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Air is compressed by an adiabatic compressor from 100 kPa and $12^{\circ}\text{C}$ to a pressure of 800 kPa at a steady rate of 0.2 kg/s. If the isentropic efficiency of the compressor is 80 percent, determine (a) the exit temperature of air and (b) the required power input to the compressor.
**SOLUTION** Air is co... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
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Nozzles are essentially adiabatic devices and are used to accelerate a fluid. Therefore, the isentropic process serves as a suitable model for nozzles. The **isentropic efficiency of a nozzle** is defined as *the ratio of the actual kinetic energy of the fluid at the nozzle exit to the kinetic energy value at the exit ... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**Isentropic Efficiency of Nozzles**",
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Air at 200 kPa and 950 K enters an adiabatic nozzle at low velocity and is discharged at a pressure of 110 kPa. If the isentropic efficiency of the nozzle is 92 percent, determine (a) the maximum possible exit velocity, (b) the exit temperature, and (c) the actual exit velocity of the air. Assume constant specific heat... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**EXAMPLE 7–16** Effect of Efficiency on Nozzle Exit Velocity",
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The property *entropy* is a measure of molecular disorder or randomness of a system, and the second law of thermodynamics states that entropy can be created but it cannot be destroyed. Therefore, the entropy change of a system during a process is greater than the entropy transfer by an amount equal to the entropy gener... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "7–13 • ENTROPY BALANCE 🕒",
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Energy and entropy balances for a system.
which is a verbal statement of Eq. 7–9. This relation is often referred to as the **entropy balance** and is applicable to any system undergoing any process. The entropy balance relation above can be stated as: *the entropy change of a system during a process is equal to the ... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**FIGURE 7-56**",
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Heat is, in essence, a form of disorganized energy, and some disorganization (entropy) will flow with heat. Heat transfer to a system increases the entropy of that system and thus the level of molecular disorder or randomness, and heat transfer from a system decreases it. In fact, heat rejection is the only way the ent... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**1 Heat Transfer**",
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Mass contains entropy as well as energy, and thus mass flow into or out of a system is always accompanied by energy and entropy transfer. Therefore, the entropy of a system increases by *ms* when mass in the amount of *m* enters and decreases by the same amount when the same amount of mass at the same state leaves the ... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**FIGURE 7–59**",
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Irreversibilities such as friction, mixing, chemical reactions, heat transfer through a finite temperature difference, unrestrained expansion, nonquasi-equilibrium compression, or expansion always cause the entropy of a system to increase, and entropy generation is a measure of the entropy created by such effects durin... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "Entropy Generation, $S_{qen}$",
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A closed system involves *no mass flow* across its boundaries, and its entropy change is simply the difference between the initial and final entropies of the system. The *entropy change* of a closed system is due to the *entropy transfer* accompanying heat transfer and the *entropy generation* within the system boundar... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**Closed Systems**",
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The entropy balance relations for control volumes differ from those for closed systems in that they involve one more mechanism of entropy exchange: *mass flow across the boundaries*. As mentioned earlier, mass possesses entropy as well as energy, and the amounts of these two extensive properties are proportional to the... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**Control Volumes**",
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Consider steady heat transfer through a $5\text{-m} \times 7\text{-m}$ brick wall of a house of thickness 30 cm. On a day when the temperature of the outdoors is $0^{\circ}$ C, the house is maintained at $27^{\circ}$ C. The temperatures of the inner and outer surfaces of the brick wall are measured to be $20^{\cir... | {
"Header 1": "EXAMPLE 7-15 Effect of Efficiency on Compressor Power Input",
"Header 3": "**■ EXAMPLE 7–17** Entropy Generation in a Wall",
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Steam at 7 MPa and 450°C is throttled in a valve to a pressure of 3 MPa during a steady-flow process. Determine the entropy generated during this process and check if the increase of entropy principle is satisfied.
