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- **2–85C** What are the mechanisms of heat transfer?
- **2–86C** Which is a better heat conductor, diamond or silver?
- **2–87C** How does forced convection differ from natural convection?
- **2–88C** What is a blackbody? How do real bodies differ from a blackbody?
- **2–89C** Define emissivity and absorptivity. What ... | {
"Header 1": "EXAMPLE 2-17 Reducing Air Pollution by Geothermal Heating",
"Header 3": "**Special Topic: Mechanisms of Heat Transfer**",
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**2–108** Some engineers have developed a device that provides lighting to rural areas with no access to grid electricity. The device is intended for indoor use. It is driven by gravity, and it works as follows: A bag of rock or sand is raised by human power to a higher location. As the bag descends very slowly, it pow... | {
"Header 1": "EXAMPLE 2-17 Reducing Air Pollution by Geothermal Heating",
"Header 3": "**Review Problems**",
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**2–123** The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90 percent. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the pressures at the inlet and... | {
"Header 1": "EXAMPLE 2-17 Reducing Air Pollution by Geothermal Heating",
"Header 3": "**Review Problems**",
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**2–125** A 2-kW electric resistance heater in a room is turned on and kept on for 50 min. The amount of energy transferred to the room by the heater is
(*d*) 6000 kJ (*e*) 12,000 kJ
(*a*) 2 kJ (*b*) 100 kJ (*c*) 3000 kJ
(*a*) 8.3 L/s (*b*) 7.2 L/s (*c*) 6.8 L/s
(*d*) 12.1 L/s (*e*) 17.8 L/s
volume flow rate ... | {
"Header 1": "EXAMPLE 2-17 Reducing Air Pollution by Geothermal Heating",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**2–135** A 10-cm-high and 20-cm-wide circuit board houses on its surface 100 closely spaced chips, each generating heat at a rate of 0.08 W and transferring it by convection to the surrounding air at 25°C. Heat transfer from the back surface of the board is negligible. If the convection heat transfer coefficient on th... | {
"Header 1": "EXAMPLE 2-17 Reducing Air Pollution by Geothermal Heating",
"Header 3": "**The Following Problems Are Based on the Optional Special Topic of Heat Transfer**",
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- **2–140** An average vehicle puts out nearly 20 lbm of carbon dioxide into the atmosphere for every gallon of gasoline it burns, and thus one thing we can do to reduce global warming is to buy a vehicle with higher fuel economy. A U.S. government publication states that a vehicle that gets 25 rather than 20 miles per... | {
"Header 1": "EXAMPLE 2-17 Reducing Air Pollution by Geothermal Heating",
"Header 3": "**Design and Essay Problems**",
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A substance that has a fixed chemical composition throughout is called a **pure substance**. Water, nitrogen, helium, and carbon dioxide, for example, are all pure substances.
A pure substance does not have to be of a single chemical element or compound, however. A mixture of various chemical elements or compounds al... | {
"Header 1": "PROPERTIES OF PURE SUBSTANCES",
"Header 3": "**3–1** ■ **PURE SUBSTANCE**",
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We all know from experience that substances exist in different phases. At room temperature and pressure, copper is a solid, mercury is a liquid, and nitrogen is a gas. Under different conditions, each may appear in a different phase. Even though there are three principal phases—solid, liquid, and gas—a substance may ha... | {
"Header 1": "PROPERTIES OF PURE SUBSTANCES",
"Header 3": "**3–2** ■ **PHASES OF A PURE SUBSTANCE**",
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Consider a piston–cylinder device containing liquid water at 20°C and 1 atm pressure (state 1, Fig. 3–5). Under these conditions, water exists in the liquid phase, and it is called a **compressed liquid**, or a **subcooled liquid**, meaning that it is *not about to vaporize.* Heat is now transferred to the water until ... | {
"Header 1": "PROPERTIES OF PURE SUBSTANCES",
"Header 3": "**Compressed Liquid and Saturated Liquid**",
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Once boiling starts, the temperature stops rising until the liquid is completely vaporized. That is, the temperature will remain constant during the entire phase-change process if the pressure is held constant. This can easily be verified by placing a thermometer into boiling pure water on top of a stove. At sea level ... | {
"Header 1": "PROPERTIES OF PURE SUBSTANCES",
"Header 3": "**Saturated Vapor and Superheated Vapor**",
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It probably came as no surprise to you that water started to boil at 100°C. Strictly speaking, the statement "water boils at 100°C" is incorrect. The correct statement is "water boils at 100°C at 1 atm pressure." The only reason water started boiling at 100°C was because we held the pressure constant at 1 atm (101.325 ... | {
"Header 1": "**Saturation Temperature and Saturation Pressure**",
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*T-U* diagram for the heating process of water at constant pressure.
