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A heat-engine cycle cannot be completed without rejecting some heat to a low-temperature sink.
medium to a low-temperature one, and never the other way around. Therefore, we cannot cool this gas from 90 to 30°C by transferring heat to a reservoir at 100°C. Instead, we have to bring the system into contact with a low-... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**FIGURE 6–15**",
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Heat is transferred to a heat engine from a furnace at a rate of 80 MW. If the rate of waste heat rejection to a nearby river is 50 MW, determine the net power output and the thermal efficiency for this heat engine.
**SOLUTION** The rates of heat transfer to and from a heat engine are given. The net power output and ... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**EXAMPLE 6-1** Net Power Production of a Heat Engine",
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A car engine with a power output of 65 hp has a thermal efficiency of 24 percent. Determine the fuel consumption rate of this car if the fuel has a heating value of 19,000 Btu/lbm (that is, 19,000 Btu of energy is released for each lbm of fuel burned).
**SOLUTION** The power output and the efficiency of a car engine ... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**EXAMPLE 6-2** Fuel Consumption Rate of a Car",
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We demonstrated earlier with reference to the heat engine shown in Fig. 6–15 that, even under ideal conditions, a heat engine must reject some heat to a low-temperature reservoir in order to complete the cycle. That is, no heat engine can convert all the heat it receives to useful work. This limitation on the thermal e... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
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The objective of a refrigerator is to remove *QL* from the cooled space.
Refrigerators, like heat engines, are cyclic devices. The working fluid used in the refrigeration cycle is called a **refrigerant**. The most frequently used refrigeration cycle is the *vapor-compression refrigeration cycle,* which involves four... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
"Header 3": "**FIGURE 6–20**",
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The *efficiency* of a refrigerator is expressed in terms of the **coefficient of performance** (COP), denoted by COPR. The objective of a refrigerator is to remove heat (*QL*) from the refrigerated space. To accomplish this objective, it requires a work input of $W_{\text{net,in}}$ . Then the COP of a refrigerator can... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
"Header 3": "**Coefficient of Performance**",
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Another device that transfers heat from a low-temperature medium to a high-temperature one is the **heat pump**, shown schematically in Fig. 6–21. Refrigerators and heat pumps operate on the same cycle but differ in their objectives.
The objective of a refrigerator is to maintain the refrigerated space at a low tempe... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
"Header 3": "**Heat Pumps**",
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The work supplied to a heat pump is used to extract energy from the cold outdoors and carry it into the warm indoors.
for fixed values of *QL* and *QH*. This relation implies that the coefficient of performance of a heat pump is always greater than unity since COPR is a positive quantity. That is, a heat pump will fu... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
"Header 3": "**FIGURE 6-22**",
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The performance of air conditioners and heat pumps is often expressed in terms of the **energy efficiency ratio** (EER) or **seasonal energy efficiency ratio** (SEER) determined by following certain testing standards. SEER is the ratio of the total amount of heat removed by an air conditioner or heat pump during a norm... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
"Header 3": "**Performance of Refrigerators, Air Conditioners, and Heat Pumps**",
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A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate of 60 kJ/min (Fig. 6-23). Determine (*a*) the electric power consumed by the refrigerator and (*b*) the rate of heat transfer to the kitchen air.
**SOLUTION** The COP and the refrigeration rate of a refrigerator are given. T... | {
"Header 1": "The Second Law of Thermodynamics: Kelvin-Planck Statement",
"Header 3": "**EXAMPLE 6-3** Analysis of a Household Refrigerator",
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A heat pump is used to meet the heating requirements of a house and maintain it at $20^{\circ}$ C. On a day when the outdoor air temperature drops to $-2^{\circ}$ C, the house is estimated to lose heat at a rate of 80,000 kJ/h. If the heat pump under these conditions has a COP of 2.5, determine (a) the power consumed... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**EXAMPLE 6-4** Heating a House with a Heat Pump",
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There are two classic statements of the second law—the Kelvin–Planck statement, which is related to heat engines and discussed in the preceding section, and the Clausius statement, which is related to refrigerators or heat pumps. The Clausius statement is expressed as follows:
It is impossible to construct a device t... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**The Second Law of Thermodynamics: Clausius Statement**",
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The Kelvin–Planck and the Clausius statements are equivalent in their consequences, and either statement can be used as the expression of the second law of thermodynamics. Any device that violates the Kelvin–Planck statement also violates the Clausius statement, and vice versa. This can be demonstrated as follows.
