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The ideal Carnot cycle is a *totally reversible cycle*, and thus it does not involve any irreversibilities. The ideal Rankine cycles (simple, reheat, or regenerative), however, are only *internally reversible*, and they may involve irreversibilities external to the system, such as heat transfer through a finite tempera... | {
"Header 1": "10-7 • SECOND-LAW ANALYSIS OF VAPOR POWER CYCLES",
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Consider a steam power plant operating on the simple ideal Rankine cycle (Fig. 10–21). Steam enters the turbine at 3 MPa and 350°C and is condensed in the condenser at a pressure of 75 kPa. Heat is supplied to the steam in a furnace maintained at 800 K, and waste heat is rejected to the surroundings at 300 K. Determine... | {
"Header 1": "EXAMPLE 10-7 Second-Law Analysis of an Ideal Rankine Cycle",
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In all the cycles discussed so far, the sole purpose was to convert a portion of the heat transferred to the working fluid to work, which is the most valuable form of energy. The remaining portion of the heat is rejected to rivers, lakes,
FIGURE 10–22
A simple process-heating plant.
... | {
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"Header 3": "10-8 • COGENERATION",
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Consider the cogeneration plant shown in Fig. 10–25. Steam enters the turbine at 7 MPa and 500°C. Some steam is extracted from the turbine at 500 kPa for process heating. The remaining steam continues to expand to 5 kPa. Steam is then condensed at constant pressure and pumped to the boiler pressure of 7 MPa. At times o... | {
"Header 1": "EXAMPLE 10-7 Second-Law Analysis of an Ideal Rankine Cycle",
"Header 3": "**EXAMPLE 10–8 An Ideal Cogeneration Plant**",
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The continued quest for higher thermal efficiencies has resulted in rather innovative modifications to conventional power plants. The *binary vapor cycle* discussed later is one such modification. A more popular modification involves a gas power cycle topping a vapor power cycle, which is called the **combined gas-vapo... | {
"Header 1": "10-9 • COMBINED GAS-VAPOR POWER CYCLES",
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Consider the combined gas—steam power cycle shown in Fig. 10–27. The topping cycle is a gas-turbine cycle that has a pressure ratio of 8. Air enters the compressor at 300 K and the turbine at 1300 K. The isentropic efficiency of the compressor is 80 percent, and that of the gas turbine is 85 percent. The bottoming cycl... | {
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"Header 3": "**EXAMPLE 10-9** A Combined Gas-Steam Power Cycle",
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With the exception of a few specialized applications, the working fluid predominantly used in vapor power cycles is water. Water is the *best* working fluid currently available, but it is far from being the *ideal* one. The binary cycle is an attempt to overcome some of the shortcomings of water and to approach the *id... | {
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"Header 3": "TOPIC OF SPECIAL INTEREST\\* Binary Vapor Cycles",
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The *Carnot cycle* is not a suitable model for vapor power cycles because it cannot be approximated in practice. The model cycle for vapor power cycles is the *Rankine cycle,* which is composed of four internally reversible processes: constant-pressure heat addition in a boiler, isentropic expansion in a turbine, const... | {
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"Header 3": "**SUMMARY**",
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- **1.** R. L. Bannister and G. J. Silvestri. "The Evolution of Central Station Steam Turbines." *Mechanical Engineering,* February 1989, pp. 70–78.
- **2.** R. L. Bannister, G. J. Silvestri, A. Hizume, and T. Fujikawa. "High Temperature Supercritical Steam Turbines." *Mechanical Engineering,* February 1987, pp. 60–65.... | {
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"Header 3": "**REFERENCES AND SUGGESTED READINGS**",
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**10–1C** Why is the Carnot cycle not a realistic model for steam power plants?
**10–2C** Why is excessive moisture in steam undesirable in steam turbines? What is the highest moisture content allowed?
**10–3** A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to satura... | {
"Header 1": "10-9 • COMBINED GAS-VAPOR POWER CYCLES",
"Header 3": "**Carnot Vapor Cycle**",
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**10–7C** What four processes make up the simple ideal Rankine cycle?
**10–8C** Consider a simple ideal Rankine cycle with fixed turbine inlet conditions. What is the effect of lowering the condenser pressure on
\*Problems designated by a "C" are concept questions, and students are encouraged to answer them all. Pr... | {
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"Header 3": "**The Simple Rankine Cycle**",
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Using appropriate software, determine how much the thermal efficiency of the cycle would change if there were a 50 kPa pressure drop across the boiler.
**10–27** The net work output and the thermal efficiency for the Carnot and the simple ideal Rankine cycles with steam as the working fluid are to be calculated and c... | {
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"Header 3": "**The Simple Rankine Cycle**",
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**10–30**°C Show the ideal Rankine cycle with three stages of reheating on a *T-s* diagram. Assume the turbine inlet
temperature is the same for all stages. How does the cycle efficiency vary with the number of reheat stages?
