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Most diets are based on *calorie counting;* that is, the conservation of energy principle: a person who consumes more calories than his or her body burns will gain weight whereas a person who consumes fewer calories than his or her body burns will lose weight. Yet, people who eat whatever they want whenever they want w... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**Dieting**",
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Approximate energy consumption of a 68-kg adult during some activities (1 Calorie = 4.1868 kJ = 3.968 Btu)
| Activity | Calories/h |
|------------------------|------------|
| Basal metabolism | 72 |
| Basketball | 550 |
| Bicycling (21 km/h) | 639 |
| Cross-cou... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**TABLE 4–2**",
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The body tends to keep the body fat level at a *set point* by speeding up metabolism when a person splurges and by slowing it down when the person starves.
Regular moderate exercise is part of any healthy dieting program for good reason: It builds or preserves muscle tissue that burns calories much faster than the fa... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**FIGURE 4–42**",
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The range of healthy weight for adults of various heights (Source: National Institute of Health)
| English | English units | | |
|---------|---------------|---------|---------|
| | Healthy | | Healthy |
| Height | weight, | Height, | weight, |
| in | lbm* | m... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "TABLE 4-3",
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A 90-kg man had two hamburgers, a regular serving of french fries, and a 200-ml Coke for lunch (Fig. 4–43). Determine how long it will take for him to burn the lunch calories off (a) by watching TV and (b) by fast swimming. What would your answers be for a 45-kg man?
**SOLUTION** A man had lunch at a restaurant. The ... | {
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"Header 3": "**EXAMPLE 4-14** Burning Off Lunch Calories",
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The fake fat olestra passes through the body undigested, and thus adds zero calorie to the diet. Although foods cooked with olestra taste pretty good, they may cause abdominal discomfort, and the long-term effects are unknown. A 1-oz (28.3-g) serving of regular potato chips has 10 g of fat and 150 Calories, whereas 1 o... | {
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Work is the energy transferred as a force acts on a system through a distance. The most common form of mechanical work is the *boundary work*, which is the work associated with the expansion and compression of substances. On a *P-V* diagram, the area under the process curve represents
the boundary work for a quasi-eq... | {
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"Header 3": "**SUMMARY**",
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**4–5E** Calculate the total work, in Btu, produced by the process of Fig. P4–5E.
**FIGURE P4–5E**
\* 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 the SI users can ignore th... | {
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"Header 3": "**FIGURE P4–4**",
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When the volume reaches $0.2 \text{ m}^3$ , the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the piston rises 20 cm more. Determine (a) the final pressure and temperature and (b) the work done during this process. Also, show the process on a P-V diagram.... | {
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"Header 3": "**FIGURE P4–4**",
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**4–27E** A closed system like that shown in Fig. P4–27E is operated in an adiabatic manner. First, 15,000 lbf·ft of work are done by this system. Then, work is applied to the stirring device to raise the internal energy of the fluid by 10.28 Btu. Calculate the net increase in the internal energy of this system.
![](... | {
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"Header 3": "**Closed System Energy Analysis**",
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**4–30** A substance is contained in a well-insulated rigid container that is equipped with a stirring device, as shown in Fig. P4–30. Determine the change in the internal energy of this substance when 15 kJ of work is applied to the stirring device.
FIGURE P4-30
- **4–31** A 0.5-m³... | {
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"Header 3": "FIGURE P4-29",
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- **4–45C** Is the energy required to heat air from 295 to 305 K the same as the energy required to heat it from 345 to 355 K? Assume the pressure remains constant in both cases.
- **4–46C** A fixed mass of an ideal gas is heated from 50 to 80°C at a constant pressure of (*a*) 1 atm and (*b*) 3 atm. For which case do y... | {
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"Header 3": "**Specific Heats, Δu, and Δh of Ideal Gases**",
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- **4–57C** Is it possible to compress an ideal gas isothermally in an adiabatic piston–cylinder device? Explain.
- **4–58** Nitrogen in a rigid vessel is cooled by rejecting 100 kJ/kg of heat. Determine the internal energy change of the nitrogen, in kJ/kg.
- **4–59E** Nitrogen at 100 psia and 300°F in a rigid containe... | {
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"Header 3": "**Closed-System Energy Analysis: Ideal Gases**",
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**FIGURE P4–77**
**4–78** A piston–cylinder device whose piston is resting on top of a set of stops initially contains 0.5 kg of helium gas at 100 kPa and 25°C. The mass of the piston is such that 500 kPa of pressure is required to raise it. How much heat must be transferred to the ... | {
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"Header 3": "**Closed-System Energy Analysis: Ideal Gases**",
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- **4–80** A 1-kg block of iron is heated from 25 to 75°C. What is the change in the iron's total internal energy and enthalpy?