Co... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**Equivalence of the Two Statements**",
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We have repeatedly stated that a process cannot take place unless it satisfies both the first and second laws of thermodynamics. Any device that violates either law is called a **perpetual-motion machine**, and despite numerous attempts, no perpetual-motion machine is known to have worked. But this has not stopped inve... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "6-5 • PERPETUAL-MOTION MACHINES",
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A perpetual-motion machine that violates the first law of thermodynamics (PMM1).
system is creating energy at a rate of $\dot{Q}_{\rm out} + \dot{W}_{\rm net,out}$ , which is clearly a violation of the first law. Therefore, this wonderful device is nothing more than a PMM1 and does not warrant any further considerat... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**FIGURE 6-27**",
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The second law of thermodynamics states that no heat engine can have an efficiency of 100 percent. Then one may ask, what is the highest efficiency that a heat engine can possibly have? Before we can answer this question, we need to define an idealized process first, which is called the ... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**6–6** ■ **REVERSIBLE AND IRREVERSIBLE PROCESSES**",
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Two familiar reversible processes.
Engineers are interested in reversible processes because work-producing devices such as car engines and gas or steam turbines *deliver the most work,* and work-consuming devices such as compressors, fans, and pumps *consume the least work* when reversible processes are used instead ... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**FIGURE 6–29**",
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The factors that cause a process to be irreversible are called **irreversibilities**. They include friction, unrestrained expansion, mixing of two fluids, heat transfer across a finite temperature difference, electric resistance, inelastic deformation of solids, and chemical reactions. T... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**Irreversibilities**",
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(*a*) Heat transfer through a temperature difference is irreversible, and (*b*) the reverse process is impossible.
Another example of irreversibility is the **unrestrained expansion of a gas** separated from a vacuum by a membrane, as shown in Fig. 6–32. When the membrane is ruptured, the gas fills the entire tank. T... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**FIGURE 6–33**",
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A typical process involves interactions between a system and its surroundings, and a reversible process involves no irreversibilities associated with either of them.
A process is called **internally reversible** if no irreversibilities occur within the boundaries of the system during the process. During an internally... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**Internally and Externally Reversible Processes**",
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We mentioned earlier that heat engines are cyclic devices and that the working fluid of a heat engine returns to its initial state at the end of each cycle. Work is done by the working fluid during one part of the cycle and on the working fluid during another part. The difference between these two is the net work deliv... | {
"Header 1": "$\\dot{Q}_H$ $\\dot{Q}_H$ $\\dot{Q}_L = 60 \\text{ kJ/min}$ Refrigerator",
"Header 3": "**6–7** ■ **THE CARNOT CYCLE**",
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Execution of the Carnot cycle in a closed system.
**FIGURE 6–37** *P-V* diagram of the Carnot cycle.
Consider a closed system that consists of a gas contained in an adiabatic piston–cylinder device, as shown in Fig. 6–36. The insulation of the cylinder head is such that it may be remo... | {
"Header 1": "**FIGURE 6–36**",
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The second law of thermodynamics puts limits on the operation of cyclic devices as expressed by the Kelvin–Planck and Clausius statements. A heat engine cannot operate by exchanging heat with a single reservoir, and a refrigerator cannot operate without a net energy input from an external source.
We can draw valuable... | {
"Header 1": "**FIGURE 6–36**",
"Header 3": "6-8 • THE CARNOT PRINCIPLES",
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A temperature scale that is independent of the properties of the substances that are used to measure temperature is called a **thermodynamic temperature scale**. Such a temperature scale offers great conveniences in thermodynamic calculations, and its derivation is given below using some reversible heat engines.
The ... | {
"Header 1": "6-9 • THE THERMODYNAMIC TEMPERATURE SCALE",
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A conceptual experimental setup to determine thermodynamic temperatures on the Kelvin scale by measuring heat transfers $Q_H$ and $Q_L$ .
$T_1$ and $T_3$ only, and not $T_2$ . That is, the value of the product on the right-hand side of this equation is independent of the value of $T_2$ . This condition will b... | {
"Header 1": "6-9 • THE THERMODYNAMIC TEMPERATURE SCALE",
"Header 3": "FIGURE 6-44",
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$$\eta_{\rm th} = 1 - \frac{Q_L}{Q_H}$$
where $Q_H$ is heat transferred to the heat engine from a high-temperature reservoir at $T_H$ , and $Q_L$ is heat rejected to a low-temperature reservoir at $T_L$ . For reversible heat engines, the heat transfer ratio in the preceding relat... | {
"Header 1": "6-9 • THE THERMODYNAMIC TEMPERATURE SCALE",
"Header 3": "6-10 • THE CARNOT HEAT ENGINE ()",
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A Carnot heat engine, shown in Fig. 6–47, receives 500 kJ of heat per cycle from a high-temperature source at 652°C and rejects heat to a low-temperature sink at 30°C. Determine (*a*) the thermal efficiency of this Carnot engine and (*b*) the amount of heat rejected to the sink per cycle.
**SOLUTION** The heat suppli... | {
"Header 1": "6-9 • THE THERMODYNAMIC TEMPERATURE SCALE",
"Header 3": "**EXAMPLE 6-5** Analysis of a Carnot Heat Engine",
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The Carnot heat engine in Example 6–5 receives heat from a source at 925 K and converts 67.2 percent of it to work while rejecting the rest (32.8 percent) to a sink at 303 K. Now let us examine how the thermal efficiency varies with the source temperature when the sink temperature is held constant.