**10–31C** Is there an optimal pressure for reheating the steam of a Rankine cycle? Explai... | {
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"Header 3": "The Reheat Rankine Cycle",
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**10–43C** Devise an ideal regenerative Rankine cycle that has the same thermal efficiency as the Carnot cycle. Show the cycle on a *T*-*s* diagram.
**10–44C** During a regeneration process, some steam is extracted from the turbine and is used to heat the liquid water leaving the pump. This does not seem like a smart... | {
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"Header 3": "**Regenerative Rankine Cycle**",
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**10–54** Reconsider Prob. 10–53. Using appropriate software, investigate the effects of turbine and pump efficiencies as they are varied from 70 percent to 100 percent on the mass flow rate and thermal efficiency. Plot the mass flow rate and the thermal efficiency as a function of turbine efficiency for pump efficienc... | {
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"Header 3": "**FIGURE P10–53**",
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**10–56** Reconsider Prob. 10–55. Using appropriate software, determine the optimum bleed pressure for the closed feedwater heater that maximizes the thermal efficiency of the cycle. Answer: 220 kPa
**10–57** Reconsider Prob. 10–55. Determine the thermal efficiency of the regenerative Rankine cycle when the isentropi... | {
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"Header 3": "**FIGURE P10–55**",
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**10–62E** A steam power plant operates on an ideal reheat– regenerative Rankine cycle with one reheater and two open feedwater heaters. Steam enters the high-pressure turbine at 1500 psia and 1100°F and leaves the low-pressure turbine at 1 psia. Steam is extracted from the turbine at 250 and 40 psia, and it is reheate... | {
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"Header 3": "**FIGURE P10–61**",
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**10–63** A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of 4 MPa in the boiler and 20 kPa in the condenser and a turbine inlet temperature of 700°C. Calculate the exergy destruction in each of the components of the cycle when heat is being rejected to the atmospheric ... | {
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"Header 3": "**Second-Law Analysis of Vapor Power Cycles**",
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**10–70C** What is the difference between cogeneration and regeneration?
**10–71C** How is the utilization factor *u* for cogeneration plants defined? Could *u* be unity for a cogeneration plant that does not produce any power?
**10–72C** Consider a cogeneration plant for which the utilization factor is 1. Is the i... | {
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**10–80C** In combined gas–steam cycles, what is the energy source for the steam?
**10–81C** Why is the combined gas–steam cycle more efficient than either of the cycles operated alone?
**10–82** The gas-turbine portion of a combined gas–steam power plant has a pressure ratio of 16. Air enters the compressor at 300... | {
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**10–94** Feedwater at 4000 kPa is heated at a rate of 6 kg/s from 200°C to 245°C in a closed feedwater heater of a regenerative Rankine cycle. Bleed steam enters this unit at 3000 kPa with a quality of 90 percent and leaves as a saturated liquid. Calculate the rate at which bleed steam is required.
**10–95** Steam e... | {
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"Header 3": "**Review Problems**",
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Steam expands in a high-pressure turbine to a pressure of 2.5 MPa and is reheated in the combustion chamber to 550°C before it expands in a low-pressure turbine to 10 kPa. The mass flow rate of steam is 12 kg/s. Assuming all the compression and expansion processes to be isentropic, determine (*a*) the mass flow rate of... | {
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**10–111** A Rankine steam cycle modified for reheat, a closed feedwater heater, and an open feedwater heater is shown below. The high-pressure turbine receives 100 kg/s of steam from the steam boiler. The feedwater heater exit states for the boiler feedwater and the condensed steam are the normally assumed ideal state... | {
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"Header 3": "**FIGURE P10–110**",
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10–113 Using appropriate software, investigate the effect of the boiler pressure on the performance of a simple ideal Rankine cycle. Steam enters the turbine at 500°C and exits at 10 kPa. The boiler pressure is varied from 0.5 to 20 MPa. Determine the thermal efficiency of the
cycle and plot it against the boiler pre... | {
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"Header 3": "**FIGURE P10-112**",
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- **10–121** Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the steam is superheated to a higher temperature,
- (*a*) the turbine work output will decrease.
- (*b*) the amount of heat rejected will decrease.
- (*c*) the cycle efficiency will decrease.
- (*d*) the moisture content at... | {
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**10–134** Stack gases exhausting from electrical power plants are at approximately 150°C. Design a basic Rankine cycle that uses water, refrigerant-134a, or ammonia as the working fluid and that produces the maximum amount of work from this energy source while rejecting heat to the ambient air at 40°C. You are to use ... | {
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"Header 3": "**Design and Essay Problems**",
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We all know from experience that heat flows in the direction of decreasing temperature, that is, from high-temperature regions to low-temperature ones. This heat-transfer process occurs in nature without requiring any devices. The reverse process, however, cannot occur by itself. The transfer of heat from a low-tempera... | {
"Header 1": "10-9 • COMBINED GAS-VAPOR POWER CYCLES",
"Header 3": "11-1 • REFRIGERATORS AND HEAT PUMPS",
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Recall from Chap. 6 that the Carnot cycle is a totally reversible cycle that consists of two reversible isothermal and two isentropic processes. It has the maximum thermal efficiency for given temperature limits, and it serves as a standard against which actual power cycles can be compared.