- **4–81E** The state of liquid water is changed from 50 psia and 50°F to 2000 psia and 100°F. Determine the change in the internal energy and enthalpy of water on the basis of the (*a*) compr... | {
"Header 1": "EXAMPLE 4-15 Losing Weight by Switching to Fat-Free Chips",
"Header 3": "**Closed-System Energy Analysis: Solids and Liquids**",
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**4–87** Long cylindrical steel rods (*ρ* = 7833 kg/m3 and *cp* = 0.465 kJ/kg·°C) of 8 cm diameter are heat-treated by drawing them at a velocity of 2 m/min through an oven maintained at 900°C. If the rods enter the oven at 30°C and leave at a mean temperature of 500°C, determine the rate of heat transfer to the rods i... | {
"Header 1": "EXAMPLE 4-15 Losing Weight by Switching to Fat-Free Chips",
"Header 3": "**FIGURE P4–86E**",
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- **4–91C** For what is the energy released during metabolism in humans used?
- **4–92C** Is the metabolizable energy content of a food the same as the energy released when it is burned in a bomb calorimeter? If not, how does it differ?
- **4–93C** Is the number of prospective occupants an important consideration in th... | {
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"Header 3": "**Special Topic: Biological Systems**",
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- **4–109** Which of two gases—neon or air—requires less work when compressed in a closed system from *P*1 to *P*2 using a polytropic process with *n* = 1.5?
- **4–110** Which of two gases—neon or air—produces more work when expanded from *P*1 to *P*2 in a closed-system polytropic process with *n* = 1.2?
- **4–111** Co... | {
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**4–128** Water is boiled at sea level in a coffeemaker equipped with an immersion-type electric heating element. The coffeemaker contains 1 L of water when full. Once boiling starts, it is observed that half of the water in the coffeemaker evaporates in 13 min. Determine the power rating of the electric heating elemen... | {
"Header 1": "EXAMPLE 4-15 Losing Weight by Switching to Fat-Free Chips",
"Header 3": "**FIGURE P4–127**",
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**4–144** In solar-heated buildings, energy is often stored as sensible heat in rocks, concrete, or water during the day for use at night. To minimize the storage space, it is desirable to use a material that can store a large amount of heat while experiencing a small temperature change. A large amount of heat can be s... | {
"Header 1": "EXAMPLE 4-15 Losing Weight by Switching to Fat-Free Chips",
"Header 3": "**FIGURE P4–143**",
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**4–145** A 3-m<sup>3</sup> rigid tank contains nitrogen gas at 500 kPa and 300 K. Now heat is transferred to the nitrogen in the tank and the pressure of nitrogen rises to 800 kPa. The work done during this process is
(*a*) 500 kJ (*b*) 1500 kJ (*c*) 0 kJ
(*d*) 900 kJ (*e*) 2400 kJ
**4–146** A 0.5-m3 rigid tank ... | {
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"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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The change in enthalpy is, in kJ/kg,
(a) 30
(b) 70
(c) 100
(d) insufficient information to determine
2. The change in internal energy is, in kJ/kg,
(b) 70(d) insufficient information to determine
3. The work done is, in kJ/kg,
(a) 30
(b) 70
(c) 100
(d) insufficient information to determine
4. Th... | {
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**4–163** Find out how the specific heats of gases, liquids, and solids are determined in national laboratories. Describe the experimental apparatus and the procedures used.
**4–164** You are asked to design a heating system for a swimming pool that is 2 m deep, 25 m long, and 25 m wide. Your client wants the heating... | {
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"Header 3": "**Design and Essay Problems**",
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The objectives of Chapter 5 are to:
- Develop the conservation of mass principle.
- Apply the conservation of mass principle to various systems including steady- and unsteadyflow control volumes.
- Apply the first law of thermodynamics as the statement of the conservation of energy principle to control volumes.
- Ide... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "**OBJECTIVES**",
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The conservation of mass principle is one of the most fundamental principles in nature. We are all familiar with this principle, and it is not difficult to understand. A person does not have to be a rocket scientist to figure out how much vinegar-and-oil dressing will be obtained by mixing 100 g of oil with 25 g of vin... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "5-1 • CONSERVATION OF MASS",
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The amount of mass flowing through a cross section per unit time is called the **mass flow rate** and is denoted by $\dot{m}$ . The dot over a symbol is used to indicate *time rate of change*.