**SOLUTION** Steam is throttled to a specified pressure. The entropy generated during this process is t... | {
"Header 1": "EXAMPLE 7-18 Entropy Generation During a Throttling Process",
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A 50-kg block of iron casting at 500 K is thrown into a large lake that is at a temperature of 285 K. The iron block eventually reaches thermal equilibrium with the lake water. Assuming an average specific heat of 0.45 kJ/kg·K for the iron, determine (a) the entropy change of the iron block, (b) the entropy change of t... | {
"Header 1": "EXAMPLE 7-19 Entropy Generated when a Hot Block Is Dropped in a Lake",
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Air in a large building is kept warm by heating it with steam in a heat exchanger (Fig. 7–67). Saturated water vapor enters this unit at 35°C at a rate of 10,000 kg/h and leaves as saturated liquid at 32°C. Air at 1-atm pressure enters the unit at 20°C and leaves at 30°C at about the same pressure. Determine the rate o... | {
"Header 1": "EXAMPLE 7-19 Entropy Generated when a Hot Block Is Dropped in a Lake",
"Header 2": "Air 20°C 32°C 2 Steam 1 35°C 10,000 kg/h",
"Header 3": "**EXAMPLE 7–20** Entropy Generation in a Heat Exchanger",
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A frictionless piston–cylinder device contains a saturated liquid–vapor mixture of water at $100^{\circ}$ C. During a constant-pressure process, 600 kJ of heat is transferred to the surrounding air at $25^{\circ}$ C. As a result, part of the water vapor contained in the cylinder condenses. Determine (a) the entropy c... | {
"Header 1": "**EXAMPLE 7–21** Entropy Generation Associated with Heat Transfer",
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In Example 7–21 it is determined that 0.4 kJ/K of entropy is generated during the heat transfer process, but it is not clear where exactly the entropy generation takes place, and how. To pinpoint the location of entropy generation, we need to be more precise about the description of the system, its surroundings, and th... | {
"Header 1": "Entropy Generation Associated with a Heat Transfer Process",
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Graphical representation of entropy generation during a heat transfer process through a finite temperature difference.

**FIGURE 7–70** A large compressor assembly. *Photo courtesy of the Dresser-Rand business, part of Siemens Power & Gas*
Compressed air at gage pressures of 550 to 10... | {
"Header 1": "Entropy Generation Associated with a Heat Transfer Process",
"Header 3": "**FIGURE 7–69**",
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Air leaks are the greatest single cause of energy loss from compressed-air systems in manufacturing facilities. It takes energy to compress the air, and thus the loss of compressed air is a loss of energy for the facility. A compressor must work harder and longer to make up for the lost air and must use more energy in ... | {
"Header 1": "Entropy Generation Associated with a Heat Transfer Process",
"Header 3": "**1 Repairing Air Leaks on Compressed-Air Lines**",
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The energy wasted as compressed air escapes through the leaks is equivalent to the energy it takes to compress it.
compressed-air lines at these points, the gaskets wear out quickly, and they need to be replaced periodically.
There are many ways of detecting air leaks in a compressed-air system. Perhaps the simples... | {
"Header 1": "Entropy Generation Associated with a Heat Transfer Process",
"Header 3": "**FIGURE 7-73**",
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The compressors of a production facility maintain the compressed-air lines at a (gauge) pressure of 700 kPa at sea level where the atmospheric pressure is 101 kPa (Fig. 7–74). The average temperature of air is 20°C at the compressor inlet and 24°C in the compressed-air lines. The facility operates 4200 hours a year, an... | {
"Header 1": "**EXAMPLE 7–22** Energy and Cost Savings by Fixing Air Leaks",
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Practically all compressors are powered by electric motors, and the *electrical* energy a motor draws for a specified power output is *inversely proportional* to its efficiency. Electric motors cannot convert the electrical energy they consume into mechanical energy completely, and the ratio of the mechanical power sup... | {
"Header 1": "**EXAMPLE 7–22** Energy and Cost Savings by Fixing Air Leaks",
"Header 3": "2 Installing High-Efficiency Motors",
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We tend to purchase *larger equipment* than needed for reasons like having a safety margin or anticipated future expansion, and compressors are no exception. The uncertainties in plant operation are partly responsible for opting for a larger compressor, since it is better to have an oversized compressor than
. The plant is currently paying \$12,000 a year in electricity cost... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
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The second law of thermodynamics leads to the definition of a new property called *entropy*, which is a quantitative measure of microscopic disorder for a system. Any quantity whose cyclic integral is zero is a property, and entropy is defined as
$$dS = \left(\frac{dQ}{T}\right)_{\text{int rev}}$$
For the special c... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**SUMMARY**",
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Any process: $s_2 - s_1 = c_{\text{avg}} \ln \frac{T_2}{T_1}$ Isentropic process: $T_2 = T_1$
3. Ideal gases:
a. Constant specific heats (approximate treatment):
Any process:
$$\begin{split} s_2 - s_1 &= c_{v,\text{avg}} \ln \frac{T_2}{T_1} + R \ln \frac{v_2}{v_1} \\ s_2 - s_1 &= c_{p,\text{avg}} \ln \frac{T... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "2. Incompressible substances:",
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- **1.** A. Bejan. *Advanced Engineering Thermodynamics*. 3rd ed. New York: Wiley Interscience, 2006.
- **2.** A. Bejan. *Entropy Generation through Heat and Fluid Flow*. New York: Wiley Interscience, 1982.
- Y. A. Çengel and H. Kimmel. "Optimization of Expansion in Natural Gas Liquefaction Processes." LNG Journal, U.K... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**REFERENCES AND SUGGESTED READINGS**",
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- **7–1C** Does a cycle for which $\oint \delta Q > 0$ violate the Clausius inequality? Why?