The thermal effici... | {
"Header 1": "6-9 • THE THERMODYNAMIC TEMPERATURE SCALE",
"Header 3": "The Quality of Energy",
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At times of energy crisis, we are bombarded with speeches and articles on how to "conserve" energy. Yet we all know that the *quantity* of energy is already conserved. What is not conserved is the *quality* of energy, or the work potential of energy. Wasting energy is synonymous with converting it to a less useful form... | {
"Header 1": "6-9 • THE THERMODYNAMIC TEMPERATURE SCALE",
"Header 3": "**Quantity versus Quality in Daily Life**",
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A refrigerator or a heat pump that operates on the reversed Carnot cycle is called a **Carnot refrigerator**, or a **Carnot heat pump**. The coefficient of performance of any refrigerator or heat pump, reversible or irreversible, is given by Eqs. 6–9 and 6–11 as
$$COP_R = \frac{1}{Q_H/Q_L - 1}$$
and $COP_{HP} = \fra... | {
"Header 1": "6-11 • THE CARNOT REFRIGERATOR AND HEAT PUMP",
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A Carnot refrigeration cycle is executed in a closed system in the saturated liquid-vapor mixture region using 0.8 kg of refrigerant-134a as the working fluid (Fig. 6-51). The maximum and the minimum temperatures in the cycle are 20 and -8°C, respectively. It is known that the refrigerant is saturated liquid at the end... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
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A heat pump is to be used to heat a house during the winter, as shown in Fig. 6–52. The house is to be maintained at 21°C at all times. The house is estimated to be losing heat at a rate of 135,000 kJ/h when the outside temperature drops to –5°C. Determine the minimum power required to drive this heat pump.
**SOLUTIO... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**EXAMPLE 6-7** Heating a House with a Carnot Heat Pump",
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Refrigerators to preserve perishable foods have long been essential appliances for households. They have proven to be highly durable and reliable, providing satisfactory service for over 15 years. A typical household refrigerator is actually a combination refrigerator-freezer since it has a freezer compartment to make ... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**TOPIC OF SPECIAL INTEREST\\* Household Refrigerators**",
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Typical operating efficiencies of some refrigeration systems for a freezer temperature of –18°C and ambient temperature of 32°C
| Type of<br>refrigeration<br>system | Coefficient<br>of<br>performance |
|------------------------------------|----------------------------------|
| Vapor-compression<br>Absorption | 1.3... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**TABLE 6–1**",
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The cross section of a refrigerator showing the relative magnitudes of various effects that constitute the predictable heat load.
- **1.** *Open the refrigerator door the fewest times possible* for the shortest duration possible. Each time the refrigerator door is opened, the cool air inside is replaced by the warmer... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**FIGURE 6–54**",
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The condenser coils of a refrigerator must be cleaned periodically, and the airflow passages must not be blocked to maintain high performance.
**FIGURE 6–57** Schematic for Example 6–8.
water droplets forming on the surfaces and sliding down. Condensation is most likely to occur in s... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "FIGURE 6-56",
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The interior lighting of refrigerators is provided by incandescent lamps whose switches are actuated by the opening of the refrigerator door. Consider a refrigerator whose 40-W lightbulb remains on continuously as a result of a malfunction of the switch (Fig. 6–57). If the refrigerator has a coefficient of performance ... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**EXAMPLE 6–8** Malfunction of a Refrigerator Light Switch",
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The second law of thermodynamics states that processes occur in a certain direction, not in any direction. A process does not occur unless it satisfies both the first and the second laws of thermodynamics. Bodies that can absorb or reject finite amounts of heat isothermally are called thermal energy reservoirs or heat ... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**SUMMARY**",
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- **6–1C** A mechanic claims to have developed a car engine that runs on water instead of gasoline. What is your response to this claim?
- **6–2C** Describe an imaginary process that violates both the first and the second laws of thermodynamics.
- **6–3C** Describe an imaginary process that satisfies the first law but ... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "Second Law of Thermodynamics and Thermal Energy Reservoirs",
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- **6–8C** What are the characteristics of all heat engines?
- **6–9C** What is the Kelvin–Planck expression of the second law of thermodynamics?
<sup>\*</sup> Problems designated by a "C" are concept questions, and students are encouraged to answer them all. Problems designated by an "E" are in English units, and th... | {
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"Header 3": "Heat Engines and Thermal Efficiency",
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- **6–30C** What is the difference between a refrigerator and a heat pump?
- **6–31C** What is the difference between a refrigerator and an air conditioner?
- **6–32C** Define the coefficient of performance of a refrigerator in words. Can it be greater than unity?
- **6–33C** Define the coefficient of performance of a ... | {
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**6–51** Reconsider Prob. 6–50. Using appropriate software, determine the power input required by the air conditioner to cool the house as a function for airconditioner EER ratings in the range 5 to 15. Discuss your results and include representative costs of air-conditioning units in the EER rating range.