A fluid flows into or out of a control volume, usually through pipes or ducts. The differential mass flow rate of fluid flow... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "**Mass and Volume Flow Rates**",
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The **conservation of mass principle** for a control volume can be expressed as: The net mass transfer to or from a control volume during a time interval $\Delta t$ is equal to the net change (increase or decrease) of the total mass within the control volume during $\Delta t$ . That is,
$$\begin{pmatrix} \text{Tot... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "**Conservation of Mass Principle**",
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The differential control volume dV and the differential control surface dA used in the derivation of the conservation of mass relation.
the velocity may cross dA at an angle $\theta$ off the normal of dA, and the mass flow rate is proportional to the normal component of velocity $\vec{V}_n = \vec{V} \cos \theta$ ... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "FIGURE 5-6",
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Conservation of mass principle for a two-inlet-one-outlet steady-flow system.
more convenient to work with. A control volume should not introduce any unnecessary complications. A wise choice of a control volume can make the solution of a seemingly complicated problem rather easy. A simple rule in selecting a control ... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "FIGURE 5-8",
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During a steady-flow process, the total amount of mass contained within a control volume does not change with time ( $m_{\rm CV} = {\rm constant}$ ). Then the conservation of mass principle requires that the total amount of mass entering a control volume equal the total amount of mass leaving it. For a garden hose nozz... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "Mass Balance for Steady-Flow Processes",
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The conservation of mass relations can be simplified even further when the fluid is incompressible, which is usually the case for liquids. Canceling the density from both sides of the general steady-flow relation gives
Steady, incompressible flow:
$$\sum_{i} \dot{V} = \sum_{m} \dot{V}$$
(m<sup>3</sup>/s) (5–20)
For... | {
"Header 1": "**M A S S A N D E N E R G Y A N A LY S I S O F C O N T R O L VOLUMES**",
"Header 3": "**Special Case: Incompressible Flow**",
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A garden hose attached with a nozzle is used to fill a 10-gal bucket. The inner diameter of the hose is 2 cm, and it reduces to 0.8 cm at the nozzle exit (Fig. 5–10). If it takes 50 s to fill the bucket with water, determine (a) the volume and mass flow rates of water through the hose, and (b) the average velocity of w... | {
"Header 1": "EXAMPLE 5-1 Water Flow Through a Garden Hose Nozzle",
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A 4-ft-high, 3-ft-diameter cylindrical water tank whose top is open to the atmosphere is initially filled with water. Now the discharge plug near the bottom of the tank is pulled out, and a water jet whose diameter is 0.5 in streams out (Fig. 5–11). The average velocity of the jet is approximated as $V = \sqrt{2gh}$ ,... | {
"Header 1": "FIGURE 5–10 Schematic for Example 5–1. © John M. Cimbala",
"Header 3": "EXAMPLE 5-2 Discharge of Water from a Tank",
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To obtain a relation for flow work, consider a fluid element of volume V as shown in Fig. 5–12. The fluid immediately upstream forces this fluid element to enter the control volume; thus, it can be regarded as an imaginary piston. The fluid element can be chosen to be sufficiently small ... | {
"Header 1": "5-2 • FLOW WORK AND THE ENERGY OF A FLOWING FLUID",
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As we discussed in Chap. 2, the total energy of a simple compressible system consists of three parts: internal, kinetic, and potential energies (Fig. 5–15). On a unit-mass basis, it is expressed as
$$e = u + \text{ke} + \text{pe} = u + \frac{V^2}{2} + gz$$
(kJ/kg) (5–25)
where V is the velocity and z is the elevati... | {
"Header 1": "5-2 • FLOW WORK AND THE ENERGY OF A FLOWING FLUID",
"Header 3": "**Total Energy of a Flowing Fluid**",
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Noting that $\theta$ is total energy per unit mass, the total energy of a flowing fluid of mass m is simply $m\theta$ , provided that the properties of the mass m are uniform. Also, when a fluid stream with uniform properties is flowing at a mass flow rate of $\dot{m}$ , the rate of energy flow with that stream is ... | {
"Header 1": "5-2 • FLOW WORK AND THE ENERGY OF A FLOWING FLUID",
"Header 3": "**Energy Transport by Mass**",
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Air flows steadily in a pipe at 300 kPa, 77°C, and 25 m/s at a rate of 18 kg/min (Fig. 5–17). Determine (a) the diameter of the pipe, (b) the rate of flow energy, (c) the rate of energy transport by mass, and (d) the error involved in part c if the kinetic energy is neglected.
**SOLUTION** Air flows steadily in a pip... | {
"Header 1": "5-2 • FLOW WORK AND THE ENERGY OF A FLOWING FLUID",
"Header 3": "**EXAMPLE 5–3** Energy Transport by Flowing Air",
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Schematic for Example 5–3.