**TABLE 3–1**
Saturation (or vapor) pressure of water at various temperatures
| Temperature<br>T, °C | Saturation<br>pressure<br>Psat, kPa |
|----------------------|-------------------------------------|
| | ... | {
"Header 1": "**Saturation Temperature and Saturation Pressure**",
"Header 3": "FIGURE 3-10",
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The liquid–vapor saturation curve of a pure substance (numerical values are for water).
all substances. A partial listing of such a table is given in Table 3–1 for water. This table indicates that the pressure of water changing phase (boiling or condensing) at 25°C must be 3.17 kPa, and the pressure of water must be ... | {
"Header 1": "**Saturation Temperature and Saturation Pressure**",
"Header 3": "**FIGURE 3–11**",
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We mentioned earlier that a substance at a specified pressure boils at the saturation temperature corresponding to that pressure. This phenomenon allows us to control the boiling temperature of a substance by simply controlling the pressure, and it has numerous applications in practice. In this section we give some exa... | {
"Header 1": "**Saturation Temperature and Saturation Pressure**",
"Header 3": "**Some Consequences of Tsat and Psat Dependence**",
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Variation of the standard atmospheric pressure and the boiling (saturation) temperature of water with altitude
| Elevation,<br>m | Atmospheric<br>pressure,<br>kPa | Boiling<br>tempera<br>ture, °C |
|-----------------|---------------------------------|--------------------------------|
| 0 | 101.33 ... | {
"Header 1": "**Saturation Temperature and Saturation Pressure**",
"Header 3": "**TABLE 3–2**",
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The variation of the temperature of fruits and vegetables with pressure during vacuum cooling from 25°C to 0°C.
FIGURE 3-14
In 1775, ice was made by evacuating the airspace in a water tank.
cooling. Products with large surface area per unit mass and a high tendency to release moist... | {
"Header 1": "**Saturation Temperature and Saturation Pressure**",
"Header 3": "**FIGURE 3–13**",
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The phase-change process of water at 1 atm pressure was described in detail in the last section and plotted on a *T*-U diagram in Fig. 3–10. Now we repeat this process at different pressures to develop the *T*-U diagram.
Let us add weights on top of the piston until the pressure inside the cylinder reaches 1 MPa. At ... | {
"Header 1": "3-4 PROPERTY DIAGRAMS FOR PHASE-CHANGE PROCESSES",
"Header 3": "1 The *T*-∪ Diagram",
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The general shape of the P-v diagram of a pure substance is very much like the T-v diagram, but the T = constant lines on this diagram have a downward trend, as shown in Fig. 3–17b.
Consider again a piston–cylinder device that contains liquid water at 1 MPa and 150°C. Water at this state exists as a compressed liquid... | {
"Header 1": "3-4 PROPERTY DIAGRAMS FOR PHASE-CHANGE PROCESSES",
"Header 3": "2 The P-U Diagram",
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The pressure in a piston–cylinder device can be reduced by reducing the weight of the piston.
**FIGURE 3–19** *P-v* diagrams of different substances.
and the solid–vapor saturation regions. The basic principles discussed in conjunction with the liquid–vapor phase-change process apply ... | {
"Header 1": "Extending the Diagrams to Include the Solid Phase",
"Header 3": "FIGURE 3-18",
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The state of a simple compressible substance is fixed by any two independent, intensive properties. Once the two appropriate properties are fixed, all the other properties become dependent properties. Remembering that any equation with two independent variables in the form z = z(x, y) represents a surface in space, we ... | {
"Header 1": "Extending the Diagrams to Include the Solid Phase",
"Header 3": "The P-U-T Surface",
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For most substances, the relationships among thermodynamic properties are too complex to be expressed by simple equations. Therefore, properties are frequently presented in the form of tables. Some thermodynamic properties can be measured easily, but others cannot, and the latter are calculated by using the relations b... | {
"Header 1": "Extending the Diagrams to Include the Solid Phase",
"Header 3": "**3–5** ■ **PROPERTY TABLES**",
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A person looking at the tables will notice two new properties: enthalpy *h* and entropy *s.* Entropy is a property associated with the second law of thermodynamics, and we will not use it until it is properly defined in Chap. 7. However, it is appropriate to introduce enthalpy at this point.
In the analysis of certai... | {
"Header 1": "Extending the Diagrams to Include the Solid Phase",
"Header 3": "**Enthalpy—A Combination Property**",
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The properties of saturated liquid and saturated vapor for water are listed in Tables A–4 and A–5. Both tables give the same information. The only difference is that in Table A–4 properties are listed under temperature and in Table A–5 under pressure. Therefore, it is more convenient to use Table A–4 when *temperature*... | {
"Header 1": "1a Saturated Liquid and Saturated Vapor States",
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A rigid tank contains 50 kg of saturated liquid water at 90°C. Determine the pressure
in the tank and the volume of the tank.