Since it is a reversible c... | {
"Header 1": "10-9 • COMBINED GAS-VAPOR POWER CYCLES",
"Header 3": "11-2 • THE REVERSED CARNOT CYCLE",
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Many of the impracticalities associated with the reversed Carnot cycle can be eliminated by vaporizing the refrigerant completely before it is compressed and by replacing the turbine with a throttling device, such as an expansion valve or capillary tube. The cycle that results is called the **ideal vapor-compression re... | {
"Header 1": "10-9 • COMBINED GAS-VAPOR POWER CYCLES",
"Header 3": "**11–3** ■ **THE IDEAL VAPOR-COMPRESSION REFRIGERATION CYCLE**",
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A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.14 and 0.8 MPa. If the mass flow rate of the refrigerant is 0.05 kg/s, determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the rate... | {
"Header 1": "**EXAMPLE 11-1** The Ideal Vapor-Compression Refrigeration Cycle",
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An actual vapor-compression refrigeration cycle differs from the ideal one in several ways, owing mostly to the irreversibilities that occur in various components. Two common sources of irreversibilities are fluid friction (causes pressure drops) and heat transfer to or from the surroundings. The *T*-*s* diagram of an ... | {
"Header 1": "**EXAMPLE 11-1** The Ideal Vapor-Compression Refrigeration Cycle",
"Header 3": "**11–4** ■ **ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLE**",
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Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 MPa and −10°C at a rate of 0.05 kg/s and leaves at 0.8 MPa and 50°C. The refrigerant is cooled in the condenser to 26°C and 0.72 MPa and is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the connecting lin... | {
"Header 1": "**EXAMPLE 11-1** The Ideal Vapor-Compression Refrigeration Cycle",
"Header 3": "**EXAMPLE 11–2 The Actual Vapor-Compression Refrigeration Cycle**",
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Consider the vapor-compression refrigeration cycle operating between a low-temperature medium at $T_L$ and a high-temperature medium at $T_H$ as shown in Fig. 11–9. The maximum COP of a refrigeration cycle operating between temperature limits of $T_L$ and $T_H$ was given in Eq. 11–4 as
$$COP_{R,max} = COP_{R,... | {
"Header 1": "**EXAMPLE 11-1** The Ideal Vapor-Compression Refrigeration Cycle",
"Header 3": "11-5 • SECOND-LAW ANALYSIS OF VAPOR-COMPRESSION REFRIGERATION CYCLE",
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The vapor-compression refrigeration cycle considered in the second-law analysis.
Expansion valve:
$$\begin{split} \dot{X}_{\text{dest},3-4} &= T_0 \dot{S}_{\text{gen},3-4} = \dot{m} \, T_0 (s_4 - s_3) \\ \eta_{\text{II,ExpValve}} &= \frac{\dot{X}_{\text{recovered}}}{\dot{X}_{\text{expended}}} = \frac{0}{\dot{X}_3 -... | {
"Header 1": "**EXAMPLE 11-1** The Ideal Vapor-Compression Refrigeration Cycle",
"Header 3": "FIGURE 11-9",
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A vapor-compression refrigeration cycle with refrigerant-134a as the working fluid is used to maintain a space at $-13^{\circ}$ C by rejecting heat to ambient air at 27°C. R-134a enters the compressor at 100 kPa superheated by 6.4°C at a rate of 0.05 kg/s. The isentropic efficiency of the compressor is 85 percent. The... | {
"Header 1": "**EXAMPLE 11–3** Exergy Analysis of Vapor-Compression Refrigeration Cycle",
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The refrigeration load, the rate of heat rejected, and the power input are
$$\dot{Q}_L = \dot{m}(h_1 - h_4) = (0.05 \text{ kg/s})[(239.52 - 107.34) \text{ kJ/kg}] = \mathbf{6.609 \text{ kW}}$$
$\dot{Q}_H = \dot{m}(h_2 - h_3) = (0.05 \text{ kg/s})[(297.90 - 107.34) \text{ kJ/kg}] = 9.528 \text{ kW}$
$\dot{W}_{in} ... | {
"Header 1": "**EXAMPLE 11–3** Exergy Analysis of Vapor-Compression Refrigeration Cycle",
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When designing a refrigeration system, there are several refrigerants from which to choose, such as chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), ammonia, hydrocarbons (propane, ethane, ethylene, etc.), carbon dioxide, air (in the air-conditioning of aircraft), and even water (in applications above the ... | {
"Header 1": "**EXAMPLE 11–3** Exergy Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "11-6 • SELECTING THE RIGHT REFRIGERANT",
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Heat pumps are generally more expensive to purchase and install than other heating systems, but they save money in the long run in some areas because they lower the heating bills. Despite their relatively higher initial costs, the popularity of heat pumps is increasing. About one-third of all single-family homes built ... | {
"Header 1": "**EXAMPLE 11–3** Exergy Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**11–7** ■ **HEAT PUMP SYSTEMS**",
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Some industrial applications require moderately low temperatures, and the temperature range they involve may be too large for a single vapor-compression refrigeration cycle to be practical. A large temperature range also means a large pressure range in the cycle and a poor performance for a reciprocating compressor. On... | {
"Header 1": "11-8 • INNOVATIVE VAPOR-COMPRESSION REFRIGERATION SYSTEMS",
"Header 3": "**Cascade Refrigeration Systems**",
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Consider a two-stage cascade refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. Each stage operates on an ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow he... | {
"Header 1": "11-8 • INNOVATIVE VAPOR-COMPRESSION REFRIGERATION SYSTEMS",