- **6–52E*... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**FIGURE P6–50**",
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**6–61C** Why are engineers interested in reversible processes even though they can never be achieved?
**6–62C** A cold canned drink is left in a warmer room where its temperature rises as a result of heat transfer. Is this a reversible process? Explain.
**6–63C** A block slides down an inclined plane with friction... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**Reversible and Irreversible Processes**",
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**6–75C** Is there any way to increase the efficiency of a Carnot heat engine other than by increasing *TH* or decreasing *TL*?
**6–76C** Consider two actual power plants operating with solar energy. Energy is supplied to one plant from a solar pond at 80°C and to the other from concentrating collectors that raise th... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**Carnot Heat Engines**",
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- **6–90C** What is the highest COP that a refrigerator operating between temperature levels *TL* and *TH* can have?
- **6–91C** A homeowner buys a new refrigerator and a new air conditioner. Which one of these devices would you expect to have a higher COP? Why?
- **6–92C** A homeowner buys a new refrigerator with no f... | {
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"Header 3": "**Carnot Refrigerators and Heat Pumps**",
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- **6–108** The performance of a heat pump degrades (i.e., its COP decreases) as the temperature of the heat source decreases. This makes using heat pumps at locations with severe weather conditions unattractive. Consider a house that is heated and maintained at 20°C by a heat pump during the winter. What is the maximu... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**FIGURE P6–107**",
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- **6–116C** Why are today's refrigerators much more efficient than those built in the past?
- **6–117C** Why is it important to clean the condenser coils of a household refrigerator a few times a year? Also, why is it important not to block airflow through the condenser coils?
- **6–118C** Someone proposes that the re... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**Special Topic: Household Refrigerators**",
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**6–125** A manufacturer of ice cream freezers claims that its product has a coefficient of performance of 1.3 while freezing ice cream at 250 K when the surrounding environment is at 300 K. Is this claim valid?
**6–126** A heat pump designer claims to have an air-source heat pump whose coefficient of performance is ... | {
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"Header 3": "**Review Problems**",
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**FIGURE P6–142**
**6–143** The maximum flow rate of a standard shower head is about 3.5 gpm (13.3 L/min) and can be reduced to 2.75 gpm (10.5 L/min) by switching to a low-flow shower head that is equipped with flow controllers. Consider a family of four, with each person taking a 6-... | {
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"Header 3": "**Review Problems**",
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*©McGraw-Hill Education/Christopher Kerrigan*
Reconsider Prob. 6–145. Using appropriate software, investigate the effect of the heat pump COP on the yearly operation costs and the number of years required to break even. Let the COP vary from 2 to 5. Plot the payback period against the COP and discuss the results.
*... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**FIGURE P6–145**",
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**6–153** Cold water at 10°C enters a water heater at the rate of 0.02 m³/min and leaves the water heater at 50°C. The water heater receives heat from a heat pump that receives heat from a heat source at 0°C.
- (a) Assuming the water to be an incompressible liquid that does not change phase during heat addition, dete... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**FIGURE P6-152**",
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**6–159** Consider a Carnot refrigerator and a Carnot heat pump operating between the same two thermal energy reservoirs. If the COP of the refrigerator is 3.4, the COP of the heat pump is
(*a*) 1.7 (*b*) 2.4 (*c*) 3.4 (*d*) 4.4 (*e*) 5.0
**6–160** A 2.4-m-high 200-m2 house is maintained at 22°C by an air-condition... | {
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"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**6–175** Show that the work produced by a reversible process exceeds that produced by an equivalent irreversible process by considering a weight moving down a plane both with and without friction.
**6–176** Devise a Carnot heat engine using steady-flow components, and describe how the Carnot cycle is executed in tha... | {
"Header 1": "**EXAMPLE 6-6** A Carnot Refrigeration Cycle Operating in the Saturation Dome",
"Header 3": "**Design and Essay Problems**",
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**I** n Chap. 6, we introduced the second law of thermodynamics and applied it to cycles and cyclic devices. In this chapter, we apply the second law to processes. The first law of thermodynamics deals with the property *energy* and the conservation of it. The second law leads to the definition of a new property called... | {
"Header 1": "**ENTROPY**",
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The second law of thermodynamics often leads to expressions that involve inequalities. An irreversible (i.e., actual) heat engine, for example, is less efficient than a reversible one operating between the same two thermal energy reservoirs. Likewise, an irreversible refrigerator or a he... | {
"Header 1": "**ENTROPY**",
"Header 3": "7-1 • ENTROPY",
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The net change in volume (a property) during a cycle is always zero.