- **7–2C** Does the cyclic integral of heat have to be zero (i.e., does a system have to reject as much heat as it receives to complete a cycle)? Explain.
- **7–3C** Is a quantity whose cyclic integral is zero necessarily a p... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Entropy and the Increase of Entropy Principle**",
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- **7–29C** Is a process that is internally reversible and adiabatic necessarily isentropic? Explain.
- **7–30E** One lbm of R-134a is expanded isentropically in a closed system from 100 psia and 100°F to 10 psia. Determine the total heat transfer and work production for this process.
- **7–31E** Two lbm of water at 30... | {
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"Header 3": "**Entropy Changes of Pure Substances**",
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**7–36** An insulated piston–cylinder device contains 0.05 m3 of saturated refrigerant- 134a vapor at 0.8-MPa pressure. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.4 MPa. Determine (*a*) the final temperature in the cylinder and (*b*) the work done by the refrigerant. ... | {
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"Header 3": "**FIGURE P7–35**",
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- **7–52** Water at 10°C and 81.4 percent quality is compressed isentropically in a closed system to 3 MPa. How much work does this process require in kJ/kg?
- **7–53** Twokg of saturated water vapor at 600 kPa are contained in a piston–cylinder device. The water expands adiabatically until the pressure is 100 kPa and ... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–51**",
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**7–61C** Consider two solid blocks, one hot and the other cold, brought into contact in an adiabatic container. After a while, thermal equilibrium is established in the container as a result of heat transfer. The first law requires that the amount of energy lost by the hot solid be equal to the amount of energy gained... | {
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"Header 3": "**Entropy Change of Incompressible Substances**",
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- **7–69C** What are *Pr* and *vr* called? Is their use limited to isentropic processes? Explain.
- **7–70C** Some properties of ideal gases such as internal energy and enthalpy vary with temperature only [that is, *u* = *u*(*T*) and *h* = *h*(*T*)]. Is this also the case for entropy?
- **7–71C** Can the entropy of an ... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Entropy Change of Ideal Gases**",
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- **7–91** Five kg of air at 427°C and 600 kPa are contained in a piston–cylinder device. The air expands adiabatically until the pressure is 100 kPa and produces 600 kJ of work output. Assume air has constant specific heats evaluated at 300 K.
- (*a*) Determine the entropy change of the air in kJ/kg·K.
- (*b*) Since t... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–90**",
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- **7–93** Oxygen at 300 kPa and 90°C flowing at an average velocity of 3 m/s is expanded in an adiabatic nozzle. What is the maximum velocity of the oxygen at the outlet of this nozzle when the outlet pressure is 120 kPa? Answer: 390 m/s
- **7–94** Air at 800 kPa and 400°C enters a steady-flow nozzle with a low veloci... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–92**",
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**7–98C** In large compressors, the gas is often cooled while being compressed to reduce the power consumed by the compressor. Explain how cooling the gas during a compression process reduces the power consumption.
**7–99C** The turbines in steam power plants operate essentially under adiabatic conditions. A plant en... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Reversible Steady-Flow Work**",
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**7–103E** Air is compressed isothermally from 13 psia and 55°F to 80 psia in a reversible steady-flow device. Calculate the work required, in Btu/lbm, for this compression. Answer: 64.2 Btu/lbm
**7–104** Saturated water vapor at 150°C is compressed in a reversible steady-flow device to 1000 kPa while its specific vo... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–102E**",
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... |
**7–113C** Describe the ideal process for an (*a*) adiabatic turbine, (*b*) adiabatic compressor, and (*c*) adiabatic nozzle, and define the isentropic efficiency for each device.
**7–114C** Is the isentropic process a suitable model for compressors that are cooled intentionally? Explain.
**7–115C** On a *T-s* diag... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Isentropic Efficiencies of Steady-Flow Devices**",
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**7–123** Reconsider Prob. 7–122. Using appropriate software, redo the problem by including the effects of the kinetic energy of the flow by assuming an inletto-exit area ratio of 1.5 for the compressor when the compressor exit pipe inside diameter is 2 cm.
**7–124** The adiabatic compressor of a refrigeration system... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–122**",
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**7–135E** A frictionless piston–cylinder device contains saturated liquid water at 40-psia pressure. Now 600 Btu of heat is transferred to water from a source at 1000°F, and part of the liquid vaporizes at constant pressure. Determine the total entropy generated during this process, in Btu/R.