"Header 3": "**EXAMPLE 11–4** A Two-Stage Cascade Refrigeration Cycle",
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When the fluid used throughout the cascade refrigeration system is the same, the heat exchanger between the stages can be replaced by a mixing chamber (called a *flash chamber*) since it has better heat-transfer characteristics. Such systems are called **multistage compression refrigeration systems**. A two-stage compr... | {
"Header 1": "11-8 • INNOVATIVE VAPOR-COMPRESSION REFRIGERATION SYSTEMS",
"Header 3": "**Multistage Compression Refrigeration Systems**",
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Consider a two-stage compression refrigeration system operating between the pressure limits of 0.8 and 0.14 MPa. The working fluid is refrigerant-134a. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.32 MPa. Part of the refrigerant evaporates during this fla... | {
"Header 1": "EXAMPLE 11-5 A Two-Stage Refrigeration Cycle with a Flash Chamber",
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Some applications require refrigeration at more than one temperature. This could be accomplished by using a separate throttling valve and a separate compressor for each evaporator operating at different temperatures. However,
**FIGURE 11–16** Schematic and *T*-*s* diagram for a refriger... | {
"Header 1": "Multipurpose Refrigeration Systems with a Single Compressor",
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The liquefaction of gases has always been an important area of refrigeration since many important scientific and engineering processes at cryogenic temperatures (temperatures below about −100°C) depend on liquefied gases. Some examples of such processes are the separation of oxygen and nitrogen from air, preparation of... | {
"Header 1": "Multipurpose Refrigeration Systems with a Single Compressor",
"Header 3": "**Liquefaction of Gases**",
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As explained in Sec. 11–2, the Carnot cycle (the standard of comparison for power cycles) and the reversed Carnot cycle (the standard of comparison for refrigeration cycles) are identical, except that the reversed Carnot cycle operates in the reverse direction. This suggests that the power cycles discussed in earlier c... | {
"Header 1": "Multipurpose Refrigeration Systems with a Single Compressor",
"Header 3": "**11–9** ■ **GAS REFRIGERATION CYCLES**",
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An ideal gas refrigeration cycle using air as the working medium is to maintain a refrigerated space at $0^{\circ}$ F while rejecting heat to the surrounding medium at $80^{\circ}$ F. The pressure ratio of the compressor is 4. Determine (a) the maximum and minimum temperatures in the cycle, (b) the coefficient of per... | {
"Header 1": "Multipurpose Refrigeration Systems with a Single Compressor",
"Header 3": "**EXAMPLE 11–6** The Simple Ideal Gas Refrigeration Cycle",
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Another form of refrigeration that becomes economically attractive when there is a source of inexpensive thermal energy at a temperature of 100 to 200°C is **absorption refrigeration**. Some examples of inexpensive thermal energy sources include geothermal energy, solar energy, and waste heat from cogeneration or proce... | {
"Header 1": "11–10 • ABSORPTION REFRIGERATION SYSTEMS",
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1859. Within a few years, the machines based on this principle were being built in the United States primarily to make ice and store food. You will immediately notice from the figure that this system looks very much like the vapor-compression system, except that the compressor has been replaced by a complex absorption ... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
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A reversible absorption refrigerator consists of a reversible heat engine and a reversible refrigerator (Fig. 11–25). The system removes heat from a cooled space at $-15^{\circ}$ C at a rate of 70 kW. The refrigerator operates in an environment at 25°C. If the heat is supplied to the cycle by condensing saturated stea... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**EXAMPLE 11–7** A Reversible Absorption Refrigerator",
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All the refrigeration systems discussed previously involve many moving parts and bulky, complex components. Then this question comes to mind: Is it really necessary for a refrigeration system to be so complex? Can we not achieve the same effect in a more direct way? The answer to this question is *yes*. It is possible ... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "Thermoelectric Power Generation and Refrigeration Systems",
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When a thermoelectric circuit is broken, a potential difference is generated.
<sup>\*</sup>This section can be skipped without a loss in continuity.
materials of the two wires used. Therefore, temperature can be measured by simply measuring voltages. The two wires used to measure the temperature in this manner form... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**FIGURE 11-27**",
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The transfer of heat from lower-temperature regions to higher-temperature ones is called *refrigeration*. Devices that produce refrigeration are called *refrigerators*, and the cycles on which they operate are called *refrigeration cycles*. The working fluids used in refrigerators are called *refrigerants*. Refrigerato... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**SUMMARY**",
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- ASHRAE Handbook of Fundamentals. Atlanta, GA: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1985.
