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- **12–14E** Verify the validity of the last Maxwell relation (Eq. 12–19) for steam at 800°F and 400 psia.
- **12–15** Verify the validity of the last Maxwell relation (Eq. 12–19) for refrigerant-134a at 50°C and 0.7 MPa.
- Reconsider Prob. 12–15. Using appropriate software, verify the validity of the last Maxwell rela... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "The Maxwell Relations",
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- **12–22**C What is the value of the Clapeyron equation in thermodynamics?
- **12–23C** What approximations are involved in the Clapeyron-Clausius equation?
**12–24** Using the Clapeyron equation, estimate the enthalpy of vaporization of refrigerant-134a at 40°C, and compare it to the tabulated value.
Reconsider P... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "**The Clapeyron Equation**",
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**12–33**°C Can the variation of specific heat $c_p$ with pressure at a given temperature be determined from a knowledge of P-U-T data alone?
**12–34** Determine the change in the internal energy of air, in kJ/kg, as it undergoes a change of state from 100 kPa and 20°C to 600 kPa and 300°C using the equation of sta... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "General Relations for du, dh, ds, $c_v$ , and $c_p$",
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- **12–54**C What does the Joule-Thomson coefficient represent?
- **12–55**C Describe the inversion line and the maximum inversion temperature.
- **12–56**C Does the Joule-Thomson coefficient of a substance change with temperature at a fixed pressure?
- **12–57**C The pressure of a fluid always decreases during an adia... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "The Joule-Thomson Coefficient",
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- **12–67C** What is the enthalpy departure?
- **12–68C** On the generalized enthalpy departure chart, the normalized enthalpy departure values seem to approach zero as the reduced pressure $P_R$ approaches zero. How do you explain this behavior?
- **12–69C** Why is the generalized enthalpy departure chart prepared b... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "The dh, du, and ds of Real Gases",
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**12–82** Develop expressions for h, u, $s^{\circ}$ , $P_r$ , and $V_r$ for an ideal gas whose $c_n^{\circ}$ is given by
$$c_p^{\,o} = \sum a_i T^{i-n} + a_0 e^{\beta/T} \left( \frac{\beta/T}{e^{\beta/T} - 1} \right)$$
where $a_i$ , $a_0$ , n, and $\beta$ are empirical constants.
- **12–83** Starting wi... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "**Review Problems**",
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- **12–102** A substance whose Joule-Thomson coefficient is negative is throttled to a lower pressure. During this process, (select the correct statement)
- (*a*) the temperature of the substance will increase.
- (*b*) the temperature of the substance will decrease.
- (*c*) the entropy of the substance will remain cons... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**12–107** There have been several attempts to represent the thermodynamic relations geometrically, the best known of these being Koenig's thermodynamic square shown in the figure. There is a systematic way of obtaining the four Maxwell relations as well as the four relations for *du, dh, dg,* and *da* from this figure... | {
"Header 1": "EXAMPLE 12-11 Thermodynamic Analysis with Nonideal Gas Properties",
"Header 3": "**Design and Essay Problems**",
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p to this point, we have limited our consideration to thermodynamic systems that involve a single pure substance such as water. Many important thermodynamic applications, however, involve *mixtures* of several pure substances rather than a single pure substance. Therefore, it is important to develop an understanding of... | {
"Header 1": "13",
"Header 3": "**GAS MIXTURES**",
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To determine the properties of a mixture, we need to know the *composition* of the mixture as well as the properties of the individual components. There are two ways to describe the composition of a mixture: either by specifying the number of moles of each component, called **molar analysis**, or by specifying the mass... | {
"Header 1": "13-1 • COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS",
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A gas mixture consists of 5 lbmol of H<sub>2</sub> and 4 lbmol of N<sub>2</sub>, as shown in Fig. 13–4.
Determine the mass of each gas and the apparent gas constant of the mixture.