That is, the cyclic integral of volume (or any other property) is zero. Conversely, a quantity whose cyclic integral is zero depends on the *state* only and not the process path, and thus it is a property. Therefore, the quantity $(\delta Q/T)_{\te... | {
"Header 1": "**ENTROPY**",
"Header 3": "FIGURE 7-2",
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Recall that isothermal heat transfer processes are internally reversible. Therefore, the entropy change of a system during an internally reversible isothermal heat transfer process can be determined by performing the integration in Eq. 7–5:
$$\Delta S = \int_{1}^{2} \left(\frac{\delta Q}{T}\right)_{\text{int rev}} = ... | {
"Header 1": "A Special Case: Internally Reversible Isothermal Heat Transfer Processes",
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A piston-cylinder device contains a liquid-vapor mixture of water at 300 K. During a constant-pressure process, 750 kJ of heat is transferred to the water. As a result, part of the liquid in the cylinder vaporizes. Determine the entropy change of the water during this process.
**SOLUTION** Heat is transferred to a li... | {
"Header 1": "A Special Case: Internally Reversible Isothermal Heat Transfer Processes",
"Header 3": "EXAMPLE 7-1 Entropy Change During an Isothermal Process",
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Consider a cycle that is made up of two processes: process 1-2, which is arbitrary (reversible or irreversible), and process 2-1, which is internally reversible, as shown in Fig. 7–5. From the Clausius inequality,
$$\oint \frac{\delta Q}{T} \le 0$$
or
$$\int_{1}^{2} \frac{\delta Q}{T} + \int_{2}^{1} \left(\frac{\... | {
"Header 1": "7-2 • THE INCREASE OF ENTROPY PRINCIPLE",
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In light of the preceding discussions, we draw the following conclusions:
- **1.** Processes can occur in a *certain* direction only, not in *any* direction. A process must proceed in the direction that complies with the increase of entropy principle, that is, *S*gen ≥ 0. A process that violates this principle is imp... | {
"Header 1": "7-2 • THE INCREASE OF ENTROPY PRINCIPLE",
"Header 3": "**Some Remarks About Entropy**",
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A heat source at 800 K loses 2000 kJ of heat to a sink at (*a*) 500 K and (*b*) 750 K. Determine which heat transfer process is more irreversible.
**SOLUTION** Heat is transferred from a heat source to two heat sinks at different temperatures. The heat transfer process that is more irreversible is to be determined. *... | {
"Header 1": "7-2 • THE INCREASE OF ENTROPY PRINCIPLE",
"Header 3": "**EXAMPLE 7–2 Entropy Generation During Heat Transfer Processes**",
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The entropy of a pure substance is determined from the tables (like other properties).
state, the entropies of substances are evaluated from measurable property data following rather involved computations, and the results are tabulated in the same manner as the other properties such as U, u, and h (Fig. 7–10).
The ... | {
"Header 1": "7-3 • ENTROPY CHANGE OF PURE SUBSTANCES",
"Header 3": "FIGURE 7-10",
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A rigid tank contains 5 kg of refrigerant-134a initially at 20°C and 140 kPa. The refrigerant is now cooled while being stirred until its pressure drops to 100 kPa. Determine the entropy change of the refrigerant during this process.
**SOLUTION** The refrigerant in a rigid tank is cooled while being stirred. The entr... | {
"Header 1": "7-3 • ENTROPY CHANGE OF PURE SUBSTANCES",
"Header 3": "**EXAMPLE 7–3** Entropy Change of a Substance in a Tank",
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During an internally reversible, adiabatic (isentropic) process, the entropy remains constant.
**SOLUTION** Liquid water in a piston–cylinder device is heated at constant pressure. The entropy change of water is to be determined.
**Assumptions** 1 The tank is stationary and thus the kinetic and potential energy cha... | {
"Header 1": "7-3 • ENTROPY CHANGE OF PURE SUBSTANCES",
"Header 2": "EXAMPLE 7-4 Entropy Change During a Constant-Pressure Process",
"Header 3": "**FIGURE 7-14**",
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We mentioned earlier that the entropy of a fixed mass can be changed by (1) heat transfer and (2) irreversibilities. Then it follows that the entropy of a fixed mass does not change during a process that is *internally reversible* and *adiabatic* (Fig. 7–14). A process during which the entropy remains constant is calle... | {
"Header 1": "7-3 • ENTROPY CHANGE OF PURE SUBSTANCES",
"Header 2": "EXAMPLE 7-4 Entropy Change During a Constant-Pressure Process",
"Header 3": "7-4 • ISENTROPIC PROCESSES",
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Steam enters an adiabatic turbine at 5 MPa and $450^{\circ}$ C and leaves at a pressure of 1.4 MPa. Determine the work output of the turbine per unit mass of steam if the process is reversible.
**SOLUTION** Steam is expanded in an adiabatic turbine to a specified pressure in a reversible manner. The work output of t... | {
"Header 1": "7-3 • ENTROPY CHANGE OF PURE SUBSTANCES",
"Header 2": "EXAMPLE 7-4 Entropy Change During a Constant-Pressure Process",
"Header 3": "**EXAMPLE 7-5** Isentropic Expansion of Steam in a Turbine",
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Property diagrams serve as great visual aids in the thermodynamic analysis of processes. We have used *P-U* and *T-U* diagrams extensively in previous chapters in conjunction with the first law of thermodynamics. In the second-law analysis, it is very helpful to plot the processes on diagrams for which one of the coord... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
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On a *T-S* diagram, the area under the process curve represents the heat transfer for internally reversible processes.
where *T*0 is the constant temperature and Δ*S* is the entropy change of the system during the process.