**SOLUTION** A rigid tank contains saturated liquid water. The pressure and volume of the tank are to be determined.
**Analysis** The state of the saturated liquid water is shown on a T-U di... | {
"Header 1": "1a Saturated Liquid and Saturated Vapor States",
"Header 3": "**■ EXAMPLE 3-1** Pressure of Saturated Liquid in a Tank",
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A piston–cylinder device contains 2 ft<sup>3</sup> of saturated water vapor at 50-psia pressure. Determine the temperature and the mass of the vapor inside the cylinder.
**SOLUTION** A cylinder contains saturated water vapor. The temperature and the mass of vapor are to be determined.
**Analysis** The state of the ... | {
"Header 1": "**EXAMPLE 3-2** Temperature of Saturated Vapor in a Cylinder",
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A mass of 200 g of saturated liquid water is completely vaporized at a constant pressure of 100 kPa. Determine (a) the volume change and (b) the amount of energy transferred to the water.
**SOLUTION** Saturated liquid water is vaporized at constant pressure. The volume change and the energy transferred are to be dete... | {
"Header 1": "EXAMPLE 3-3 Volume and Energy Change during Evaporation",
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During a vaporization process, a substance exists as part liquid and part vapor. That is, it is a mixture of saturated liquid and saturated vapor (Fig. 3–31). To analyze this mixture properly, we need to know the proportions of the liquid and vapor phases in the mixture. This is done by defining a new property called t... | {
"Header 1": "EXAMPLE 3-3 Volume and Energy Change during Evaporation",
"Header 3": "1b Saturated Liquid-Vapor Mixture",
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The U value of a saturated liquid—vapor mixture lies between the $U_f$ and $U_o$ values at the specified T or P.
Based on this equation, quality can be related to the horizontal distances on a *P-U* or *T-U* diagram (Fig. 3–33). At a given temperature or pressure, the numerator of Eq. 3–5 is the distance between ... | {
"Header 1": "EXAMPLE 3-3 Volume and Energy Change during Evaporation",
"Header 3": "FIGURE 3-34",
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A rigid tank contains 10 kg of water at 90°C. If 8 kg of the water is in the liquid form and the rest is in the vapor form, determine (a) the pressure in the tank and (b) the volume of the tank.
**SOLUTION** A rigid tank contains saturated mixture. The pressure and the volume of the tank are to be determined.
**Ana... | {
"Header 1": "EXAMPLE 3-3 Volume and Energy Change during Evaporation",
"Header 3": "**EXAMPLE 3-4** Pressure and Volume of a Saturated Mixture",
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An 80-L vessel contains 4 kg of refrigerant-134a at a pressure of 160 kPa. Determine (a) the temperature, (b) the quality, (c) the enthalpy of the refrigerant, and (d) the volume occupied by the vapor phase.
**SOLUTION** A vessel is filled with refrigerant-134a. Some properties of the refrigerant are to be determined... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
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Schematic and *P-v* diagram for Example 3–5.
(d) The mass of the vapor is
$$m_g = x m_t = (0.157)(4 \text{ kg}) = 0.628 \text{ kg}$$
and the volume occupied by the vapor phase is
$$V_g = m_g V_g = (0.628 \text{ kg})(0.12355 \text{ m}^3/\text{kg}) = 0.0776 \text{ m}^3 \text{ (or 77.6 L)}$$
The rest of the volu... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
"Header 3": "FIGURE 3-36",
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In the region to the right of the saturated vapor line and at temperatures above the critical point temperature, a substance exists as superheated vapor. Since the superheated region is a single-phase region (vapor phase only), temperature and pressure are no longer dependent properties, and they can conveniently be us... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
"Header 3": "2 Superheated Vapor",
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... |
One pound-mass of water fills a 2.29-ft<sup>3</sup> rigid container at an initial pressure of 250 psia. The container is then cooled to 100°F. Determine the initial temperature and final pressure of the water.
**SOLUTION** A rigid container that is filled with water is cooled. The initial temperature and final pressu... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
"Header 3": "**EXAMPLE 3-6** Cooling of Superheated Water Vapor",
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Determine the temperature of water at a state of *P* = 0.5 MPa and *h* = 2890 kJ/kg.
**SOLUTION** The temperature of water at a specified state is to be determined. **Analysis** At 0.5 MPa, the enthalpy of saturated water vapor is *hg* = 2748.1 kJ/kg. Since *h* > *hg,* as shown in Fig. 3–39, we again have superheated... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
"Header 3": "**EXAMPLE 3–7 Temperature of Superheated Vapor**",
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Compressed liquid tables are not as commonly available, and Table A–7 is the only compressed liquid table in this text. The format of Table A–7 is very much like the format of the superheated vapor tables. One reason for the lack of compressed liquid data is the relative independence of compressed liquid properties fro... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
"Header 3": "**3 Compressed Liquid**",
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A compressed liquid may be approximated as a saturated liquid at the given temperature.
h at low to moderate pressures and temperatures can be reduced significantly by evaluating it from
$$h \cong h_{f @ T} + \mathsf{U}_{f @ T} (P - P_{\text{sat } @ T})$$
(3-9)
instead of taking it to be just $h_f$ . Note, howev... | {
"Header 1": "**EXAMPLE 3-5** Properties of Saturated Liquid-Vapor Mixture",
"Header 3": "**FIGURE 3–40**",
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Determine the internal energy of compressed liquid water at 80°C and 5 MPa, using (a) data from the compressed liquid table and (b) saturated liquid data. What is the error involved in the second case?