**SOLUTION** The mole numbers of the constituents of a gas mixture are given. The mass of each gas and the apparent gas constant are to... | {
"Header 1": "13-1 • COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS",
"Header 3": "**EXAMPLE 13-1** The Gas Constant of a Gas Mixture",
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An ideal gas is defined as a gas whose molecules are spaced far apart so that the behavior of a molecule is not influenced by the presence of other molecules—a situation encountered at low densities. We also mentioned that real gases approximate this behavior closely when they are at a low pressure or high temperature ... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
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Amagat's law of additive volumes for a mixture of two ideal gases.
The prediction of the *P-U-T* behavior of gas mixtures is usually based on two models: *Dalton's law of additive pressures* and *Amagat's law of additive volumes*. Both models are described and discussed below.
**Dalton's law of additive pressures:*... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "FIGURE 13-6",
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For ideal gases, $P_i$ and $V_i$ can be related to $y_i$ by using the ideal-gas relation for both the components and the gas mixture:
$$\begin{split} \frac{P_{i}(T_{m}, V_{m})}{P_{m}} &= \frac{N_{i}R_{u}T_{m}/V_{m}}{N_{m}R_{u}T_{m}/V_{m}} = \frac{N_{i}}{N_{m}} = y_{i} \\ \frac{V_{i}(T_{m}, P_{m})}{V_{m}} &= \fr... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "**Ideal-Gas Mixtures**",
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Dalton's law of additive pressures and Amagat's law of additive volumes can also be used for real gases, often with reasonable accuracy. This time, however, the component pressures or component volumes should be evaluated from relations that take into account the deviation of each component from ideal-gas behavior. One... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "**Real-Gas Mixtures**",
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Another way of predicting the P-U-T behavior of a real-gas mixture is to treat it as a pseudopure substance with critical properties $P'_{cr}$ and $T'_{cr}$ .
the mixture, defined in terms of the critical pressures and temperatures of the mixture components as
$$P'_{\text{cr},m} = \sum_{i=1}^{k} y_i P_{\text{cr}... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "FIGURE 13-9",
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A rigid tank contains 2 kmol of $N_2$ and 6 kmol of $CO_2$ gases at 300 K and 15 MPa (Fig. 13–10). Estimate the volume of the tank on the basis of (a) the ideal-gas equation of state, (b) Kay's rule, (c) compressibility factors and Amagat's law, and (d) compressibility factors and Dalton's law.
**SOLUTION** The c... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "**EXAMPLE 13-2** P-U-T Behavior of Nonideal Gas Mixtures",
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Consider a gas mixture that consists of 2 kg of N2 and 3 kg of CO2. The total mass (an *extensive property*) of this mixture is 5 kg. How did we do it? Well, we simply added the mass of each component. This example suggests a simple way of evaluating the **extensive properties** of a nonreacting ideal- or real-gas mixt... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "**13–3** ■ **PROPERTIES OF GAS MIXTURES: IDEAL AND REAL GASES**",
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The extensive properties of a mixture are determined by simply adding the properties of the components.
$$\Delta H_m = \sum_{i=1}^k \Delta H_i = \sum_{i=1}^k m_i \Delta h_i = \sum_{i=1}^k N_i \Delta \overline{h}_i \qquad \text{(kJ)}$$
$$\Delta S_m = \sum_{i=1}^k \Delta S_i = \sum_{i=1}^k m_i \Delta s_i = \sum_{i=1}... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "**FIGURE 13–11**",
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... |
The intensive properties of a mixture are determined by weighted averaging.
Partial pressures (not the mixture pressure) are used in the evaluation of entropy changes of ideal-gas mixtures.