- **2.** Heat Pump Systems—A Technology Review. OECD Report, Paris, 1982.
- **3.** B. Nagengast. "A Historical Look at CFC Refrigerants." *ASHRAE Journal*, Vol. 30, No. 11 (November 1988), p... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**REFERENCES AND SUGGESTED READINGS**",
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- **11–1C** Why do we study the reversed Carnot cycle even though it is not a realistic model for refrigeration cycles?
- **11–2C** Why is the reversed Carnot cycle executed within the saturation dome not a realistic model for refrigeration cycles?
- **11–3** A steady-flow Carnot refrigeration cycle uses refrigerant-13... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**The Reversed Carnot Cycle**",
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- **11–5C** Does the ideal vapor-compression refrigeration cycle involve any internal irreversibilities?
- **11–6C** Why is the throttling valve not replaced by an isentropic turbine in the ideal vapor-compression refrigeration cycle?
- **11–7C** In a refrigeration system, would you recommend condensing the refrigerant... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**Ideal and Actual Vapor-Compression Refrigeration Cycles**",
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**11–19E** A refrigerator uses refrigerant-134a as its working fluid and operates on the ideal vapor-compression refrigeration cycle. The refrigerant evaporates at 5°F and condenses at 180 psia. This unit serves a 45,000 Btu/h cooling load. Determine the mass flow rate of the refrigerant and the power that this unit wi... | {
"Header 1": "FIGURE 11–23 Ammonia absorption refrigeration cycle.",
"Header 3": "**FIGURE P11–18**",
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- **11–25**C How is the second-law efficiency of a refrigerator operating on the vapor-compression refrigeration cycle defined? Provide two alternative definitions and explain each term.
- **11–26**C How is the second-law efficiency of a heat pump operating on the vapor-compression refrigeration cycle defined? Provide ... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
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11–32 A refrigerator operates on the ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. The refrigerant evaporates at $-10^{\circ}$ C and condenses at $57.9^{\circ}$ C.
The refrigerant absorbs heat from a space at 5°C and rejects heat to ambient air at 25°C. Determine (*a*) the ... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "FIGURE P11-31",
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- **11–34C** When selecting a refrigerant for a certain application, what qualities would you look for in the refrigerant?
- **11–35C** A refrigerant-134a refrigerator is to maintain the refrigerated space at −10°C. Would you recommend an evaporator pressure of 0.12 or 0.14 MPa for this system? Why?
- **11–36C** Consid... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Selecting the Right Refrigerant**",
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- **11–39C** Do you think a heat pump system will be more cost-effective in New York or in Miami? Why?
- **11–40C** What is a water-source heat pump? How does the COP of a water-source heat pump system compare to that of an air-source system?
- **11–41** A heat pump operates on the ideal vapor-compression refrigeration... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Heat Pump Systems**",
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- **11–43E** A heat pump that operates on the ideal vaporcompression cycle with refrigerant-134a is used to heat a house and maintain it at 75°F by using underground water at 50°F as the heat source. The house is losing heat at a rate of 80,000 Btu/h. The evaporator and condenser pressures are 50 and 120 psia, respecti... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**FIGURE P11–42**",
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**11–50C** What is cascade refrigeration? What are the advantages and disadvantages of cascade refrigeration?
**11–51C** How does the COP of a cascade refrigeration system compare to the COP of a simple vapor-compression cycle operating between the same pressure limits?
**11–52C** Consider a two-stage cascade refri... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Innovative Refrigeration Systems**",
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**11–61E** A two-stage compression refrigeration system with an adiabatic liquid-vapor separation unit like that in Fig. P11–60 uses refrigerant-134a as the working fluid. The system operates the evaporator at 60 psia, the condenser at 300 psia, and the separator at 120 psia. The compressors use 25 kW of power. Determi... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**FIGURE P11–60**",
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**11–63E** A two-evaporator compression refrigeration system like that in Fig. P11–62 uses refrigerant-134a as the working fluid. The system operates evaporator 1 at 30 psia, evaporator 2 at 10 psia, and the condenser at 180 psia. The cooling load for evaporator 1 is 9000 Btu/h and that for evaporator 2 is 24,000 Btu/h... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**FIGURE P11–62**",
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- **11–66C** How does the ideal gas refrigeration cycle differ from the Carnot refrigeration cycle?
- **11–67C** How does the ideal gas refrigeration cycle differ from the Brayton cycle?
- **11–68C** Devise a refrigeration cycle that works on the reversed Stirling cycle. Also, determine the COP for this cycle.
- **11–6... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Gas Refrigeration Cycle**",
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**11–82C** What is absorption refrigeration? How does an absorption refrigeration system differ from a vaporcompression refrigeration system?
**11–83C** What are the advantages and disadvantages of absorption refrigeration?
**11–84C** Can water be used as a refrigerant in air-conditioning applications? Explain.
*... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Absorption Refrigeration Systems**",
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**11–92C** What is a thermoelectric circuit?
