 400 kPa.
The temperature of 5 kg of water changes from 40° C to 400° C, while the pressure remains constant at 200 kPa. Calculate the required heat transfer and the entropy increase of the universe if the heat comes from a 600° C reservoir.
Air is compressed from 400 K and 100 kPa in an isentropic process. Assuming constant specific heats from Table B-2 and variable specific heats, calculate the final temperature if the final pressure is a) 500 kPa, b) 1000 kPa, c) 2000 kPa.
A piston compresses air in a cylinder from 20 8 C and 100 kPa to 2 MPa. The final temperature, assuming an ideal gas with constant specific heats, is approximately: (A) 690° C (B) 540° C (C) 490° C (D) 420° C
Air is allowed to quadruple its volume in an isentropic process. If the final temperature of the air is 17° C and we assume variable specific heats, what is the initial temperature? What would it be if constant specific heats (from Table B-2) were assumed?
The farmer in Fig. 6.52 inserts nitrogen from a pressurized tank to fertilize a field. An isentropic process can be assumed as the gas leaves the tank. Estimate the temperature of the nitrogen at the point where it enters the soil if the pressure in the tank isa) 8 MPab) 14 MPa. Make any necessary
Rework the following problems assuming variable specific heats: a) Prob. 6.22(a) b) Prob. 6.22(b) c) Prob. 6.23(a) d) Prob. 6.24(a) e) Prob. 6.25(a) f) Prob. 6.26(b) g) Prob. 6.27(a)
R134a enters the valve of Fig. 6.53 at 1.2 MPa and x = 0. It leaves the valve at 120 kPa. Determine the entropy change.Figure 6.53
Ammonia enters a throttle as a saturated liquid at 600 kPa. It exits the throttle to a pressure of 120 kPa. Calculate the exit temperature of the refrigerant and the change in specific entropy for this process. Use the tables.
Refrigerant 134a enters a heat exchanger at 120 psia and a temperature of 160 8 F and leaves at the same pressure with a quality of 0.6. The mass flow rate is 20 lbm/s. What are the heat transfer and rate of change of entropy for the refrigerant?
Water enters a boiler at 6 MPa and 60° C and leaves at 400° C. Calculate the rate of heat transfer if 2000 kg of water pass through the boiler each minute. What is the entropy generated if the heat that stokes the boiler comes from a flame maintained at 2000 8 C?
Steam at 20 kPa and a quality of 0.9 enters the condenser of Fig. 6.54 and leaves as saturated liquid. Calculate the heat transfer and entropy change. If the heat is transferred to a 10° C lake, what entropy is generated due to this process?Figure 6.54
Two kilograms of steam at 6 MPa and 600° C enter an insulated turbine each second. If the losses as the steam moves over the blades in the turbine are neglected, estimate the maximum horsepower output of the turbine if the exit pressure is 20 kPa.
Superheated steam enters an insulated turbine at 20 MPa and 600° C at a mass flow rate of 1000 kg/min. If the steam leaves the turbine at a) 10 kPa, b) 40 kPa, c) 80 kPa as a saturated vapor, what are the power output and the rate of change of entropy of the steam?
Superheated steam flows into an insulated turbine at 4 MPa and 500° C. Calculate the maximum horsepower output if the exit pressure a) P2 = 10 kPa, b) P2 = 60 kPa, c) T2 = 50° C, d) T2 = 80° C. The mass flux is 4000 kg per minute.
Saturated R134a vapor is compressed from 15 psia using an insulated compressor. Determine the minimum horsepower needed to compress 4000 lbm each hour if the compressor outlet pressure is a) 200 psia, b) 300 psia, c) 400 psia. Saturated liquid leaves the condenser.
Saturated ammonia at 120 kPa is compressed to 1200 kPa by the insulated compressor of Fig. 6.55. Neglect any losses and determine the horsepower requirement if 40 kg passes through the compressor each minute. What is the entropy change of the universe due to this compression process if the
Two kilograms per second of superheated steam leave a steam generator and enter a turbine at 6 MPa and 500° C. The turbine produces 2500 hp by expanding the steam to a pressure of 20 kPa with x = 0.9. Calculate the rate of entropy production by the turbine if the surroundings are at 25° C.

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