An isentropic process on a *T-s* diagram is easily recognized as a *vertical-line segment.* T... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**FIGURE 7-16**",
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Show the Carnot cycle on a *T-S* diagram and indicate the areas that represent the heat supplied *QH*, heat rejected *QL*, and the net work output *W*net,out on this diagram.
**SOLUTION** The Carnot cycle is to be shown on a *T-S* diagram, and the areas that represent *QH*, *QL*, and *W*net,out are to be indicated. ... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**EXAMPLE 7–6 The T-S Diagram of the Carnot Cycle**",
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The *T-S* diagram of a Carnot cycle (Example 7–6).
**FIGURE 7–20**
The level of molecular disorder (entropy) of a substance increases as it melts or evaporates.
what is entropy? Not being able to describe entropy fully, however, does not take anything away from its usefulness. We co... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**FIGURE 7–19**",
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During a heat transfer process, the net entropy increases. (The increase in the entropy of the cold body more than offsets the decrease in the entropy of the hot body.)
reduced, molecular disorder is produced, and associated with all this is an increase in entropy.
The *quantity* of energy is always preserved durin... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**FIGURE 7–25**",
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The concept of entropy can also be applied to other areas. Entropy can be viewed as a measure of disorder or disorganization in a system. Likewise, entropy generation can be viewed as a measure of disorder or disorganization generated during a process. The concept of entropy is not used in daily life nearly as extensiv... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**Entropy and Entropy Generation in Daily Life**",
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Recall that the quantity (*δQ*/*T*)int rev corresponds to a differential change in the property *entropy.* The entropy change for a process, then, can be evaluated by integrating *δQ*/*T* along some imaginary internally reversible path between the actual end states. For isothermal internally reversible processes, this ... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**7–7** ■ **THE T ds RELATIONS**",
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As in mechanical systems, friction in the workplace is bound to generate entropy and reduce performance.
*©Purestock/SuperStock RF*
Thus,
$$TdS = dU + PdV \qquad \text{(kJ)} \tag{7-22}$$
or
$$Tds = du + PdV \qquad (kJ/kg) \tag{7-23}$$
This equation is known as the first T ds, or Gibbs equation. Notice that ... | {
"Header 1": "7-5 • PROPERTY DIAGRAMS INVOLVING ENTROPY",
"Header 3": "**FIGURE 7–26**",
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Recall that liquids and solids can be approximated as *incompressible sub-stances* since their specific volumes remain nearly constant during a process. Thus, $dv \cong 0$ for liquids and solids, and Eq. 7–25 for this case reduces to
$$ds = \frac{du}{T} = \frac{c \, dT}{T} \tag{7-27}$$
since $c_p = c_v = c$ and... | {
"Header 1": "7-8 • ENTROPY CHANGE OF LIQUIDS AND SOLIDS",
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Liquid methane is commonly used in various cryogenic applications. The critical temperature of methane is 191 K (or –82°C), and thus methane must be maintained below 191 K to keep it in liquid phase. The properties of liquid methane at various temperatures and pressures are given in Table 7–1. Determine the entropy cha... | {
"Header 1": "7-8 • ENTROPY CHANGE OF LIQUIDS AND SOLIDS",
"Header 3": "**EXAMPLE 7–7** Effect of Density of a Liquid on Entropy",
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A cryogenic manufacturing facility handles liquid methane at 115 K and 5 MPa at a rate of 0.280 m<sup>3</sup>/s. A process requires dropping the pressure of liquid methane to 1 MPa, which is done by throttling the liquid methane by passing it through a flow resistance such as a valve. A recently hired engineer proposes... | {
"Header 1": "7-8 • ENTROPY CHANGE OF LIQUIDS AND SOLIDS",
"Header 3": "■ EXAMPLE 7-8 Economics of Replacing a Valve with a Turbine",
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Liquefied natural gas (LNG) turbine after being removed from an LNG tank.