**11–93C** Describe the Seebeck and the Peltier effects.
**11–94C** Consider a circular copper wire formed by connecting the two ends of a copper wire. The connection point is now heated by a burning candle. Do you expect any current to flow through the wire?
**11–95C*... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Special Topic: Thermoelectric Power Generation and Refrigeration Systems**",
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**11–107** Rooms with floor areas of up to 15 m2 are cooled adequately by window air conditioners whose cooling capacity is 5000 Btu/h. Assuming the COP of the air conditioner to be 3.5, determine the rate of heat gain of the room, in Btu/h, when the air conditioner is running continuously to maintain a constant room t... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Review Problems**",
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Assuming the
refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (*a*) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (*b*) the amount of heat removed from the refrigerated space and the compressor work per unit mass of refriger... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Review Problems**",
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... |
**11–121E** Reconsider Prob. 11–120E. The refrigeration system of that problem cools one reservoir at −15°F and one at 40°F while rejecting heat to a reservoir at 80°F. Which process has the highest exergy destruction?
**11–122** The refrigeration system of Fig. P11–122 is another variation of the basic vapor-compres... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**FIGURE P11–120E**",
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... |
**11–127** An ideal gas refrigeration system with three stages of compression with intercooling operates with air entering the first compressor at 50 kPa and −30°C. Each compressor in this system has a pressure ratio of 7, and the air temperature at the outlet of all intercoolers is 15°C. Calculate the COP of this syst... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**FIGURE P11–126**",
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**11–133** A refrigerator removes heat from a refrigerated space at 0°C at a rate of 1.5 kJ/s and rejects it to an environment at 20°C. The minimum required power input is
(*a*) 102 W (*b*) 110 W (*c*) 140 W
(*d*) 150 W (*e*) 1500 W
**11–134** Consider a refrigerator that operates on the vaporcompression refriger... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**11–143** Develop and discuss techniques that apply the principle of regeneration to improve the performance of vaporcompression refrigeration systems.
**11–144** The heat supplied by a heat pump used to maintain a building's temperature is often supplemented by another source of direct heat. The fraction of the tot... | {
"Header 1": "Second-Law Analysis of Vapor-Compression Refrigeration Cycle",
"Header 3": "**Design and Essay Problems**",
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**I** n the preceding chapters we made extensive use of the property tables. We tend to take the property tables for granted, but thermodynamic laws and principles are of little use to engineers without them. In this chapter, we focus our attention on how the property tables are prepared and how some unknown properties... | {
"Header 1": "**T H E R M O DY N A M I C PROPERTY RELATIONS** 12",
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The objectives of Chapter 12 are to:
- Develop fundamental relations between commonly encountered thermodynamic properties and express the properties that cannot be measured directly in terms of easily measurable properties.
- Develop the Maxwell relations, which form the basis for many thermodynamic relations.
- Dev... | {
"Header 1": "**T H E R M O DY N A M I C PROPERTY RELATIONS** 12",
"Header 3": "**OBJECTIVES**",
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Many of the expressions developed in this chapter are based on the state postulate, which expresses that the state of a simple, compressible substance is completely specified by any two independent, intensive properties. All other properties at that state can be expressed in terms of those two properties. Mathematicall... | {
"Header 1": "12-1 • A LITTLE MATH—PARTIAL DERIVATIVES AND ASSOCIATED RELATIONS",
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The $c_p$ of ideal gases depends on temperature only, and it is expressed as $c_p(T) = dh(T)/dT$ . Determine the $c_p$ of air at 300 K, using the enthalpy data from Table A–17, and compare it to the value listed in Table A–2b.
**SOLUTION** The $c_p$ value of air at a specified temperature is to be determined u... | {
"Header 1": "**EXAMPLE 12-1** Approximating Differential Quantities by Differences",
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Now consider a function that depends on two (or more) variables, such as z = z(x, y). This time the value of z depends on both x and y. It is sometimes desirable to examine the dependence of z on only one of the variables. This is done by allowing one variable to change while holding the others constant and observing t... | {
"Header 1": "**EXAMPLE 12-1** Approximating Differential Quantities by Differences",
"Header 3": "**Partial Differentials**",
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Consider air at 300 K and 0.86 m<sup>3</sup>/kg. The state of air changes to 302 K and 0.87 m<sup>3</sup>/kg as a result of some disturbance. Using Eq. 12–3, estimate the change in the pressure of air.
**SOLUTION** The temperature and specific volume of air change slightly during a process. The resulting change in pr... | {
"Header 1": "**EXAMPLE 12-1** Approximating Differential Quantities by Differences",
"Header 3": "**EXAMPLE 12–2** Total Differential Versus Partial Differential",
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Now let us rewrite Eq. 12-3 as
$$dz = M dx + N dy ag{12-4}$$
where
$$M = \left(\frac{\partial z}{\partial x}\right)_{y}$$
and $N = \left(\frac{\partial z}{\partial y}\right)_{x}$
Taking the partial derivative of M with respect to y and of N with respect to x yields
$$\left(\frac{\partial M}{\partial y}\right... | {
"Header 1": "**EXAMPLE 12-1** Approximating Differential Quantities by Differences",
"Header 3": "**Partial Differential Relations**",
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Using the ideal-gas equation of state, verify (a) the cyclic relation, and (b) the reciprocity relation at constant P.