**Analysis** (a) The diameter is determined as follows:
$$V = \frac{RT}{P} = \frac{(0.287 \text{ kJ/kg} \cdot \text{K})(77 + 273 \text{ K})}{300 \text{ kPa}} = 0.3349 \text{ m}^3/\text{kg}$$
$$A = \frac{\dot{m} v}{V} = \frac{(18/60 \text{ kg/s})(0.3349 \text{ m}^3/\text{kg})}{25 \text{ ... | {
"Header 1": "5-2 • FLOW WORK AND THE ENERGY OF A FLOWING FLUID",
"Header 3": "**FIGURE 5-17**",
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A large number of engineering devices such as turbines, compressors, and nozzles operate for long periods of time under the same conditions once the transient start-up period is completed and steady operation is established, and they are classified as *steady-flow devices* (Fig. 5–18). Processes involving such devices ... | {
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Under steady-flow conditions, the fluid properties at an inlet or exit remain constant (do not change with time).
FIGURE 5-21
A water heater in steady operation.
or
$$\dot{Q}_{\rm in} + \dot{W}_{\rm in} + \sum_{\rm in} \underline{\dot{m}} \left( h + \frac{V^2}{2} + gz \right) = \... | {
"Header 1": "5-3 • ENERGY ANALYSIS OF STEADY-FLOW SYSTEMS",
"Header 3": "**FIGURE 5-20**",
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Nozzles and diffusers are commonly utilized in jet engines, rockets, space-craft, and even garden hoses. A **nozzle** is a device that *increases the velocity of a fluid* at the expense of pressure. A **diffuser** is a device that *increases the pressure of a fluid* by slowing it down. That is, nozzles and diffusers pe... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "1 Nozzles and Diffusers",
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Air at $10^{\circ}$ C and 80 kPa enters the diffuser of a jet engine steadily with a velocity of 200 m/s. The inlet area of the diffuser is 0.4 m<sup>2</sup>. The air leaves the diffuser with a velocity that is very small compared with the inlet velocity. Determine (a) the mass flow rate of the air and (b) the tempera... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "■ EXAMPLE 5-4 Deceleration of Air in a Diffuser",
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Steam at 250 psia and 700°F steadily enters a nozzle whose inlet area is 0.2 ft<sup>2</sup>. The mass flow rate of steam through the nozzle is 10 lbm/s. Steam leaves the nozzle at 200 psia with a velocity of 900 ft/s. Heat losses from the nozzle per unit mass of the steam are estimated to be 1.2 Btu/lbm. Determine (*a*... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "**EXAMPLE 5-5** Acceleration of Steam in a Nozzle",
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In steam, gas, or hydroelectric power plants, the device that drives the electric generator is the turbine. As the fluid passes through the turbine, work is done against the blades, which are attached to the shaft. As a result, the shaft rotates, and the turbine produces work (Fig. 5–29).
Compressors, as well as pump... | {
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"Header 3": "2 Turbines and Compressors",
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Schematic for Example 5–7.
**SOLUTION** Air is compressed steadily by a compressor to a specified temperature and pressure. The power input to the compressor is to be determined.
**Assumptions** 1 This is a steady-flow process since there is no change with time at any point and thus $\Delta m_{\rm CV} = 0$ and $... | {
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"Header 3": "**FIGURE 5-31**",
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The power output of an adiabatic steam turbine is 5 MW, and the inlet and the exit conditions of the steam are as indicated in Fig. 5–31. (a) Compare the magnitudes of $\Delta h$ , $\Delta ke$ , and $\Delta pe$ . (b) Determine the work done per unit mass of the steam flowing through the turbine. (c) Calculate the ma... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "**EXAMPLE 5-7** Power Generation by a Steam Turbine",
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Throttling valves are *any kind of flow-restricting devices* that cause a significant pressure drop in the fluid. Some familiar examples are ordinary adjustable valves, capillary tubes, and porous plugs (Fig. 5–32). Unlike turbines, they produce a pressure drop without involving any work. The pressure drop in the fluid... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "**3 Throttling Valves**",
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Refrigerant-134a enters the capillary tube of a refrigerator as saturated liquid at 0.8 MPa and is throttled to a pressure of 0.12 MPa. Determine the quality of the refrigerant at the final state and the temperature drop during this process.