**SOLUTION** The exact and approximate values of the internal energy of liquid water are to be determined.
**Analy... | {
"Header 1": "**EXAMPLE 3-8** Approximating Compressed Liquid as Saturated Liquid",
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The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between thermodynamic properties. However, those relations give the *changes* in properties, not the values of properties at specified states. Therefore, we need to choose a convenient *referenc... | {
"Header 1": "**EXAMPLE 3-8** Approximating Compressed Liquid as Saturated Liquid",
"Header 3": "**Reference State and Reference Values**",
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Determine the missing properties and the phase descriptions in the following table for water:
| | T, °C | <i>P</i> , kPa | u, kJ/kg | х | Phase description |
|--------------|-------|----------------|----------|-----|-------------------|
| (a) | | 200 | | 0.6 | ... | {
"Header 1": "EXAMPLE 3-9 The Use of Steam Tables to Determine Properties",
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Property tables provide very accurate information about the properties, but they are bulky and vulnerable to typographical errors. A more practical and desirable approach would be to have some simple relations among the properties that are sufficiently general and accurate.
Any equation that relates the pressure, tem... | {
"Header 1": "EXAMPLE 3-9 The Use of Steam Tables to Determine Properties",
"Header 3": "3-6 • THE IDEAL-GAS EQUATION OF STATE",
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The gage pressure of an automobile tire is measured to be 210 kPa before a trip and 220 kPa after the trip at a location where the atmospheric pressure is 95 kPa (Fig. 3–45). Assuming the volume of the tire remains constant and the air temperature before the trip is 25°C, determine air temperature in the tire after the... | {
"Header 1": "EXAMPLE 3-10 Temperature Rise of Air in a Tire During a Trip",
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The ideal-gas equation is very simple and thus very convenient to use. However, as illustrated in Fig. 3–47, gases deviate from ideal-gas behavior significantly at states near the saturation region and the critical point. This deviation from ideal-gas behavior at a given temperature and pressure can accurately be accou... | {
"Header 1": "3-7 • COMPRESSIBILITY FACTOR—A MEASURE OF DEVIATION FROM IDEAL-GAS BEHAVIOR",
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Determine the specific volume of refrigerant-134a at 1 MPa and 50°C, using (a) the ideal-gas equation of state and (b) the generalized compressibility chart. Compare the values obtained to the actual value of 0.021796 m³/kg and determine the error involved in each case.
**SOLUTION** The specific volume of refrigerant... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "**EXAMPLE 3–11** The Use of Generalized Charts",
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Determine the pressure of water vapor at $600^{\circ}$ F and 0.51431 ft<sup>3</sup>/lbm, using (a) the steam tables, (b) the ideal-gas equation, and (c) the generalized compressibility chart.
**SOLUTION** The pressure of water vapor is to be determined in three different ways.
**Analysis** A sketch of the system i... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "■ EXAMPLE 3-12 Using Generalized Charts to Determine Pressure",
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The van der Waals equation of state was proposed in 1873, and it has two constants that are determined from the behavior of a substance at the critical point. It is given by
$$\left(P + \frac{a}{\mathsf{V}^2}\right)(\mathsf{V} - b) = RT \tag{3-22}$$
Van der Waals intended to improve the ideal-gas equation of state ... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "van der Waals Equation of State",
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Constants that appear in the Beattie-Bridgeman and the Benedict-Webb-Rubin equations of state
(a) When P is in kPa, $\overline{U}$ is in m<sup>3</sup>/kmol, T is in K, and $R_u = 8.314 \text{ kPa} \cdot \text{m}^3/\text{kmol} \cdot \text{K}$ , the five constants in the Beattie-Bridgeman equation are as follows:
... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "TABLE 3-4",
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Benedict, Webb, and Rubin extended the Beattie-Bridgeman equation in 1940 by raising the number of constants to eight. It is expressed as
$$P = \frac{R_u T}{\overline{U}} + \left(B_0 R_u T - A_0 - \frac{C_0}{T^2}\right) \frac{1}{\overline{U}^2} + \frac{b R_u T - a}{\overline{U}^3} + \frac{a \alpha}{\overline{U}^6} + ... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "**Benedict-Webb-Rubin Equation of State**",
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The equation of state of a substance can also be expressed in a series form as
$$P = \frac{RT}{V} + \frac{a(T)}{V^2} + \frac{b(T)}{V^3} + \frac{c(T)}{V^4} + \frac{d(T)}{V^5} + \dots$$
(3-27)
This and similar equations are called the *virial equations of state*, and the coefficients a(T), b(T), c(T), and so on, that... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "**Virial Equation of State**",
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Predict the pressure of nitrogen gas at T = 175 K and U = 0.00375 m³/kg on the
basis of (a) the ideal-gas equation of state, (b) the van der Waals equation of state,
(c) the Beattie-Bridgeman equation of state, and (d) the Benedict-Webb-Rubin equation of state. Compare the values obtained to the experimentally determin... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "■ EXAMPLE 3-13 Different Methods of Evaluating Gas Pressure",
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Atmospheric pressure is the sum of the dry air pressure $P_a$ and the vapor pressure $P_{v'}$
The pressure in a gas container is due to the individual molecules striking the wall of the container and exerting a force on it. This force is proportional to the average velocity of the molecules and the number of molec... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "FIGURE 3-58",
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When open to the atmosphere, water is in phase equilibrium with the vapor in the air if the vapor pressure is equal to the saturation pressure of water. to the vapor phase, and the two phases are in **phase equilibrium**. For liquid water that is open to the atmosphere, the criterion for phase equilibrium can be expres... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "**FIGURE 3-60**",
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On a summer day, the air temperature over a lake is measured to be 25°C. Determine the water temperature of the lake when phase equilibrium conditions are established between the water in the lake and the vapor in the air for relative humidities of 10, 80, and 100 percent for the air (Fig. 3–62).