Evaluation of $\Delta u$ or $\Delta h$ of the components of... | {
"Header 1": "13-2 • P-∪-T BEHAVIOR OF GAS MIXTURES: IDEAL AND REAL GASES (▶)",
"Header 3": "**FIGURE 13-12**",
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... |
A mixture of oxygen $(O_2)$ , carbon dioxide $(CO_2)$ , and helium (He) gases with mass fractions of 0.0625, 0.625, and 0.3125, respectively, enter an adiabatic turbine at 1000 kPa and 600 K steadily and expand to 100 kPa pressure (Fig. 13–14). The isentropic efficiency of the turbine is 90 percent. For gas component... | {
"Header 1": "**EXAMPLE 13-3** Expansion of an Ideal Gas Mixture in a Turbine",
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An insulated rigid tank is divided into two compartments by a partition, as shown in Fig. 13–15. One compartment contains 3 kmol of $\rm O_2$ , and the other compartment contains 5 kmol of $\rm CO_2$ . Both gases are initially at 25°C and 200 kPa. Now the partition is removed, and the two gases are allowed to mix. As... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
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When the components of a gas mixture do not behave as ideal gases, the analysis becomes more complex because the properties of real (nonideal) gases such as u, h, $c_v$ , and $c_p$ depend on the pressure (or specific volume) as well as on the temperature. In such cases, the effects of deviation from ideal-gas behavi... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**Real-Gas Mixtures**",
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Air is a mixture of $N_2$ , $O_2$ , and small amounts of other gases, and it can be approximated as 79 percent $N_2$ and 21 percent $O_2$ on a mole basis. During a steady-flow process, air is cooled from 220 to 160 K at a constant pressure of 10 MPa (Fig. 13–17). Determine the heat transfer during this process pe... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**EXAMPLE 13-5** Cooling of a Nonideal Gas Mixture",
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$$\begin{split} \overline{h}_{m_1,\text{ideal}} &= y_{\text{N}_2} \overline{h}_{1,\text{ideal},\text{N}_2} + y_{\text{O}_2} \overline{h}_{1,\text{ideal},\text{O}_2} \\ &= (0.79) (6391 \text{ kJ/kmol}) + (0.21) (6404 \text{ kJ/kmol}) \\ &= 6394 \text{ kJ/kmol} \\ \overline{h}_{m_2,\text{ideal}} &= y_{\text{N}_2} \over... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**EXAMPLE 13-5** Cooling of a Nonideal Gas Mixture",
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When two gases or two miscible liquids are brought into contact, they mix and form a homogeneous mixture or solution without requiring any work input. That is, the natural tendency of miscible substances brought into contact is to mix with each other. These are irreversible processes, and thus it is impossible for the ... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "TOPIC OF SPECIAL INTEREST\\* Chemical Potential and the Separation Work of Mixtures",
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For a pure substance, the chemical potential is equivalent to the Gibbs function.
The amount of heat released or absorbed during a mixing process is called the enthalpy (or heat) of mixing, which is zero for ideal solutions. volume of an ethyl alcohol—water mixture is a few percent les... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**FIGURE 13-18**",
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When the effect of dissimilar molecules in a mixture on each other is negligible, the mixture is said to be an **ideal mixture** or **ideal solution** and the *chemical potential of a component in such a mixture equals the Gibbs function of the pure component*. Many liquid solutions encountered in practice, especially ... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**Ideal-Gas Mixtures and Ideal Solutions**",
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The entropy balance for a steady-flow system simplifies to $S_{\rm in} - S_{\rm out} + S_{\rm gen} = 0$ . Noting that entropy can be transferred by heat and mass only, the entropy generation during an adiabatic mixing process that forms an ideal solution becomes
$$S_{\text{gen}} = S_{\text{out}} - S_{\text{in}} = \D... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**Minimum Work of Separation of Mixtures**",
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For a naturally occurring process during which no work is produced or consumed, the reversible work is equal to the exergy destruction.