**SOLUTION** Refrigerant-134a that enters a capillary tube as saturated liqu... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "**EXAMPLE 5–8 Expansion of Refrigerant-134a in a Refrigerator**",
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In engineering applications, mixing two streams of fluids is not a rare occurrence. The section where the mixing process takes place is commonly referred to as a **mixing chamber**. The mixing chamber does not have to be a distinct "chamber." An ordinary T-elbow or a Y-elbow in a shower, for example, serves as the mixi... | {
"Header 1": "5-4 • SOME STEADY-FLOW ENGINEERING DEVICES",
"Header 3": "4a Mixing Chambers",
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Consider an ordinary shower where hot water at 140°F is mixed with cold water at 50°F. If it is desired that a steady stream of warm water at 110°F be supplied, determine the ratio of the mass flow rates of the hot to cold water. Assume the heat losses from the mixing chamber to be negligible and the mixing to take pla... | {
"Header 1": "T<sub>sat</sub> Compressed liquid states",
"Header 3": "**EXAMPLE 5-9** Mixing of Hot and Cold Waters in a Shower",
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As the name implies, **heat exchangers** are devices where two moving fluid streams exchange heat without mixing. Heat exchangers are widely used in various industries, and they come in various designs.
The simplest form of a heat exchanger is a *double-tube heat exchanger*, shown in Fig. 5–38. It is composed of two ... | {
"Header 1": "T<sub>sat</sub> Compressed liquid states",
"Header 3": "**4b Heat Exchangers**",
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Refrigerant-134a is to be cooled by water in a condenser. The refrigerant enters the condenser with a mass flow rate of 6 kg/min at 1 MPa and 70°C and leaves at 35°C. The cooling water enters at 300 kPa and 15°C and leaves at 25°C. Neglecting any pressure drops, determine (*a*) the mass flow rate of the cooling water r... | {
"Header 1": "T<sub>sat</sub> Compressed liquid states",
"Header 3": "**EXAMPLE 5–10** Cooling of Refrigerant-134a by Water",
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The transport of liquids or gases in pipes and ducts is of great importance in many engineering applications. Flow through a pipe or a duct usually satisfies the steady-flow conditions and thus can be analyzed as a steady-flow process. This, of course, excludes the transient start-up and shut-down periods. The control ... | {
"Header 1": "T<sub>sat</sub> Compressed liquid states",
"Header 3": "**5 Pipe and Duct Flow**",
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The error involved in $\Delta h = c_p \Delta T$ , where $c_p = 1.005$ kJ/kg.°C, is less than 0.5 percent for air in the temperature range -20 to 70°C.
temperature difference between the flowing fluid and the surroundings is large. Heat transfer in this case is negligible.
If the control volume involves a heating... | {
"Header 1": "T<sub>sat</sub> Compressed liquid states",
"Header 3": "**FIGURE 5-45**",
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The electric heating systems used in many houses consist of a simple duct with resistance heaters. Air is heated as it flows over resistance wires. Consider a 15-kW electric heating system. Air enters the heating section at 100 kPa and 17°C with a volume flow rate of 150 m³/min. If heat is lost from the air in the duct... | {
"Header 1": "T<sub>sat</sub> Compressed liquid states",
"Header 3": "**EXAMPLE 5–11** Electric Heating of Air in a House",
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During a steady-flow process, no changes occur within the control volume; thus, one does not need to be concerned about what is going on within the boundaries. Not having to worry about any changes within the control volume with time greatly simplifies the analysis.
Many processes of interest, however, involve *chang... | {
"Header 1": "5-5 • ENERGY ANALYSIS OF UNSTEADY-FLOW PROCESSES",
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The shape and size of a control volume may change during an unsteady-flow process.
$m_i = 0$ if no mass enters the control volume during the process, $m_e = 0$ if no mass leaves, and $m_1 = 0$ if the control volume is initially evacuated.
The energy content of a control volume changes with time during an unste... | {
"Header 1": "5-5 • ENERGY ANALYSIS OF UNSTEADY-FLOW PROCESSES",
"Header 3": "**FIGURE 5-47**",
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A rigid, insulated tank that is initially evacuated is connected through a valve to a supply line that carries steam at 1 MPa and 300°C. Now the valve is opened, and steam is allowed to flow slowly into the tank until the pressure reaches 1 MPa, at which point the valve is closed. Determine the final temperature of the... | {
"Header 1": "5-5 • ENERGY ANALYSIS OF UNSTEADY-FLOW PROCESSES",
"Header 3": "■ EXAMPLE 5-12 Charging of a Rigid Tank by Steam",
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The temperature of steam rises from 300 to 456.1°C as it enters a tank as a result of flow energy being converted to internal energy.