**SOLUTION** Air at ... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "**EXAMPLE 3–14** Temperature Drop of a Lake Due to Evaporation",
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A substance that has a fixed chemical composition throughout is called a *pure substance*. A pure substance exists in different phases depending on its energy level. In the liquid phase, a substance that is not about to vaporize is called a *compressed* or *subcooled liquid*. In the gas phase, a substance that is not a... | {
"Header 1": "$\\begin{array}{c} C \\\\ P_R = \\frac{P}{P_{cr}} \\\\ V_R = \\frac{V}{RT_{cr}/P_{cr}} \\end{array}$ $Z = \\dots$ (Fig. A-15)",
"Header 3": "**SUMMARY**",
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- **3–1C** A propane tank is filled with a mixture of liquid and vapor propane. Can the contents of this tank be considered a pure substance? Explain.
- **3–2C** Is iced water a pure substance? Why?
- **3–3C** What is the difference between saturated vapor and superheated vapor?
\*Problems designated by a "C" are con... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
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- **3–10**C What is quality? Does it have any meaning in the superheated vapor region?
- **3–11C** Does the amount of heat absorbed as 1 kg of saturated liquid water boils at 100°C have to be equal to the amount of heat released as 1 kg of saturated water vapor condenses at 100°C?
- **3–12C** Does the reference point s... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Property Tables**",
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} |
**3–29E** One pound-mass of water fills a container whose volume is 2 ft<sup>3</sup>. The pressure in the container is 100 psia. Calculate the total internal energy and enthalpy in the container. *Answers*: 661 Btu, 698 Btu
**3–30** A piston–cylinder device contains 0.85 kg of refrigerant-134a at –10°C. The piston th... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "FIGURE P3-28",
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} |
Plot the total mass of water against pressure, and discuss the results. Also, show the process in Prob. 3–51 on a *P-v* diagram using the property plot feature of the software.
- **3–53E** A 5-ft<sup>3</sup> rigid tank contains a saturated mixture of refrigerant-134a at 50 psia. If the saturated liquid occupies 20 perc... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "FIGURE P3-28",
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} |
- **3–65C** Under what conditions is the ideal-gas assumption suitable for real gases?
- **3–66C** What is the difference between mass and molar mass? How are these two related?
- **3–67C** Propane and methane are commonly used for heating in winter, and the leakage of these fuels, even for short periods, poses a fire ... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Ideal Gas**",
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- **3–81C** What is the physical significance of the compressibility factor *Z*?
- **3–82** Determine the specific volume of refrigerant-134a vapor at 0.9 MPa and 70°C based on (*a*) the ideal-gas equation, (*b*) the generalized compressibility chart, and (*c*) data from tables. Also, determine the error involved in th... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Compressibility Factor**",
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- **3–90E** Ethane in a rigid vessel is to be heated from 50 psia and 100°F until its temperature is 540°F. What is the final pressure of the ethane as predicted by the compressibility chart?
- **3–91** A 0.016773-m<sup>3</sup> tank contains 1 kg of refrigerant-134a at 110°C. Determine the pressure of the refrigerant u... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**FIGURE P3–89**",
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- **3–94C** What is the physical significance of the two constants that appear in the van der Waals equation of state? On what basis are they determined?
- **3–95E** Refrigerant-134a at 400 psia has a specific volume of 0.1144 ft<sup>3</sup> /lbm. Determine the temperature of the refrigerant based on (*a*) the ideal-ga... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Other Equations of State**",
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- **3–103** During a hot summer day at the beach when the air temperature is 30°C, someone claims the vapor pressure in the air to be 5.2 kPa. Is this claim reasonable?