Courtesy of Ebara International Corp., Cryodynamics Division, Sparks, Nevada
Annual power production =
$$\dot{W}_{\text{out}} \times \Delta t = (1123 \text{ kW})(8760 \text{ h/yr})$$
= $0.9837 \times 10^7 \text{ kWh/yr}$
At \$0.075/kWh, ... | {
"Header 1": "7-8 • ENTROPY CHANGE OF LIQUIDS AND SOLIDS",
"Header 3": "FIGURE 7-29",
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An expression for the entropy change of an ideal gas can be obtained from Eq. 7–25 or 7–26 by employing the property relations for ideal gases (Fig. 7–30). By substituting $du = c_v dT$ and P = RT/V into Eq. 7–25, the differential entropy change of an ideal gas becomes
$$ds = c_{\nu} \frac{dT}{T} + R \frac{d\nu}{\n... | {
"Header 1": "7-9 • THE ENTROPY CHANGE • OF IDEAL GASES",
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Assuming constant specific heats for ideal gases is a common approximation, and we used this assumption before on several occasions. It usually simplifies the analysis greatly, and the price we pay for this convenience is some loss in accuracy. The magnitude of the error introduced by this assumption depends on the sit... | {
"Header 1": "7-9 • THE ENTROPY CHANGE • OF IDEAL GASES",
"Header 3": "**Constant Specific Heats (Approximate Analysis)**",
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When the temperature change during a process is large and the specific heats of the ideal gas vary nonlinearly within the temperature range, the assumption of constant specific heats may lead to considerable errors in entropy-change calculations. For those cases, the variation of specific heats with temperature should ... | {
"Header 1": "7-9 • THE ENTROPY CHANGE • OF IDEAL GASES",
"Header 3": "Variable Specific Heats (Exact Analysis)",
"token_count": 856,
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Air is compressed from an initial state of 100 kPa and 17°C to a final state of 600 kPa and 57°C. Determine the entropy change of air during this compression process by using (a) property values from the air table and (b) average specific heats.
**SOLUTION** Air is compressed between two specified states. The entropy... | {
"Header 1": "7-9 • THE ENTROPY CHANGE • OF IDEAL GASES",
"Header 3": "**EXAMPLE 7–9** Entropy Change of an Ideal Gas",
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For small temperature differences, the exact and approximate relations for entropy changes of ideal gases give almost identical results.
or
$$\left(\frac{T_2}{T_1}\right)_{\text{c-const}} = \left(\frac{U_1}{U_2}\right)^{k-1} \qquad \text{(ideal gas)}$$
(7-42)
since $R = c_p - c_v$ , $k = c_p/c_v$ , and thus $R... | {
"Header 1": "7-9 • THE ENTROPY CHANGE • OF IDEAL GASES",
"Header 3": "FIGURE 7-34",
"token_count": 495,
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} |
The isentropic relations of ideal gases are valid for the isentropic processes of ideal gases only.
of specific heats with temperature. However, it involves tedious iterations when the volume ratio is given instead of the pressure ratio. This is quite an inconvenience in optimization studies, which usually require ma... | {
"Header 1": "7-9 • THE ENTROPY CHANGE • OF IDEAL GASES",
"Header 3": "**FIGURE 7-35**",
"token_count": 752,
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} |
The use of $V_r$ data for calculating the final temperature during an isentropic process (Example 7–10).
**SOLUTION** Air is compressed in a car engine isentropically. For a given compression ratio, the final air temperature is to be determined.
**Assumptions** At specified conditions, air can be treated as an id... | {
"Header 1": "EXAMPLE 7-10 Isentropic Compression of Air in a Car Engine",
"Header 3": "**FIGURE 7-38**",
"token_count": 744,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
Air enters an isentropic turbine at 150 psia and 900°F through a 0.5-ft<sup>2</sup> inlet section with a velocity of 500 ft/s (Fig. 7–39). It leaves at 15 psia with a velocity of 100 ft/s. Calculate the air temperature at the turbine exit and the power produced, in hp, by this turbine.
**SOLUTION** Air is expanded in... | {
"Header 1": "EXAMPLE 7-10 Isentropic Compression of Air in a Car Engine",
"Header 3": "EXAMPLE 7-11 Isentropic Expansion of an Ideal Gas",
"token_count": 1347,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - ... |
The work done during a process depends on the path followed as well as on the properties at the end states. Recall that reversible (quasi-equilibrium) moving boundary work associated with closed systems is expressed in terms of the fluid properties as
$$W_b = \int_{1}^{2} P dV$$
We mentioned that the quasi-equilibr... | {
"Header 1": "EXAMPLE 7-10 Isentropic Compression of Air in a Car Engine",
"Header 3": "7-10 • REVERSIBLE STEADY-FLOW WORK",
"token_count": 646,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.... |
Reversible work relations for steady-flow and closed systems.
Obviously, one needs to know $\upsilon$ as a function of P for the given process to perform the integration. When the working fluid is *incompressible*, the specific volume $\upsilon$ remains constant during the process and can be taken out of the inte... | {
"Header 1": "EXAMPLE 7-10 Isentropic Compression of Air in a Car Engine",
"Header 3": "**FIGURE 7-40**",
"token_count": 656,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
a liquid
Schematic and *T-s* diagram for Example 7–12.
a vapor
**SOLUTION** Steam is to be compressed from a given pressure to a specified pressure isentropically. The work input is to be determined for the cases of steam being a saturated liquid and saturated vapor at the inlet.