Combining the mass and energy balances gives
$$u_2 = h_i$$
That is, the final internal energy of the steam in the tank is equal to the enthalpy of the steam entering the tank. The ... | {
"Header 1": "**FIGURE 5–50** Schematic for Example 5–12.",
"Header 3": "FIGURE 5-51",
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An insulated 8-m<sup>3</sup> rigid tank contains air at 600 kPa and 400 K. A valve connected to the tank is now opened, and air is allowed to escape until the pressure inside drops to 200 kPa. The air temperature during the process is maintained constant by an electric resistance heater placed in the tank. Determine th... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
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One of the most fundamental laws in nature is the **first law of thermodynamics**, also known as the **conservation of energy principle**, which provides a sound basis for studying the relationships among the various forms of energy and energy interactions. It states that *energy can be neither created nor destroyed du... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "TOPIC OF SPECIAL INTEREST\\* General Energy Equation",
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The pressure force acting on (a) the moving boundary of a system in a piston–cylinder device, and (b) the differential surface area of a system of arbitrary shape.
This section can be skipped without a loss in continuity.
piston, the boundary work done *on* the system is $\delta W_{\text{boundary}} = PA \, ds$ . D... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE 5-53**",
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... |
The conservation of energy equation is obtained by replacing an extensive property *B* in the Reynolds transport theorem with energy *E* and its associated intensive property *b* with *e* (Ref. 3).
which can be stated as
The net rate of energy transfer into a CV by heat and work transfer
$$=$$
The time rate of chan... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE 5-54**",
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... |
In a typical engineering problem, the control volume may contain many inlets and outlets; energy flows in at each inlet, and energy flows out at each outlet. Energy also enters the control volume through net heat transfer and net shaft work.
or
$$\dot{Q}_{\text{net,in}} - \dot{W}_{\text{shaft,net out}} = \frac{d}{d... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "FIGURE 5-55",
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The *conservation of mass principle* states that the net mass transfer to or from a system during a process is equal to the net change (increase or decrease) in the total mass of the system during that process, and it is expressed as
$$m_{\rm in} - m_{\rm out} = \Delta m_{\rm system}$$
and $\dot{m}_{\rm in} - \dot{m... | {
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"Header 3": "**SUMMARY**",
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- **5–1C** Name four physical quantities that are conserved and two quantities that are not conserved during a process.
- **5–2C** Define mass and volume flow rates. How are they related to each other?
- **5–3C** Does the amount of mass entering a control volume have to be equal to the amount of mass leaving during an ... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Conservation of Mass**",
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**5–7E** A steam pipe is to transport 200 lbm/s of steam at 200 psia and 600°F. Calculate the minimum diameter this pipe can have so that the steam velocity does not exceed 59 ft/s. *Answer*: 3.63 ft
**5–8E** A garden hose attached with a nozzle is used to fill a 20-gal bucket. The inner diameter of the hose is 1 in ... | {
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"Header 3": "FIGURE P5-6",
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- **5–18C** What are the different mechanisms for transferring energy to or from a control volume?
- **5–19C** How do the energies of a flowing fluid and a fluid at rest compare? Name the specific forms of energy associated with each case.
- **5–20** An air compressor compresses 6 L of air at 120 kPa and 20°C to 1000 k... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Flow Work and Energy Transfer by Mass**",
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- **5–24C** How is a steady-flow system characterized?
- **5–25C** Can a steady-flow system involve boundary work?
- **5–26C** A diffuser is an adiabatic device that decreases the kinetic energy of the fluid by slowing it down. What happens to this *lost* kinetic energy?
- **5–27C** The kinetic energy of a fluid increa... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Steady-Flow Energy Balance: Nozzles and Diffusers**",
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- **5–34** Air at 80 kPa and 127°C enters an adiabatic diffuser steadily at a rate of 6000 kg/h and leaves at 100 kPa. The velocity of the airstream is decreased from 230 to 30 m/s as it passes through the diffuser. Find (*a*) the exit temperature of the air and (*b*) the exit area of the diffuser.
- **5–35E** Air at 1... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5–33**",
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- **5–36** Refrigerant-134a at 700 kPa and 120°C enters an adiabatic nozzle steadily with a velocity of 20 m/s and leaves at 400 kPa and 30°C. Determine (a) the exit velocity and (b) the ratio of the inlet to exit area $A_1/A_2$ .
- **5–37** Refrigerant-134a enters a diffuser steadily as saturated vapor at 600 kPa wit... | {
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"Header 3": "FIGURE P5-35E",
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- **5–41C** Consider an adiabatic turbine operating steadily. Does the work output of the turbine have to be equal to the decrease in the energy of the steam flowing through it?
- **5–42**C Will the temperature of air rise as it is compressed by an adiabatic compressor? Why?
- **5–43C** Somebody proposes the followin... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Turbines and Compressors**",
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**5–49** Reconsider Prob. 5–48. Using appropriate software, investigate the effect of the turbine exit pressure on the power output of the turbine. Let the exit pressure vary from 10 to 200 kPa. Plot the power output against the exit pressure, and discuss the results.