- **3–104** Consider a glass of water in a room that is at 20°C and 40 percent relative humidity. If the water temperature is 15°C, determine the vapor... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Special Topic: Vapor Pressure and Phase Equilibrium**",
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**3–109** Complete the blank cells in the following table of properties of steam. In the last column, describe the condition of steam as compressed liquid, saturated mixture, superheated vapor, or insufficient information, and, if applicable, give the quality.
| P, kPa | T, °C | v, m3<br>/kg | u, kJ/kg | Phase d... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Review Problems**",
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- **3–113** The gage pressure of an automobile tire is measured to be 200 kPa before a trip and 220 kPa after the trip at a location where the atmospheric pressure is 90 kPa. Assuming the volume of the tire remains constant at 0.035 m<sup>3</sup> , determine the percent increase in the absolute temperature of the air i... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**FIGURE P3–112**",
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} |
Place the value of the specific volume on its axis.
- **3–129** Water initially at 300 kPa and 0.5 m<sup>3</sup> /kg is contained in a piston–cylinder device fitted with stops so that the water supports the weight of the piston and the force of the atmosphere. The water is heated until it reaches the saturated vapor st... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**FIGURE P3–112**",
"token_count": 224,
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} |
- **3–130** Ethane at 10 MPa and 100°C is heated at constant pressure until its volume has increased by 60 percent. Determine the final temperature using (*a*) the ideal-gas equation of state and (*b*) the compressibility factor. Which of these two results is the more accurate?
- **3–131** Steam at 400°C has a specific... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**FIGURE P3–129**",
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} |
**3–135** A 1-m3 rigid tank contains 10 kg of water (in any phase or phases) at 160°C. The pressure in the tank is
(*a*) 738 kPa (*b*) 618 kPa (*c*) 370 kPa
(*d*) 2000 kPa (*e*) 1618 kPa
**3–136** A 3-m3 rigid vessel contains steam at 2 MPa and 500°C. The mass of the steam is
(*a*) 13 kg (*b*) 17 kg (*c*) 22 kg... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**3–144** A solid normally absorbs heat as it melts, but there is a known exception at temperatures close to absolute zero. Find out which solid it is, and give a physical explanation for it.
**3–145** In an article on tire maintenance, it is stated that tires lose air over time, and pressure losses as high as 90 kPa... | {
"Header 1": "Pure Substances, Phase-Change Processes, Property Diagrams",
"Header 2": "**Design and Essay Problems**",
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**I** n Chap. 2, we considered various forms of energy and energy transfer, and we developed a general relation for the conservation of energy principle or energy balance. Then in Chap. 3, we learned how to determine the thermodynamics properties of substances. In this chapter, we apply the energy balance relation to s... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
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One form of mechanical work often encountered in practice is associated with the expansion or compression of a gas in a piston–cylinder device. During this process, part of the boundary (the inner face of the piston) moves back and forth. Therefore, the expansion and compression work is often called **moving boundary w... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**4–1** ■ **MOVING BOUNDARY WORK**",
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Schematic and *P*-*v* diagram for Example 4–2.
to account for it since energy is conserved. In a car engine, for example, the boundary work done by the expanding hot gases is used to overcome friction between the piston and the cylinder, to push atmospheric air out of the way, and to rotate the crankshaft. Therefore,... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**FIGURE 4–7**",
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A rigid tank contains air at 500 kPa and 150°C. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 65°C and 400 kPa, respectively. Determine the boundary work done during this process.
**SOLUTION** Air in a rigid tank is cooled, and both the pressure and temperature... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**EXAMPLE 4–1 Boundary Work for a Constant-Volume Process**",
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A frictionless piston–cylinder device contains 10 lbm of steam at 60 psia and 320°F. Heat is now transferred to the steam until the temperature reaches 400°F. If the piston is not attached to a shaft and its mass is constant, determine the work done by the steam during this process.
**SOLUTION** Steam in a piston–cyl... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**EXAMPLE 4–2 Boundary Work for a Constant-Pressure Process**",
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A piston–cylinder device initially contains 0.4 m<sup>3</sup> of air at 100 kPa and 80°C. The air is now compressed to 0.1 m<sup>3</sup> in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process.