**7–136** Air enters a ... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–134E**",
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... |
**7–138** In an ice-making plant, water at 0°C is frozen at atmospheric pressure by evaporating saturated R-134a liquid at –16°C. The refrigerant leaves this evaporator as a saturated vapor, and the plant is sized to produce ice at 0°C at a rate of 5500 kg/h. Determine the rate of entropy generation in this plant. Answ... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–137**",
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**7–142** Air $(c_p = 1.005 \text{ kJ/kg} \cdot ^{\circ}\text{C})$ is to be preheated by hot exhaust gases in a crossflow heat exchanger before it enters the furnace. Air enters the heat exchanger at 95 kPa and 20°C at a rate of 1.6 m³/s. The combustion gases $(c_p = 1.10 \text{ kJ/kg} \cdot ^{\circ}\text{C})$ ente... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7-141**",
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**7–144** Steam is to be condensed in the condenser of a steam power plant at a temperature of 60°C with cooling water from a nearby lake, which enters the tubes of the condenser at 18°C at a rate of 75 kg/s and leaves at 27°C. Assuming the condenser to be perfectly insulated, determine (*a*) the rate of condensation o... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7-143**",
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... |
**7–157** The compressed-air requirements of a plant at sea level are being met by a 90-hp compressor that takes in air at the local atmospheric pressure of 101.3 kPa and the average temperature of 15°C and compresses it to 1100 kPa. An investigation of the compressed-air system and the equipment using the compressed a... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Special Topic: Reducing the Cost of Compressed Air**",
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**7–167** A proposed heat pump design creates a heating effect of 25 kW while using 5 kW of electrical power. The thermal energy reservoirs are at 300 K and 260 K. Is this possible according to the increase of entropy principle?
**7–168** A refrigerator with a coefficient of performance of 4 transfers heat from a col... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Review Problems**",
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**7–181** Air at 500 kPa and 400 K enters an adiabatic nozzle at a velocity of 30 m/s and leaves at 300 kPa and 350 K. Using variable specific heats, determine (*a*) the isentropic efficiency, (*b*) the exit velocity, and (*c*) the entropy generation.

**FIGURE P7–181**
**7–182E** Hel... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–180**",
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**7–185** Helium gas is throttled steadily from 400 kPa and 60°C. Heat is lost from the helium in the amount of 1.75 kJ/ kg to the surroundings at 25°C and 100 kPa. If the entropy of the helium increases by 0.34 kJ/kg·K in the valve, determine (*a*) the exit temperature and pressure and (*b*) the entropy generation dur... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–184**",
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**7–187** Carbon dioxide is compressed in a reversible, isothermal process from 100 kPa and 20°C to 400 kPa using a steadyflow device with one inlet and one outlet. Determine the work required and the heat transfer, both in kJ/kg, for this compression.
**7–188** Reconsider Prob. 7–187. Determine the change in the wor... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–186**",
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- **7–191** Three kg of helium gas at 100 kPa and 27°C are adiabatically compressed to 900 kPa. If the isentropic compression efficiency is 80 percent, determine the required work input and the final temperature of helium.
- **7–192** Steam at 6 MPa and 500°C enters a two-stage adiabatic turbine at a rate of 15 kg/s. T... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–190**",
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... |
**7–199E** An engineer has proposed that compressed air be used to "level the load' in an electrical-generation and distribution system. The proposed system is illustrated in Fig. P7–199E. During those times when electrical-generation capacity exceeds the demand for electrical energy, the excess electrical energy is us... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–198E**",
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... |
**7–200E** Reconsider Prob. 7–199E. The filled compressed-air storage tank is discharged at a later time through the turbine until the pressure in the tank is 1 atm. During this discharge, the temperature of the air in the storage tank remains constant at 70°F. Calculate the total work produced by the turbine and the t... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7–199E**",
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Using air properties for the exhaust gases, determine (*a*) the air temperature at the compressor exit and (*b*) the isentropic efficiency of the compressor. Answers: (a) 126°C, (b) 64.2 percent

**FIGURE P7–214**
**7–215** Consider a 50-L evacuated rigid bottle that is surrounded by ... | {
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"Header 3": "**FIGURE P7–199E**",
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... |
**7–222** Consider a three-stage isentropic compressor with two intercoolers that cool the gas to the initial temperature between the stages. Determine the two intermediate pressures $(P_x \text{ and } P_y)$ in terms of inlet and exit pressures $(P_1 \text{ and } P_2)$ that will minimize the work input to the compr... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**FIGURE P7-221**",
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7–227 Steam is condensed at a constant temperature of 30°C as it flows through the condensor of a power plant by rejecting heat at a rate of 55 MW. The rate of entropy change of steam as it flows through the condenser is