- **5–50E** Steam flows steadily through a turbin... | {
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"Header 3": "FIGURE P5-48",
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- **5–58C** Why are throttling devices commonly used in refrigeration and air-conditioning applications?
- **5–59C** Would you expect the temperature of air to drop as it undergoes a steady-flow throttling process? Explain.
- **5–60C** During a throttling process, the temperature of a fluid drops from 30 to –20°C. Can ... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Throttling Valves**",
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- **5–64** An adiabatic capillary tube is used in some refrigeration systems to drop the pressure of the refrigerant from the condenser level to the evaporator level. The R-134a enters the capillary tube as a saturated liquid at $50^{\circ}$ C and leaves at $-20^{\circ}$ C. Determine the quality of the refrigerant at... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "FIGURE P5-63",
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**5–69C** Consider a steady-flow mixing process. Under what conditions will the energy transported into the control volume by the incoming streams be equal to the energy transported out of it by the outgoing stream?
- **5–70C** Consider a steady-flow heat exchanger involving two different fluid streams. Under what co... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Mixing Chambers and Heat Exchangers**",
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5–77 Cold water ( $c_p = 4.18 \text{ kJ/kg} \cdot ^{\circ}\text{C}$ ) leading to a shower enters a thin-walled double-pipe counterflow heat exchanger at 15°C at a rate of 0.60 kg/s and is heated to 45°C by hot water ( $c_p = 4.19 \text{ kJ/kg} \cdot ^{\circ}\text{C}$ ) that enters at 100°C at a rate of 3 kg/s. Determin... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "FIGURE P5-76",
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} |
**5–80E** An open feedwater heater heats the feedwater by mixing it with hot steam. Consider an electric power plant with an
open feedwater heater that mixes 0.1 lbm/s of steam at 10 psia and 200°F with 2.0 lbm/s of feedwater at 10 psia and 100°F to produce 10 psia and 120°F feedwater at the outlet. The diameter of t... | {
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"Header 3": "FIGURE P5-79",
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5–82 The evaporator of a refrigeration cycle is basically a heat exchanger in which a refrigerant is evaporated by absorbing heat from a fluid. Refrigerant-22 enters an evaporator at 200 kPa with a quality of 22 percent and a flow rate of 2.65 L/h. R-22 leaves the evaporator at the same pressure superheated by 5°C. The... | {
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"Header 3": "FIGURE P5-81",
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- **5–90** Water is heated in an insulated, constant-diameter tube by a 7-kW electric resistance heater. If the water enters the heater steadily at 20°C and leaves at 75°C, determine the mass flow rate of water.
- **5–91** A 110-volt electrical heater is used to warm 0.3 m3 /s of air at 100 kPa and 15°C to 100 kPa and ... | {
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**5–103** Reconsider Prob. 5–102. Using appropriate software, investigate the effect of the moving velocity of the steel plate on the rate of heat transfer from the oil bath. Let the velocity vary from 5 to 50 m/min. Plot the rate of heat transfer against the plate velocity, and discuss the results.
**5–104E** The ho... | {
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"Header 3": "**FIGURE P5–102**",
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**5–108** A hair dryer is basically a duct in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. Air enters a 1200-W hair dryer at 100 kPa and 22°C and leaves at 47°C. The cross-sectional area of the hair dryer at the exit is 60 cm<s... | {
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"Header 3": "**FIGURE P5–107**",
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**5–112** An insulated rigid tank is initially evacuated. A valve is opened, and atmospheric air at 95 kPa and 17°C enters the tank until the pressure in the tank reaches 95 kPa, at which point the valve is closed. Determine the final temperature of the air in the tank. Assume constant specific heats.
**5–113** A rig... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Charging and Discharging Processes**",
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**5–116** A 2-m<sup>3</sup> rigid tank initially contains air at 100 kPa and 22°C. The tank is connected to a supply line through a valve. Air is flowing in the supply line at 600 kPa and 22°C. The valve is opened, and air is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which p... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5–115**",
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A valve connected to the cylinder is now opened, and air is allowed to escape until three-quarters of the mass leaves the cylinder, at which point the volume is 0.05 m3 . Determine the final temperature in the cylinder and the boundary work during this process.
**FIGURE P5–130**
- **... | {
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"Header 3": "**FIGURE P5–115**",
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- **5–136** Underground water is being pumped into a pool whose cross section is 6 m × 9 m while water is discharged through a 7-cm-diameter orifice at a constant average velocity of 4 m/s. If the water level in the pool rises at a rate of 2.5 cm/ min, determine the rate at which water is supplied to the pool, in m<sup... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Review Problems**",
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**5–150** Saturated steam at 1 atm condenses on a vertical plate that is maintained at 90°C by circulating cooling water through the other side. If the rate of heat transfer by condensation to the plate is 180 kJ/s, determine the rate at which the condensate drips off the plate at the bottom.