**SOLUTION** Air in a piston–cylinder device is compressed isot... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**EXAMPLE 4-3** Isothermal Compression of an Ideal Gas",
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During actual expansion and compression processes of gases, pressure and volume are often related by $PV^n = C$ , where n and C are constants. A process of this kind is called a **polytropic process** (Fig. 4–9). Next we develop a general expression for the work done during a polytropic process. The pressure for a pol... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**Polytropic Process**",
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A piston–cylinder device contains $0.05 \text{ m}^3$ of a gas initially at 200 kPa. At this state, a linear spring that has a spring constant of 150 kN/m is touching the piston but exerting no force on it. Now heat is transferred to the gas, causing the piston to rise and to compress the spring until the volume insid... | {
"Header 1": "**E N E R G Y A N A LY S I S O F CLOSED SYSTEMS**",
"Header 3": "**EXAMPLE 4-4** Expansion of a Gas Against a Spring",
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Energy balance for any system undergoing any kind of process was expressed as (see Chap. 2)
$$E_{\text{in}} - E_{\text{out}} = \Delta E_{\text{system}}$$
(kJ) (4–11)
Net energy transfer y heat, work, and mass potential, etc., energies
or, in the rate form, as
$$\dot{E}_{\rm in} - \dot{E}_{\rm out} = dE_{\rm syste... | {
"Header 1": "4-2 • ENERGY BALANCE FOR CLOSED SYSTEMS",
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A piston–cylinder device contains 25 g of saturated water vapor that is maintained at a constant pressure of 300 kPa. A resistance heater within the cylinder is turned on and passes a current of 0.2 A for 5 min from a 120-V source. At the same time, a heat loss of 3.7 kJ occurs. (a) Show that for a closed system the bo... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
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For a closed system undergoing a quasi-equilibrium, P = constant process, $\Delta U + W_b = \Delta H$ . Note that this relation is NOT valid for closed systems processes during which pressure DOES NOT remain constant.
*process* since the boundary work is automatically taken care of by the enthalpy terms, and one no ... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**FIGURE 4-14**",
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A rigid tank is divided into two equal parts by a partition. Initially, one side of the tank contains 5 kg of water at 200 kPa and 25°C, and the other side is evacuated. The partition is then removed, and the water expands into the entire tank. The water is allowed to exchange heat with its surroundings until the tempe... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**EXAMPLE 4–6** Unrestrained Expansion of Water",
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Constant-volume and constant-pressure specific heats $c_{\rm u}$ and $c_{\rm p}$ (values given are for helium gas).
The quality at the final state is determined from the specific volume information:
$$x_2 = \frac{\mathbf{v}_2 - \mathbf{v}_f}{\mathbf{v}_{fg}} = \frac{0.002 - 0.001}{43.34 - 0.001} = 2.3 \times 10... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**FIGURE 4-19**",
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We know from experience that it takes different amounts of energy to raise the temperature of identical masses of different substances by one degree. For example, we need about 4.5 kJ of energy to raise the temperature of 1 kg of iron from 20 to 30°C, whereas it takes about nine times this much energy (41.8 kJ to be ex... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "4-3 • SPECIFIC HEATS",
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... |
We defined an ideal gas as a gas whose temperature, pressure, and specific volume are related by
$$PU = RT$$
It has been demonstrated mathematically (Chap. 12) and experimentally (Joule, 1843) that for an ideal gas the internal energy is a function of the temperature only. That is,
$$u = u(T) \tag{4-21}$$
In hi... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "4-4 INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF IDEAL GASES",
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Three ways of calculating $\Delta u$ .
evaluated from this table at the average temperature $(T_1 + T_2)/2$ , as shown in Fig. 4–26. If the final temperature $T_2$ is not known, the specific heats may be evaluated at $T_1$ or at the anticipated average temperature. Then $T_2$ can be determined by using these ... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**FIGURE 4-28**",
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} |
A special relationship between $c_p$ and $c_v$ for ideal gases can be obtained by differentiating the relation h = u + RT, which yields
$$dh = du + R dT$$
Replacing dh with $c_p dT$ and du with $c_0 dT$ and dividing the resulting expression by dT, we obtain
$$c_p = c_u + R \qquad \text{(kJ/kg·K)} \tag{4-2... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**Specific Heat Relations of Ideal Gases**",
"token_count": 329,
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Air at 300 K and 200 kPa is heated at constant pressure to 600 K. Determine the change in internal energy of air per unit mass, using (a) data from the air table (Table A–17), (b) the functional form of the specific heat (Table A–2c), and (c) the average specific heat value (Table A–2b).
**SOLUTION** The internal ene... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**EXAMPLE 4–7** Evaluation of the $\\Delta u$ of an Ideal Gas",
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The $c_p$ of an ideal gas can be determined from a knowledge of $c_0$ and R.
The change in the internal energy on a unit-mass basis is determined by dividing this value by the molar mass of air (Table A-1):
$$\Delta u = \frac{\Delta \overline{u}}{M} = \frac{6447 \text{ kJ/kmol}}{28.97 \text{ kg/kmol}} = 222.5 \... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**FIGURE 4-29**",
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} |
An insulated rigid tank initially contains 1.5 lbm of helium at 80°F and 50 psia. A paddle wheel with a power rating of 0.02 hp is operated within the tank for 30 min. Determine (a) the final temperature and (b) the final pressure of the helium gas.