A reversible process, by definition, is a process that can be reversed without leaving a net effect on the surroundings. This requires that the direction of all interactions be rever... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**FIGURE 13-21**",
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The mixing processes that occur naturally are irreversible, and all the work potential is wasted during such processes. For example, when the fresh water from a river mixes with the saline water in an ocean, an opportunity to produce work is lost. If this mixing is done reversibly (through the use of semipermeable memb... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**Reversible Mixing Processes**",
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The second-law efficiency is a measure of how closely a process approximates a corresponding reversible process, and it indicates the range available for potential improvements. Noting that the second-law efficiency ranges from 0 for a totally irreversible process to 100 percent for a totally reversible process, the se... | {
"Header 1": "**EXAMPLE 13-4** Exergy Destruction During Mixing of Ideal Gases",
"Header 3": "**Second-Law Efficiency**",
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Consider a mixture of two components A and B whose mole fractions are $y_A$ and $y_B$ . Noting that $y_B = 1 - y_A$ , the minimum work input required to separate 1 kmol of this mixture at temperature $T_0$ completely into pure A and pure B is, from Eq. 13–54,
$$\overline{w}_{\min} = -R_{\nu} T_0(y_A \ln y_A + y... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
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The potable water needs of the world are increasing steadily due to population growth, rising living standards, industrialization, and irrigation in agriculture. There are over 10,000 desalination plants in the world, with a total desalted water capacity of over 5 billion gallons a day. Saudi Arabia is the largest user... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**An Application: Desalination Processes**",
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Fresh water is to be obtained from seawater at $15^{\circ}$ C with a salinity of 3.48 percent on mass basis (or TDS = 34,800 ppm). Determine (a) the mole fractions of the water and the salts in the seawater, (b) the minimum work input required to separate 1 kg of seawater completely into pure water and pure salts, (c)... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**EXAMPLE 13–6** Obtaining Fresh Water from Seawater",
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The osmotic pressure and the osmotic rise of saline water.
Fresh and saline water mixing reversibly through semipermeable membranes, and producing power.
Power can be produced by mixing solutions of different concentrations reversibly.
Note that it takes about five times more work t... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**FIGURE 13-24**",
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A mixture of two or more gases of fixed chemical composition is called a *nonreacting gas mixture*. The composition of a gas mixture is described by specifying either the *mole fraction* or the *mass fraction* of each component, defined as
$$\mathrm{mf}_i = \frac{m_i}{m_m}$$
and $y_i = \frac{N_i}{N_m}$
where
$$m... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**SUMMARY**",
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- **13–1C** What are mass and mole fractions?
- **13–2C** Consider a mixture of several gases of identical masses. Will all the mass fractions be identical? How about the mole fractions?
- **13–3C** The sum of the mole fractions for an ideal-gas mixture is equal to 1. Is this also true for a real-gas mixture?
- **13–4C... | {
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"Header 3": "**Composition of Gas Mixtures**",
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- **13–15C** Is a mixture of ideal gases also an ideal gas? Give an example.
- **13–16C** Express Dalton's law of additive pressures. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?
- **13–17C** Express Amagat's law of additive volumes. Does this law hold exactly for ideal-gas mixtur... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "P-U-T Behavior of Gas Mixtures",
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- **13–34** An engineer has proposed mixing extra oxygen with normal air in internal combustion engines to control some of the exhaust products. If an additional 5 percent (by volume) of oxygen is mixed with standard atmospheric air, how will this change the mixture's molecular weight?
- **13–35** A rigid tank contains... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**FIGURE P13–33**",
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- **13–40E** The dry stack gas of an electrical-generation station boiler has the following Orsat analysis: 15 percent CO2, 15 percent O2, and 1 percent CO. This gas passes through a 10-ft2 cross-section metering duct at a velocity of 20 ft/s at standard atmospheric pressure and 200°F. Determine the gas mixture's mass ... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**FIGURE P13–39**",
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**13–46**C Is the total internal energy of an ideal-gas mixture equal to the sum of the internal energies of each individual gas in the mixture? Answer the same question for a real-gas mixture.