**SOLUTION** The cyclic and reciprocity relations are to be verified for an ideal gas. **Analysis** The ideal-gas equation of state PU = RT involves the three variables P, U, and T. Any two of these ... | {
"Header 1": "EXAMPLE 12-3 Verification of Cyclic and Reciprocity Relations",
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The equations that relate the partial derivatives of properties *P*, *U*, *T*, and *s* of a simple compressible system to each other are called the *Maxwell relations*. They are obtained from the four Gibbs equations by exploiting the exactness of the differentials of thermodynamic properties.
Two of the Gibbs relati... | {
"Header 1": "EXAMPLE 12-3 Verification of Cyclic and Reciprocity Relations",
"Header 3": "12-2 • THE MAXWELL RELATIONS",
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Verify the validity of the last Maxwell relation (Eq. 12–19) for steam at 250°C and 300 kPa.
**SOLUTION** The validity of the last Maxwell relation is to be verified for steam at a specified state.
**Analysis** The last Maxwell relation states that for a simple compressible substance, the change in entropy with pre... | {
"Header 1": "EXAMPLE 12-3 Verification of Cyclic and Reciprocity Relations",
"Header 3": "**EXAMPLE 12–4** Verification of the Maxwell Relations",
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The Maxwell relations have far-reaching implications in thermodynamics and are often used to derive useful thermodynamic relations. The Clapeyron equation is one such relation, and it enables us to determine the enthalpy change
associated with a phase change (such as the enthalpy of vaporization $h_{fg}$ ) from a kn... | {
"Header 1": "EXAMPLE 12-3 Verification of Cyclic and Reciprocity Relations",
"Header 3": "12-3 • THE CLAPEYRON EQUATION",
"token_count": 728,
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The slope of the saturation curve on a *P-T* diagram is constant at a constant *T* or *P*.
**FIGURE 12–9** Schematic for Example 12–5.
(Fig. 12–9). During the phase conversion, the volume of the system increases by 1000 cm<sup>3</sup>; 5 kJ of heat are required; and the temperature o... | {
"Header 1": "EXAMPLE 12-5 Estimating Boiling Temperature with the Clapeyron Equation",
"Header 3": "FIGURE 12-8",
"token_count": 912,
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Estimate the saturation pressure of refrigerant-134a at $-50^{\circ}$ F, using the data available in the refrigerant tables.
**SOLUTION** The saturation pressure of refrigerant-134a is to be determined using other tabulated data.
**Analysis** Table A–11E lists saturation data at temperatures –40°F and above. There... | {
"Header 1": "**EXAMPLE 12–6** Extrapolating Tabular Data with the Clapeyron Equation",
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} |
We choose the internal energy to be a function of T and U; that is, u = u(T, U) and take its total differential (Eq. 12–3):
$$du = \left(\frac{\partial u}{\partial T}\right)_{\mathsf{U}} dT + \left(\frac{\partial u}{\partial \mathsf{U}}\right)_{T} d\mathsf{U}$$
Using the definition of $c_{v}$ , we have
$$du = c_... | {
"Header 1": "**EXAMPLE 12–6** Extrapolating Tabular Data with the Clapeyron Equation",
"Header 3": "**Internal Energy Changes**",
"token_count": 728,
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The general relation for dh is determined in exactly the same manner. This time we choose the enthalpy to be a function of T and P, that is, h = h(T, P), and take its total differential,
$$dh = \left(\frac{\partial h}{\partial T}\right)_{p} dT + \left(\frac{\partial h}{\partial P}\right)_{T} dP$$
Using the definiti... | {
"Header 1": "**EXAMPLE 12–6** Extrapolating Tabular Data with the Clapeyron Equation",
"Header 3": "**Enthalpy Changes**",
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Next we develop two general relations for the entropy change of a simple compressible system.
The first relation is obtained by replacing the first partial derivative in the total differential *ds* (Eq. 12–26) with Eq. 12–28 and the second partial derivative with the third Maxwell relation (Eq. 12–18), yielding
$$d... | {
"Header 1": "**EXAMPLE 12–6** Extrapolating Tabular Data with the Clapeyron Equation",
"Header 3": "**Entropy Changes**",
"token_count": 405,
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Recall that the specific heats of an ideal gas depend on temperature only. For a general pure substance, however, the specific heats depend on specific volume or pressure as well as the temperature. Next we develop some general relations to relate the specific heats of a substance to pressure, specific volume, and temp... | {
"Header 1": "**EXAMPLE 12–6** Extrapolating Tabular Data with the Clapeyron Equation",
"Header 3": "Specific Heats $c_{\\nu}$ and $c_{p}$",
"token_count": 1510,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf -... |
Derive a relation for the internal energy change as a gas that obeys the van der Waals equation of state. Assume that in the range of interest $c_0$ varies according to the relation $c_0 = c_1 + c_2 T$ , where $c_1$ and $c_2$ are constants.