**SOLUTION** Helium gas in an insulated rigid tank is stirred by a p... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**EXAMPLE 4-8** Heating of a Gas in a Tank by Stirring",
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A piston–cylinder device initially contains 0.5 m³ of nitrogen gas at 400 kPa and 27°C. An electric heater within the device is turned on and is allowed to pass a current of 2 A for 5 min from a 120-V source. Nitrogen expands at constant pressure, and a heat loss of 2800 J occurs during the process. Determine the final... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**EXAMPLE 4-9** Heating of a Gas by a Resistance Heater",
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A piston–cylinder device initially contains air at 150 kPa and 27°C. At this state, the piston is resting on a pair of stops, as shown in Fig. 4–32, and the enclosed volume is 400 L. The mass of the piston is such that a 350-kPa pressure is required to move it. The air is now heated until its volume has doubled. Determ... | {
"Header 1": "EXAMPLE 4-5 Electric Heating of a Gas at Constant Pressure",
"Header 3": "**EXAMPLE 4-10** Heating of a Gas at Constant Pressure",
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A substance whose specific volume (or density) is constant is called an **incompressible substance**. The specific volumes of solids and liquids essentially remain constant during a process (Fig. 4–33). Therefore, liquids and solids can be approximated as incompressible substances without sacrificing much in accuracy. ... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"token_count": 240,
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} |
Like those of ideal gases, the specific heats of incompressible substances depend on temperature only. Thus, the partial differentials in the defining equation of $c_v$ can be replaced by ordinary differentials, which yield
$$du = c_{u}dT = c(T) dT ag{4-33}$$
The change in internal energy between states 1 and 2 i... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**Internal Energy Changes**",
"token_count": 205,
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Using the definition of enthalpy h = u + PU and noting that U = constant, the differential form of the enthalpy change of incompressible substances can be determined by differentiation to be
$$dh = du + v dP + P dv^{\nearrow}^{0} = du + v dP$$
(4–36)
Integrating,
$$\Delta h = \Delta u + \cup \Delta P \cong c_{\te... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**Enthalpy Changes**",
"token_count": 518,
"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... |
Determine the enthalpy of liquid water at $100^{\circ}$ C and 15 MPa (a) by using compressed liquid tables, (b) by approximating it as a saturated liquid, and (c) by using the correction given by Eq. 4–38.
**SOLUTION** The enthalpy of liquid water is to be determined exactly and approximately.
**Analysis** At 100°... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "■ EXAMPLE 4-11 Enthalpy of Compressed Liquid",
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A 50-kg iron block at 80°C is dropped into an insulated tank that contains 0.5 m³ of liquid water at 25°C. Determine the temperature when thermal equilibrium is reached.
**SOLUTION** An iron block is dropped into water in an insulated tank. The final temperature when thermal equilibrium is reached is to be determined... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**EXAMPLE 4–12** Cooling of an Iron Block by Water",
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Carbon steel balls ( $\rho = 7833 \text{ kg/m}^3$ and $c_p = 0.465 \text{ kJ/kg} \cdot ^\circ\text{C}$ ) 8 mm in diameter are annealed by heating them first to 900°C in a furnace, and then allowing them to cool slowly to 100°C in ambient air at 35°C, as shown in Fig. 4-36. If 2500 balls are to be annealed per hour, d... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**EXAMPLE 4–13** Cooling of Carbon Steel Balls in Air",
"token_count": 752,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-editi... |
An important and exciting application area of thermodynamics is biological systems, which are the sites of rather complex and intriguing energy transfer and transformation processes. Biological systems are not in thermodynamic equilibrium, and thus they are not easy to analyze. Despite their complexity, biological syst... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "TOPIC OF SPECIAL INTEREST\\* Thermodynamic Aspects of Biological Systems",
"token_count": 393,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-an... |
Two fast-dancing people supply more energy to a room than a 1-kW electric resistance heater.
refers to the burning of foods such as carbohydrates, fat, and protein. The rate of metabolism in the resting state is called the *basal metabolic rate,* which is the rate of metabolism required to keep a body performing the ... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**FIGURE 4–38**",
"token_count": 722,
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The energy requirements of a body are met by the food we eat. The nutrients in the food are considered in three major groups: carbohydrates, proteins, and fats. *Carbohydrates* are characterized by having hydrogen and oxygen atoms in a 2:1 ratio in their molecules. The molecules of carbohydrates range from very simple ... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**Food and Exercise**",
"token_count": 944,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineering-thermodynamics-by-cengel-boles-and-kanoglu-9th-edition-pdf-free.pdf - 2023.01.13 - 0... |
Evaluating the calorie content of one serving of chocolate chip cookies (values are for Chips Ahoy cookies made by Nabisco).
©Comstock/Getty Images RF
The daily calorie needs of people vary greatly with age, gender, the state of health, the activity level, the body weight, and the composition of the body as well as... | {
"Header 1": "4-5 • INTERNAL ENERGY, ENTHALPY, AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS",
"Header 3": "**FIGURE 4-41**",
"token_count": 1313,
"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.... |
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