**Assumptions** 1 Steady operat... | {
"Header 1": "EXAMPLE 7-12 Compressing a Substance in the Liquid Versus Gas Phases",
"Header 3": "**FIGURE 7-42**",
"token_count": 804,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.p... |
We have shown in Chap. 6 that cyclic devices (heat engines, refrigerators, and heat pumps) deliver the most work and consume the least when reversible
processes are used. Now we demonstrate that this is also the case for individual devices such as turbines and compressors in steady operation.
Consider two steady-fl... | {
"Header 1": "Proof that Steady-Flow Devices Deliver the Most and Consume the Least Work When the Process Is Reversible",
"token_count": 517,
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We have just shown that the work input to a compressor is minimized when the compression process is executed in an internally reversible manner. When the changes in kinetic and potential energies are negligible, the compressor work is given by (Eq. 7–53)
$$w_{\text{rev,in}} = \int_{1}^{2} U dP$$
(7–56)
Obviously on... | {
"Header 1": "Proof that Steady-Flow Devices Deliver the Most and Consume the Least Work When the Process Is Reversible",
"Header 3": "7-11 • MINIMIZING THE COMPRESSOR WORK",
"token_count": 825,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-k... |
It is clear from these arguments that cooling a gas as it is compressed is desirable since this reduces the required work input to the compressor. However, often it is not possible to have adequate cooling through the casing of the compressor, and it becomes necessary to use other techniques to achieve effective coolin... | {
"Header 1": "Proof that Steady-Flow Devices Deliver the Most and Consume the Least Work When the Process Is Reversible",
"Header 3": "**Multistage Compression with Intercooling**",
"token_count": 761,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-bole... |
Air is compressed steadily by a reversible compressor from an inlet state of 100 kPa and 300 K to an exit pressure of 900 kPa. Determine the compressor work per unit mass for (a) isentropic compression with k = 1.4, (b) polytropic compression with n = 1.3, (c) isothermal compression, and (d) ideal two-stage compression... | {
"Header 1": "**EXAMPLE 7–13** Work Input for Various Compression Processes",
"token_count": 263,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
Schematic and *P*-*U* diagram for Example 7–13.
**Analysis** We take the compressor to be the system. This is a control volume since mass crosses the boundary. A sketch of the system and the *T-s* diagram for the process are given in Fig. 7–46.
The steady-flow compression work for all these four cases is determined... | {
"Header 1": "**EXAMPLE 7–13** Work Input for Various Compression Processes",
"Header 3": "**FIGURE 7-46**",
"token_count": 931,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
We have said repeatedly that irreversibilities accompany all actual processes and that their effect is always to downgrade the performance of devices. In engineering analysis, it would be very useful to have some parameters that would enable us to quantify the degree of degradation of energy in these devices. In Chap. ... | {
"Header 1": "7-12 • ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES",
"token_count": 484,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
For a turbine under steady operation, the inlet state of the working fluid and the exhaust pressure are fixed. Therefore, the ideal process for an adiabatic turbine is an isentropic process between the inlet state and the exhaust pressure. The desired output of a turbine is the work produced, and the **isentropic effic... | {
"Header 1": "7-12 • ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES",
"Header 3": "**Isentropic Efficiency of Turbines**",
"token_count": 215,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32... |
Schematic and *T-s* diagram for Example 7–14.
Usually the changes in kinetic and potential energies associated with a fluid stream flowing through a turbine are small relative to the change in enthalpy and can be neglected. Then, the work output of an adiabatic turbine simply becomes the change in enthalpy, and Eq. 7... | {
"Header 1": "7-12 • ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES",
"Header 3": "**FIGURE 7-49**",
"token_count": 279,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
Steam enters an adiabatic turbine steadily at 3 MPa and 400°C and leaves at 50 kPa and 100°C. If the power output of the turbine is 2 MW, determine (a) the isentropic efficiency of the turbine and (b) the mass flow rate of the steam flowing through the turbine.
**SOLUTION** Steam flows steadily in a turbine between i... | {
"Header 1": "7-12 • ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES",
"Header 3": "**EXAMPLE 7–14** Isentropic Efficiency of a Steam Turbine",
"token_count": 954,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf ... |
The **isentropic efficiency of a compressor** is defined as the ratio of the work input required to raise the pressure of a gas to a specified value in an isentropic manner to the actual work input:
$$\eta_C = \frac{\text{Isentropic compressor work}}{\text{Actual compressor work}} = \frac{w_s}{w_a}$$
(7–62)
Notice ... | {
"Header 1": "**Isentropic Efficiencies of Compressors** and Pumps",
"token_count": 442,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
Schematic and *T-s* diagram for Example 7–15.
When the changes in potential and kinetic energies of a liquid are negligible, the isentropic efficiency of a pump is defined similarly as
$$\eta_P = \frac{w_s}{w_a} = \frac{U(P_2 - P_1)}{h_{2a} - h_1}$$
(7-64)
When no attempt is made to cool the gas as it is compress... | {
"Header 1": "**Isentropic Efficiencies of Compressors** and Pumps",
"Header 3": "**FIGURE 7-52**",
"token_count": 320,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 06.32.12pm.pdf"
} |
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