(a) -1.83 MW/K (b) -0.18 MW/K (c) 0 MW/K (d) 0.56 MW/K (e) 1.22 MW/K
**7–228** Steam is compres... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "Fundamentals of Engineering (FE) Exam Problems",
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If the water temperature rises by 0.2°C during flow due to friction, the rate of entropy generation in the pipe is
(a) 23 W/K (b) 55 W/K (c) 68 W/K (d) 220 W/K (e) 443 W/K
**7–243** Liquid water is to be compressed by a pump whose isentropic efficiency is 85 percent from 0.2 MPa to 5 MPa at a rate of 0.15 m³/min. T... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "Fundamentals of Engineering (FE) Exam Problems",
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**7–247** Compressors powered by natural gas engines are increasing in popularity. Several major manufacturing facilities have already replaced the electric motors that drive their compressors with gas-driven engines in order to reduce their energy bills since the cost of natural gas is much lower than the cost of elec... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**Design and Essay Problems**",
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he increased awareness that the world's energy resources are limited has caused many countries to reexamine their energy policies and take drastic measures in eliminating waste. It has also sparked interest in the scientific community to take a closer look at the energy conversion devices and to develop new techniques ... | {
"Header 1": "**EXAMPLE 7–23** Reducing the Pressure Setting to Reduce Cost",
"Header 3": "**EXERGY**",
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When a new energy source, such as a geothermal well, is discovered, the first thing the explorers do is estimate the amount of energy contained in the source. This information alone, however, is of little value in deciding whether to build a power plant on that site. What we really need to know is the *work potential* ... | {
"Header 1": "Air $25^{\\circ}$ C 101 kPa V = 0 z = 0 $T_0 = 25^{\\circ}$ C $P_0 = 101 \\text{ kPa}$",
"Header 3": "8-1 • EXERGY: WORK POTENTIAL OF ENERGY",
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Kinetic energy is a form of *mechanical energy,* and thus it can be converted to work entirely. Therefore, the *work potential* or *exergy* of the kinetic energy of a system is equal to the kinetic energy itself regardless of the temperature and pressure of the environment. That is,
Exergy of kinetic energy:
$$x_{ke}... | {
"Header 1": "Air $25^{\\circ}$ C 101 kPa V = 0 z = 0 $T_0 = 25^{\\circ}$ C $P_0 = 101 \\text{ kPa}$",
"Header 3": "**Exergy (Work Potential) Associated with Kinetic and Potential Energy**",
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A wind turbine with a 12-m-diameter rotor, as shown in Fig. 8–5, is to be installed at a location where the wind is blowing steadily at an average velocity of 10 m/s. Determine the maximum power that can be generated by the wind turbine.
**SOLUTION** A wind turbine is being considered for a specified location. The ma... | {
"Header 1": "Air $25^{\\circ}$ C 101 kPa V = 0 z = 0 $T_0 = 25^{\\circ}$ C $P_0 = 101 \\text{ kPa}$",
"Header 2": "EXAMPLE 8-1 Maximum Power Generation by a Wind Turbine",
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Consider a large furnace that can transfer heat at a temperature of 2000 R at a steady rate of 3000 Btu/s. Determine the rate of exergy flow associated with this heat transfer. Assume an environment temperature of 77°F.
**SOLUTION** Heat is being supplied by a large furnace at a specified temperature. The rate of exe... | {
"Header 1": "Air $25^{\\circ}$ C 101 kPa V = 0 z = 0 $T_0 = 25^{\\circ}$ C $P_0 = 101 \\text{ kPa}$",
"Header 2": "EXAMPLE 8-1 Maximum Power Generation by a Wind Turbine",
"Header 3": "**■ EXAMPLE 8-2** Exergy Transfer from a Furnace",
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The difference between reversible work and actual useful work is the irreversibility.
In this section, we describe two quantities that are related to the actual initial and final states of processes and serve as valuable tools in the thermodynamic analysis of components or systems. These two quantities are the *rever... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 3": "**FIGURE 8–9**",
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A heat engine receives heat from a source at 1200 K at a rate of 500 kJ/s and rejects the waste heat to a medium at 300 K (Fig. 8-10). The power output of the heat engine is 180 kW. Determine the reversible power and the irreversibility rate for this process.
**SOLUTION** The operation of a heat engine is considered.... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 3": "■ EXAMPLE 8-3 The Rate of Irreversibility of a Heat Engine",
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A 500-kg iron block shown in Fig. 8–11 is initially at 200°C and is allowed to cool to 27°C by transferring heat to the surrounding air at 27°C. Determine the reversible work and the irreversibility for this process.
**SOLUTION** A hot iron block is allowed to cool in air. The reversible work and irreversibility asso... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
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An irreversible heat transfer process can be made reversible by the use of a reversible heat engine. It probably came as a surprise to you that we are asking to find the "reversible work" for a process that does not involve any work interactions. Well, even if no attempt is made to produce work during this process, the... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "FIGURE 8-12",
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The iron block discussed in Example 8–4 is to be used to maintain a house at 27°C when the outdoor temperature is 5°C. Determine the maximum amount of heat that can be supplied to the house as the iron cools to 27°C.