**13–47**C Is the specific internal energy of a gas mixture equal to the sum of the specific internal energies of each indiv... | {
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"Header 3": "**Properties of Gas Mixtures**",
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**13–65E** A gaseous mixture consists of 75 percent methane and 25 percent ethane by mass. 2 million cubic feet of this mixture is trapped in a geological formation as natural gas at 300°F and 1300 psia. This natural gas is pumped 6000 ft to the surface. At the surface, the gas pressure is 20 psia and its temperature i... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**FIGURE P13–64**",
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**13–74C** What is an ideal solution? Comment on the volume change, enthalpy change, entropy change, and chemical potential change during the formation of ideal and nonideal solutions.
**13–75C** It is common experience that two gases brought into contact mix by themselves. In the future, could it be possible to inve... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**Special Topic: Chemical Potential and the Separation Work of Mixtures**",
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**13–85** Air has the following composition on a mole basis: 21 percent O2, 78 percent N2, and 1 percent Ar. Determine the gravimetric analysis of air and its molar mass. Answers: 23.2 percent O2, 75.4 percent N2, 1.4 percent Ar, 28.96 kg/kmol
**13–86** The products of combustion of a hydrocarbon fuel and air are com... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**Review Problems**",
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**13–102** An ideal-gas mixture consists of 3 kmol of N2 and 6 kmol of CO2. The mass fraction of CO2 in the mixture is (*a*) 0.241 (*b*) 0.333 (*c*) 0.500 (*d*) 0.667 (*e*) 0.759
**13–103** An ideal-gas mixture whose apparent molar mass is 20 kg/kmol consists of N2 and three other gases. If the mole fraction of nitro... | {
"Header 1": "**Special Case: Separation of a Two-Component Mixture**",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**13–112** The simple additive rule may not be appropriate for the volume of binary mixtures of gases, Prove this for a pair of gases of your choice at several different temperatures and pressures using Kay's rule and the principle of corresponding states.
**13–113** You have a rigid tank equipped with a pressure gau... | {
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"Header 3": "**Design and Essay Problems**",
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t temperatures below the critical temperature, the gas phase of a substance is frequently referred to as a *vapor*. The term *vapor* implies a gaseous state that is close to the saturation region of the substance, raising the possibility of condensation during a process.
In Chap. 13, we discussed mixtures of gases th... | {
"Header 1": "GAS-VAPOR MIXTURES AND AIR-CONDITIONING",
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The objectives of Chapter 14 are to:
- Differentiate between dry air and atmospheric air.
- Define and calculate the specific and relative humidity of atmospheric air.
- Calculate the dew-point temperature of atmospheric air.
- Relate the adiabatic saturation temperature and wet-bulb temperatures of atmospheric air.
... | {
"Header 1": "GAS-VAPOR MIXTURES AND AIR-CONDITIONING",
"Header 3": "**OBJECTIVES**",
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Air is a mixture of nitrogen, oxygen, and small amounts of some other gases. Air in the atmosphere normally contains some water vapor (or *moisture*) and is referred to as **atmospheric air**. By contrast, air that contains no water vapor is called **dry air**. It is often convenient to treat air as a mixture of water ... | {
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"Header 3": "**14–1** ■ **DRY AND ATMOSPHERIC AIR**",
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The amount of water vapor in the air can be specified in various ways. Probably the most logical way is to specify directly the mass of water vapor present in a unit mass of dry air. This is called **absolute** or **specific humidity** (also called *humidity ratio*) and is denoted by $\omega$ :
$$\omega = \frac{m_y}... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
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Schematic for Example 14–1.
where
$$P_{a} = P_{\text{sat } @ T} \tag{14-10}$$
Combining Eqs. 14–8 and 14–9, we can also express the relative humidity as
$$\phi = \frac{\omega P}{(0.622 + \omega)P_g} \quad \text{and} \quad \omega = \frac{0.622\phi P_g}{P - \phi P_g}$$
(14–11a, b)
The relative humidity ranges f... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**FIGURE 14-7**",
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A 5-m $\times$ 5-m $\times$ 3-m room shown in Fig. 14–7 contains air at 25°C and 100 kPa at a relative humidity of 75 percent. Determine (a) the partial pressure of dry air, (b) the specific humidity, (c) the enthalpy per unit mass of the dry air, and (d) the masses of the dry air and water vapor in the room.