**SOLUTION** A relation is to be obtained for the internal energy chan... | {
"Header 1": "**EXAMPLE 12–6** Extrapolating Tabular Data with the Clapeyron Equation",
"Header 3": "EXAMPLE 12-7 Internal Energy Change of a van der Waals Gas",
"token_count": 504,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-ed... |
Show that the internal energy of (a) an ideal gas and (b) an incompressible substance is a function of temperature only, u = u(T).
**SOLUTION** It is to be shown that u = u(T) for ideal gases and incompressible substances.
**Analysis** The differential change in the internal energy of a general simple compressible ... | {
"Header 1": "EXAMPLE 12-8 Internal Energy as a Function of Temperature Alone",
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} |
The internal energies and specific heats of ideal gases and incompressible substances depend on temperature only. **Analysis** This relation is easily proved by showing that the right-hand side of Eq. 12–46 is equivalent to the gas constant *R* of the ideal gas:
$$\begin{split} c_p - c_{_{\boldsymbol{U}}} &= -T \Bigg... | {
"Header 1": "EXAMPLE 12-9 The Specific Heat Difference of an Ideal Gas",
"Header 3": "**FIGURE 12-11**",
"token_count": 378,
"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"
} |
When a fluid passes through a restriction such as a porous plug, a capillary tube, or an ordinary valve, its pressure decreases. As we have shown in Chap. 5, the enthalpy of the fluid remains approximately constant during such a throttling process. You will remember that a fluid may experience a large drop in its tempe... | {
"Header 1": "EXAMPLE 12-9 The Specific Heat Difference of an Ideal Gas",
"Header 3": "12-5 • THE JOULE-THOMSON COEFFICIENT",
"token_count": 1084,
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An alternative process path to evaluate the enthalpy changes of real gases.
Substituting this into Eq. 12-52 yields
$$\mu_{\rm JT} = \frac{-1}{c_p} \left[ \mathbf{V} - T \left( \frac{\partial \mathbf{U}}{\partial T} \right)_p \right] = \frac{-1}{c_p} \left( \mathbf{V} - T \frac{R}{P} \right) = -\frac{1}{c_p} (\math... | {
"Header 1": "EXAMPLE 12–10 Joule-Thomson Coefficient of an Ideal Gas Show that the Joule-Thomson coefficient of an ideal gas is zero. SOLUTION It is to be shown that $\\mu_{JT} = 0$ for an ideal gas. Analysis For an ideal gas V = RT/P, and thus $\\left(\\frac{\\partial U}{\\partial T}\\right)_{P} = \\frac{R}{P}$",
... |
The enthalpy of a real gas, in general, depends on the pressure as well as on the temperature. Thus the enthalpy change of a real gas during a process can be evaluated from the general relation for dh (Eq. 12–36)
$$h_2 - h_1 = \int_{T_1}^{T_2} c_p dT + \int_{P_1}^{P_2} \left[ \mathbf{U} - T \left( \frac{\partial \mat... | {
"Header 1": "EXAMPLE 12–10 Joule-Thomson Coefficient of an Ideal Gas Show that the Joule-Thomson coefficient of an ideal gas is zero. SOLUTION It is to be shown that $\\mu_{JT} = 0$ for an ideal gas. Analysis For an ideal gas V = RT/P, and thus $\\left(\\frac{\\partial U}{\\partial T}\\right)_{P} = \\frac{R}{P}$",
... |
The entropy change of a real gas is determined by following an approach similar to that used above for the enthalpy change. There is some difference in derivation, however, owing to the dependence of the ideal-gas entropy on pressure as well as the temperature.
The general relation for ds was expressed as (Eq. 12–41)... | {
"Header 1": "$T_2$ Actual process path 2 $b^*$ $P_1$ Alternative process path",
"Header 3": "**Entropy Changes of Real Gases**",
"token_count": 1392,
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Propane is compressed isothermally by a piston–cylinder device from 200°F and 200 psia to 800 psia (Fig. 12–18). Using the generalized charts, determine the work done and the heat transfer per unit mass of propane.
**SOLUTION** Propane is compressed isothermally by a piston–cylinder device. The work done and the heat... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"token_count": 1407,
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} |
Some thermodynamic properties can be measured directly, but many others cannot. Therefore, it is necessary to develop some relations between these two groups so that the properties that cannot be measured directly can be evaluated. The derivations are based on the fact that properties are point functions, and the state... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "**SUMMARY**",
"token_count": 1502,
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} |
- **12–1C** What is the difference between partial differentials and ordinary differentials?
- **12–2C** Consider the function z(x, y). Plot a differential surface on x-y-z coordinates and indicate $\partial x$ , $\partial x$ , $\partial y$ , $\partial y$ , $\partial z$ , $\partial z$ , and $\partial z$ .
- **12... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "**Partial Derivatives and Associated Relations**",
"token_count": 851,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.p... |
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