**SOLUTION** The iron block is now reconsidered for heating a house. The maximum amount of heating th... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "**EXAMPLE 8-5** Heating Potential of a Hot Iron Block",
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In Chap. 6 we defined the *thermal efficiency* and the *coefficient of performance* for devices as a measure of their performance. They are defined on the basis of the first law only, and they are sometimes referred to as the *first-law efficiencies*. The first-law efficiency, however, makes no reference to the best po... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "8-3 • SECOND-LAW EFFICIENCY",
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A dealer advertises that he has just received a shipment of electric resistance heaters for residential buildings that have an efficiency of 100 percent (Fig. 8–18). Assuming an indoor temperature of 21°C and outdoor temperature of 10°C, determine the second-law efficiency of these heaters.
**SOLUTION** Electric resi... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "**EXAMPLE 8–6** Second-Law Efficiency of Resistance Heaters",
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The property *exergy* is the work potential of a system in a specified environment and represents the maximum amount of useful work that can be obtained as the system is brought to equilibrium with the environment. Unlike energy, the value of exergy depends on the state of the environment as well as the state of the sy... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "**8-4** • EXERGY CHANGE OF A SYSTEM",
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The *exergy* of a specified mass at a specified state is the useful work that can be produced as the mass undergoes a reversible process to the state of the environment.
To answer that question, we need to consider a stationary closed system at a specified state that undergoes a *reversible* process to the state of t... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "**FIGURE 8-19**",
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In Chap. 5 it was shown that a flowing fluid has an additional form of energy, called the *flow energy*, which is the energy needed to maintain flow in a pipe or duct, and this was expressed as $w_{\text{flow}} = P U$ where U is the specific volume of the fluid, which is equivalent to the *volume change* of a unit ma... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "**Exergy of a Flow Stream: Flow (or Stream) Exergy**",
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A 200-m<sup>3</sup> rigid tank contains compressed air at 1 MPa and 300 K. Determine how much work can be obtained from this air if the environment conditions are 100 kPa and 300 K.
**SOLUTION** Compressed air stored in a large tank is considered. The work potential of this air is to be determined.
**Assumptions** ... | {
"Header 1": "8-2 • REVERSIBLE WORK AND IRREVERSIBILITY",
"Header 2": "EXAMPLE 8-4 Irreversibility During the Cooling of an Iron Block",
"Header 3": "**EXAMPLE 8-7** Work Potential of Compressed Air in a Tank",
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Refrigerant-134a is to be compressed from 0.14 MPa and -10°C to 0.8 MPa and 50°C steadily by a compressor. Taking the environment conditions to be 20°C and 95 kPa, determine the exergy change of the refrigerant during this process and the minimum work input that needs to be supplied to the compressor per unit mass of t... | {
"Header 1": "**EXAMPLE 8–8** Exergy Change During a Compression Process",
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Recall from Chap. 6 that the work potential of the energy transferred from a heat source at temperature T is the maximum work that can be obtained from that energy in an environment at temperature $T_0$ and is equivalent to the work produced by a Carnot heat engine operating between the source and the environment. Th... | {
"Header 1": "8-5 • EXERGY TRANSFER BY HEAT, WORK, AND MASS",
"Header 3": "**Exergy Transfer by Heat, Q**",
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There is no useful work transfer associated with boundary work when the pressure of the system is maintained constant at atmospheric pressure.
medium eventually becomes zero when its temperature reaches $T_0$ . Equation 8–24 can also be viewed as the *exergy associated with thermal energy Q* at temperature T.
When... | {
"Header 1": "8-5 • EXERGY TRANSFER BY HEAT, WORK, AND MASS",
"Header 3": "**FIGURE 8-27**",
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Exergy is the useful work potential, and the exergy transfer by work can simply be expressed as
Exergy transfer by work:
$$X_{\text{work}} = \begin{cases} W - W_{\text{surr}} & \text{(for boundary work)} \\ W & \text{(for other forms of work)} \end{cases}$$
(8–26)
where $W_{\rm surr} = P_0(V_2 - V_1)$ , $P_0$ is... | {
"Header 1": "8-5 • EXERGY TRANSFER BY HEAT, WORK, AND MASS",
"Header 3": "**Exergy Transfer by Work, W**",
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Mass contains *exergy* as well as energy and entropy, and the exergy, energy, and entropy contents of a system are proportional to mass. Also, the rates of exergy, entropy, and energy transport into or out of a system are proportional to
the mass flow rate. Mass flow is a mechanism to transport exergy, entropy, and e... | {
"Header 1": "8-5 • EXERGY TRANSFER BY HEAT, WORK, AND MASS",
"Header 3": "Exergy Transfer by Mass, m",
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In Chap. 2 we presented the *conservation of energy principle* and indicated that energy cannot be created or destroyed during a process. In Chap. 7 we established the *increase of entropy principle*, which can be regarded as one of the statements of the second law, and we indicated that entropy can be created but cann... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
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The isolated system considered in the development of the decrease of exergy principle.