**S... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**EXAMPLE 14 –1** The Amount of Water Vapor in Room Air",
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Constant-pressure cooling of moist air and the dew-point temperature on the *T-s* diagram of water.
When the temperature of a cold drink is below the dew-point temperature of the surrounding air, it "sweats."
**FIGURE 14–10**
Schematic for Example 14... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**FIGURE 14–8**",
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In cold weather, condensation often occurs on the inner surfaces of the windows due to the lower air temperatures near the window surface. Consider a house, shown in Fig. 14–10, that contains air at 20°C and 75 percent relative humidity. At what window temperature will the moisture in the air start condensing on the in... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**EXAMPLE 14–2 Fogging of the Windows in a House**",
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Relative humidity and specific humidity are frequently used in engineering and atmospheric sciences, and it is desirable to relate them to easily measurable quantities such as temperature and pressure. One way of determining the relative humidity is to determine the dew-point temperature of air, as discussed in the las... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "14-4 • ADIABATIC SATURATION AND WET-BULB TEMPERATURES",
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The adiabatic saturation process and its representation on a T-s diagram of water. Energy balance:
$$\dot{E}_{\rm in}=\dot{E}_{\rm out} \quad ({\rm since}\ \dot{Q}=0\ {\rm and}\ \dot{W}=0)$$
$$\dot{m}_ah_1+\dot{m}_fh_f=\dot{m}_ah_2$$
or
$$\dot{m}_a h_1 + \dot{m}_a (\omega_2 - \omega_1) h_{f_2} = \dot{m}_a h_2$$... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**FIGURE 14-11**",
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The dry- and the wet-bulb temperatures of atmospheric air at 1 atm (101.325 kPa) pressure are measured with a sling psychrometer and determined to be 25 and 15°C, respectively. Determine (a) the specific humidity, (b) the relative humidity, and (c) the enthalpy of the air.
**SOLUTION** Dry- and wet-bulb temperatures ... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**EXAMPLE 14-3** The Specific and Relative Humidity of Air",
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The state of the atmospheric air at a specified pressure is completely specified by two independent intensive properties. The rest of the properties can be calculated easily from the previous relations. The sizing of a typical air-conditioning system involves numerous such calculations, which may eventually get on the ... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "14-5 • THE PSYCHROMETRIC CHART",
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Consider a room that contains air at 1 atm, 35°C, and 40 percent relative humidity. Using the psychrometric chart, determine (*a*) the specific humidity, (*b*) the enthalpy, (*c*) the wet-bulb temperature, (*d*) the dew-point temperature, and (*e*) the specific volume of the air.
**SOLUTION** The relative humidity of... | {
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"Header 3": "**EXAMPLE 14–4 The Use of the Psychrometric Chart**",
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(*c*) The wet-bulb temperature is determined by drawing a line parallel to the *T*wb = constant lines from the specified state until it intersects the saturation line, giving
$$T_{\rm wb} = 24^{\circ}{\rm C}$$
(*d*) The dew-point temperature is determined by drawing a horizontal line from the specified state to the... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "*h* = **71.5 kJ/kg dry air**",
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A body feels comfortable when it can freely dissipate its waste heat, and no more.