![](_page_286_Picture_14... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5-149E**",
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**5–163** Repeat Prob. 5–162 for a copper wire (*ρ* = 8950 kg/m<sup>3</sup> and *cp* = 0.383 kJ/kg·°C).
**5–164E** Steam at 80 psia and 400°F is mixed with water at 60°F and 80 psia steadily in an adiabatic device. Steam enters the device at a rate of 0.05 lbm/s, while the water enters at 1 lbm/s. Determine the tempe... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5–162**",
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**5–166E** It is well established that indoor air quality (IAQ) has a significant effect on general health and productivity of employees at a workplace. A study showed that enhancing IAQ by increasing the building ventilation from 5 cfm (cubic feet per minute) to 20 cfm increased the productivity by 0.25 percent, value... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5–165**",
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**5–180** It is proposed to have a water heater that consists of an insulated pipe of 7.5-cm diameter and an electric resistor inside. Cold water at 20°C enters the heating section steadily at a rate of 24 L/min. If water is to be heated to 48°C, determine (*a*) the power rating of the resistance heater and (*b*) the... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5–165**",
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5–188 The turbocharger of an internal combustion engine consists of a turbine and a compressor. Hot exhaust gases flow through the turbine to produce work, and the work output from the turbine is used as the work input to the compressor. The pressure of ambient air is increased as it flows through the compressor before... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5-187**",
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**5–189** A $D_0 = 10$ -m-diameter tank is initially filled with water 2 m above the center of a D = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through a L = 100-m-long pipe connected to the valve. The friction factor of the pipe is given to be f = 0.015, and ... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**FIGURE P5-188**",
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**5–191** An adiabatic heat exchanger is used to heat cold water at 15°C entering at a rate of 5 kg/s with hot air at 90°C entering also at a rate of 5 kg/s. If the exit temperature of hot air is 20°C, the exit temperature of cold water is
(*a*) 27°C (*b*) 32°C (*c*) 52°C
(*d*) 85°C (*e*) 90°C
**5–192** A heat ex... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**5–208** Pneumatic nail drivers used in construction require 0.02 ft<sup>3</sup> of air at 100 psia and 1 Btu of energy to drive a single nail. You have been assigned the task of designing a compressed-air storage tank with enough capacity to drive 500 nails. The pressure in this tank cannot exceed 500 psia, and the t... | {
"Header 1": "**EXAMPLE 5–13** Discharge of Heated Air at Constant Temperature",
"Header 3": "**Design and Essay Problems**",
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The objectives of Chapter 6 are to:
- Introduce the second law of thermodynamics.
- Identify valid processes as those that satisfy both the first and second laws of thermodynamics.
- Discuss thermal energy reservoirs, reversible and irreversible processes, heat engines, refrigerators, and heat pumps.
- Describe the K... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**OBJECTIVES**",
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In Chaps. 4 and 5, we applied the *first law of thermodynamics,* or the *conservation of energy principle,* to processes involving closed and open systems. As pointed out repeatedly in those chapters, energy is a conserved property, and no process is known to have taken place in violation of the first law of thermodyna... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**6–1** ■ **INTRODUCTION TO THE SECOND LAW**",
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In the development of the second law of thermodynamics, it is very convenient to have a hypothetical body with a relatively large *thermal energy capacity* (mass × specific heat) that can supply or absorb finite amounts of heat without undergoing any change in temperature. Such a body is called a **thermal energy reser... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**6–2** ■ **THERMAL ENERGY RESERVOIRS**",
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As pointed out earlier, work can easily be converted to other forms of energy, but converting other forms of energy to work is not that easy. The mechanical work done by the shaft shown in Fig. 6–8, for example, is first converted to the internal energy of the water. This energy may then leave the water as heat. We kno... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**6–3** ■ **HEAT ENGINES**",
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} |
Some heat engines perform better than others (convert more of the heat they receive to work).
**FIGURE 6–13** Schematic of a heat engine.
For heat engines, the desired output is the net work output, and the required input is the amount of heat supplied to the working fluid. Then the ... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "FIGURE 6-12",
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} |
In a steam power plant, the condenser is the device where large quantities of waste heat are rejected to rivers, lakes, or the atmosphere. Then one may ask, can we not just take the condenser out of the plant and save all that waste energy? The answer to this question is, unfortunately, a firm *no* for the simple reaso... | {
"Header 1": "THE SECOND LAW OF THERMODYNAMICS",
"Header 3": "**Can We Save Qout?**",
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} |
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