since $V_2 = V_1$ for an isolated system (it cannot involve any moving boundary and thus any boundary work). Combining Eqs. 8–29 and 8–30 gives
$$-T_0 S_{\text{gen}} = X_2 - X_1 \le 0 {(8-31)}$$
since $T_0$ is the thermodyn... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**FIGURE 8-29**",
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Irreversibilities such as friction, mixing, chemical reactions, heat transfer through a finite temperature difference, unrestrained expansion, nonquasi-equilibrium compression or expansion always *generate entropy*, and anything that generates entropy always *destroys exergy*. The **exergy destroyed** is proportional t... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**Exergy Destruction**",
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The nature of exergy is opposite to that of entropy in that exergy can be *destroyed*, but it cannot be created. Therefore, the *exergy change* of a system during a process is less than the *exergy transfer* by an amount equal to the *exergy destroyed* during the process within the system boundaries. Then the *decrease... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "8-7 • EXERGY BALANCE: CLOSED SYSTEMS",
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Exergy destroyed outside system boundaries can be accounted for by writing an exergy balance on the extended system that includes the system and its immediate surroundings. A *closed system* does not involve any mass flow and thus any exergy transfer associated with mass flow. Taking the positive direction of heat tran... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "FIGURE 8-33",
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Starting with energy and entropy balances, derive the general exergy balance relation for a closed system (Eq. 8–41).
**SOLUTION** Starting with energy and entropy balance relations, a general relation for exergy balance for a closed system is to be obtained.
**Analysis** We consider a general closed system (a fixe... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**EXAMPLE 8-9** General Exergy Balance for Closed Systems",
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Consider steady heat transfer through a $5\text{-m} \times 6\text{-m}$ brick wall of a house of thickness 30 cm. On a day when the temperature of the outdoors is 0°C, the house is maintained at 27°C. The temperatures of the inner and outer surfaces of the brick wall are measured to be 20°C and 5°C, respectively, and ... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**EXAMPLE 8–10** Exergy Destruction During Heat Conduction",
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A piston–cylinder device contains 0.05 kg of steam at 1 MPa and 300°C. Steam now expands to a final state of 200 kPa and 150°C, doing work. Heat losses from the system to the surroundings are estimated to be 2 kJ during this process. Assuming the surroundings to be at $T_0 = 25$ °C and $P_0 = 100$ kPa, determine (a)... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**EXAMPLE 8–11** Exergy Destruction During Expansion of Steam",
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The useful work is the difference between the two:
$$\begin{split} W_u &= W - W_{\text{surr}} = W_{b,\text{out}} - P_0(V_2 - V_1) = W_{b,\text{out}} - P_0 m (\text{U}_2 - \text{U}_1) \\ &= 8.8 \text{ kJ} - (100 \text{ kPa})(0.05 \text{ kg})[\,(0.9599 - 0.25799) \text{ m}^3/\text{kg}] \bigg( \frac{1 \text{ kJ}}{1 \tex... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**EXAMPLE 8–11** Exergy Destruction During Expansion of Steam",
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An insulated rigid tank contains 2 lbm of air at 20 psia and 70°F. A paddle wheel inside the tank is now rotated by an external power source until the temperature in the tank rises to 130°F (Fig. 8–37). If the surrounding air is at $T_0 = 70$ °F, determine (a) the exergy destroyed and (b) the reversible work for this ... | {
"Header 1": "8-6 • THE DECREASE OF EXERGY PRINCIPLE AND EXERGY DESTRUCTION",
"Header 3": "**EXAMPLE 8–12** Exergy Destroyed During Stirring of a Gas",
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A 50-L electrical radiator containing heating oil is placed in a well-sealed 75-m<sup>3</sup> room (Fig. 8-39). Both the air in the room and the oil in the radiator are initially at the environment temperature of 6°C. Electricity with a rating of 2.4 kW is now turned on. Heat is also lost from the room at an average ra... | {
"Header 1": "EXAMPLE 8-13 Exergy Analysis of Heating a Room with a Radiator",
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That is,
$$\begin{split} \Delta X_a &= m [c_0 (T_2 - T_1)] - T_0 \Delta S_a \\ &= (94.88 \text{ kg}) [(0.718 \text{ kJ/kg} \cdot ^\circ \text{C})(20 - 6)^\circ \text{C}] - (6 + 273 \text{ K})(3.335 \text{ kJ/K}) \\ &= 23.16 \text{ kJ} \\ \Delta X_{\text{oil}} &= m [c(T_2 - T_1)] - T_0 \Delta S_{\text{oil}} \\ &= (47.... | {
"Header 1": "EXAMPLE 8-13 Exergy Analysis of Heating a Room with a Radiator",
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} |
Two constant-volume tanks, each filled with 30 kg of air, have temperatures of 900 K and 300 K (Fig. 8–40). A heat engine placed between the two tanks extracts heat from the high-temperature tank, produces work, and rejects heat to the low-temperature tank. Determine the maximum work that can be produced by the heat en... | {
"Header 1": "EXAMPLE 8-14 Work Potential of Heat Transfer Between Two Tanks",
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The exergy balance relations for control volumes differ from those for closed systems in that they involve one more mechanism of exergy transfer: *mass flow across the boundaries*. As mentioned earlier, mass possesses exergy as well as energy and entropy, and the amounts of these three extensive properties are proporti... | {
"Header 1": "8-8 • EXERGY BALANCE: CONTROL VOLUMES",
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Most control volumes encountered in practice such as turbines, compressors, nozzles, diffusers, heat exchangers, pipes, and ducts operate steadily, and thus they experience no changes in their mass, energy, entropy, and exergy contents as well as their volumes. Therefore, $dV_{\rm CV}/dt = 0$ and $dX_{\rm CV}/dt = 0... | {
"Header 1": "8-8 • EXERGY BALANCE: CONTROL VOLUMES",
"Header 3": "**Exergy Balance for Steady-Flow Systems**",
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... |
The exergy transfer to a steady-flow system is equal to the exergy transfer from it plus the exergy destruction within the system.