It did not take long for people to realize that they could not change the weather in an area. All they can do is change it in a confined space such as a house or a workplace (Fig. 14–17). In the past, this was partially accomplished by... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**FIGURE 14–18**",
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Maintaining a living space or an industrial facility at the desired temperature and humidity requires some processes called air-conditioning processes. These processes include *simple heating* (raising the temperature), *simple cooling* (lowering the temperature), *humidifying* (adding moisture), and *dehumidifying* (r... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**14–7** ■ **AIR-CONDITIONING PROCESSES**",
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Many residential heating systems consist of a stove, a heat pump, or an electric resistance heater. The air in these systems is heated by circulating it through a duct that contains the tubing for the hot gases or the electric resistance wires, as shown in Fig. 14–20. The amount of moisture in the air remains constant ... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "Simple Heating and Cooling ( $\\omega = constant$ )",
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Humid air at 1 atm, 100°F, and 70 percent relative humidity is cooled at constant pressure to the dew-point temperature (Fig. 14–22). Determine the cooling, in Btu/lbm dry air, required for this process.
**SOLUTION** Humid air at a specified state is cooled at constant pressure to the dew-point temperature. The cooli... | {
"Header 1": "14-2 • SPECIFIC AND RELATIVE HUMIDITY OF AIR",
"Header 3": "**EXAMPLE 14–5** Cooling of Air",
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Problems associated with the low relative humidity resulting from simple heating can be eliminated by humidifying the heated air. This is accomplished by passing the air first through a heating section (process 1-2) and then through a humidifying section (process 2-3), as shown in Fig. 14–23.
The location of state 3 ... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**Heating with Humidification**",
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An air-conditioning system is to take in outdoor air at 10°C and 30 percent relative humidity at a steady rate of 45 m³/min and to condition it to 25°C and 60 percent relative humidity. The outdoor air is first heated to 22°C in the heating section and then humidified by the injection of hot steam in the humidifying se... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**EXAMPLE 14–6** Heating and Humidification of Air",
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The specific humidity of air remains constant during a simple cooling process, but its relative humidity increases. If the relative humidity reaches undesirably high levels, it may be necessary to remove some moisture from the air, that is, to dehumidify it. This requires cooling the air below its dew-point temperature... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**Cooling with Dehumidification**",
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Air enters a window air conditioner at 1 atm, 30°C, and 80 percent relative humidity at a rate of 10 m<sup>3</sup>/min, and it leaves as saturated air at 14°C. Part of the moisture in the air that condenses during the process is also removed at 14°C. Determine the rates of heat and moisture removal from the air.
**SO... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**EXAMPLE 14–7** Cooling and Dehumidification of Air",
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Conventional cooling systems operate on a refrigeration cycle, and they can be used in any part of the world. But they have a high initial and operating cost. In desert (hot and dry) climates, we can avoid the high cost of cooling by using *evaporative coolers*, also known as *swamp coolers*.
Evaporative cooling is b... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**Evaporative Cooling**",
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Desert dwellers often wrap their heads with a water-soaked porous cloth (Fig. 14–28). On a desert where the pressure is 1 atm, temperature is 120°F, and relative humidity is 10 percent, what is the temperature of this cloth?
**SOLUTION** Desert dwellers often wrap their heads with a water-soaked porous cloth. The tem... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**EXAMPLE 14–8 Evaporative Cooling with Soaked Head Cover**",
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Many air-conditioning applications require the mixing of two airstreams. This is particularly true for large buildings, most production and process plants, and hospitals, which require that the conditioned air be mixed with a certain fraction of fresh outside air before it is routed into the living space. The mixing is... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**Adiabatic Mixing of Airstreams**",
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Saturated air leaving the cooling section of an air-conditioning system at 14°C at a rate of 50 m³/min is mixed adiabatically with the outside air at 32°C and 60 percent relative humidity at a rate of 20 m³/min. Assuming that the mixing process occurs at a pressure of 1 atm, determine the specific humidity, the relativ... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "■ EXAMPLE 14-9 Mixing of Conditioned Air with Outdoor Air",
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Power plants, large air-conditioning systems, and some industries generate large quantities of waste heat that is often rejected to cooling water from nearby lakes or rivers. In some cases, however, the cooling water supply is limited, or thermal pollution is a serious concern. In such cases, the waste heat must be rej... | {
"Header 1": "Cooling coils $\\begin{array}{c} 100^{\\circ}F \\\\ \\phi = 0.70 \\end{array}$ $\\begin{array}{c} 1 \\text{ atm} \\end{array}$ $\\begin{array}{c} Air \\\\ \\phi = 1 \\end{array}$",
"Header 3": "**Wet Cooling Towers**",
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Cooling water leaves the condenser of a power plant and enters a wet cooling tower at $35^{\circ}$ C at a rate of 100 kg/s. Water is cooled to $22^{\circ}$ C in the cooling tower by air that enters the tower at 1 atm, $20^{\circ}$ C, and 60 percent relative humidity and leaves saturated at $30^{\circ}$ C. Neglectin... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
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In this chapter we discussed the air—water vapor mixture, which is the most commonly encountered gas—vapor mixture in practice. The air in the atmosphere normally contains some water vapor, and it is referred to as *atmospheric air*. By contrast, air that contains no water vapor is called *dry air*. In the temperature ... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**SUMMARY**",
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- **14–1C** What is the difference between dry air and atmospheric air?