For example, the reversible power for a single-stream steady-flow device is, from Eq. 8–48,
Single-stream:
$$\dot{W}_{\text{rev}} = \dot{m}(\psi_1 - \psi_2) + \sum \left(1 - \frac{T_0}{... | {
"Header 1": "8-8 • EXERGY BALANCE: CONTROL VOLUMES",
"Header 3": "**FIGURE 8-42**",
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} |
The second-law efficiency of various steady-flow devices can be determined from its general definition, $\eta_{\rm II}$ = (Exergy recovered)/(Exergy expended). When the changes in kinetic and potential energies are negligible, the second-law efficiency of an *adiabatic turbine* can be determined from
$$\eta_{\text{... | {
"Header 1": "8-8 • EXERGY BALANCE: CONTROL VOLUMES",
"Header 3": "**Second-Law Efficiency of Steady-Flow Devices**",
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A heat exchanger with two unmixed fluid streams.
where $T_b$ is the temperature of the system boundary through which the lost heat crosses at a rate of $\dot{Q}_{\rm loss}$ . Also, $\dot{S}_{\rm gen} = \dot{m}_{\rm hot}(s_2 - s_1) + \dot{m}_{\rm cold}(s_4 - s_3) + \dot{Q}_{\rm loss}/T_b$ in this case.
Although... | {
"Header 1": "8-8 • EXERGY BALANCE: CONTROL VOLUMES",
"Header 3": "**FIGURE 8-43**",
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Steam enters a turbine steadily at 3 MPa and 450°C at a rate of 8 kg/s and exits at 0.2 MPa and 150°C (Fig. 8–44). The steam is losing heat to the surrounding air at 100 kPa and 25°C at a rate of 300 kW, and the kinetic and potential energy changes are negligible. Determine (a) the actual power output, (b) the maximum ... | {
"Header 1": "8-8 • EXERGY BALANCE: CONTROL VOLUMES",
"Header 3": "**■ EXAMPLE 8-15** Second-Law Analysis of a Steam Turbine",
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Water at 20 psia and 50°F enters a mixing chamber at a rate of 300 lbm/min, where it is mixed steadily with steam entering at 20 psia and 240°F. The mixture leaves the chamber at 20 psia and 130°F, and heat is being lost to the surrounding air at $T_0 = 70$ °F at a rate of 180 Btu/min (Fig. 8–45). Neglecting the chang... | {
"Header 1": "**EXAMPLE 8–16** Exergy Destroyed During Mixing of Fluid Streams",
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} |
A 200-m<sup>3</sup> rigid tank initially contains atmospheric air at 100 kPa and 300 K and is to be used as a storage vessel for compressed air at 1 MPa and 300 K (Fig. 8–46). Compressed air is to be supplied by a compressor that takes in atmospheric air at $P_0 = 100 \text{ kPa}$ and $T_0 = 300 \text{ K}$ . Determi... | {
"Header 1": "**EXAMPLE 8–16** Exergy Destroyed During Mixing of Fluid Streams",
"Header 3": "**EXAMPLE 8-17** Charging a Compressed Air Storage System",
"token_count": 1396,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-p... |
Thermodynamics is a fundamental natural science that deals with various aspects of energy, and even nontechnical people have a basic understanding of energy and the first law of thermodynamics since there is hardly any aspect of life that does not involve the transfer or transformation of energy in different forms. All... | {
"Header 1": "**EXAMPLE 8–16** Exergy Destroyed During Mixing of Fluid Streams",
"Header 3": "**Second-Law Aspects of Daily Life**",
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"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01... |
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