- **14–2C** What is vapor pressure?
- **14–3C** What is the difference between the specific humidity and the relative humidity?
- **14–4C** Can the water vapor in air be treated as an ideal gas? Explain.
- **14–5C** Explain how vapor pressure of th... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Dry and Atmospheric Air: Specific and Relative Humidity**",
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- **14–21C** What is the dew-point temperature?
- **14–22C** In summer, the outer surface of a glass filled with iced water often "sweats." How can you explain this sweating?
- **14–23C** In some climates, cleaning the ice off the windshield of a car is a common chore on winter mornings. Explain how ice forms on the wi... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Dew-Point, Adiabatic Saturation, and Wet-Bulb Temperatures**",
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- **14–34C** How do constant-enthalpy and constant-wet-bulbtemperature lines compare on the psychrometric chart?
- **14–35C** At what states on the psychrometric chart are the dry-bulb, wet-bulb, and dew-point temperatures identical?
- **14–36C** How is the dew-point temperature at a specified state determined on the p... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Psychrometric Chart**",
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- **14–40E** Reconsider Prob. 14–39E. Determine the adiabatic saturation temperature of the humid air. Answer: 85°F
- **14–41** The air in a room has a pressure of 1 atm, a drybulb temperature of 24°C, and a wet-bulb temperature of 17°C. Using the psychrometric chart, determine (*a*) the specific humidity, (*b*) the en... | {
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"Header 3": "**FIGURE P14–39E**",
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**14–45C** What does a modern air-conditioning system do besides heating or cooling the air?
**14–46C** How does the human body respond to (*a*) hot weather, (*b*) cold weather, and (*c*) hot and humid weather?
**14–47C** How does the air motion in the vicinity of the human body affect human comfort?
**14–48C** C... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Human Comfort and Air-Conditioning**",
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**14–63C** How do relative and specific humidities change during a simple heating process? Answer the same question for a simple cooling process.
**14–64C** Why does a simple heating or cooling process appear as a horizontal line on the psychrometric chart?
**14–65** Humid air at 150 kPa, 40°C, and 70 percent relat... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Simple Heating and Cooling**",
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**14–71C** Why is heated air sometimes humidified?
**14–72** Air at 1 atm, 15°C, and 60 percent relative humidity is first heated to 20°C in a heating section and then humidified by introducing water vapor. The air leaves the humidifying section at 25°C and 65 percent relative humidity. Determine (*a*) the amount of ... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Heating with Humidification**",
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**14–76C** Why is cooled air sometimes reheated in summer before it is discharged to a room?
**14–77** Atmospheric air at 1 atm, 30°C, and 80 percent relative humidity is cooled to 20°C while the mixture pressure remains constant. Calculate the amount of water, in kg/kg dry air, removed from the air and the cooling r... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Cooling with Dehumidification**",
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**14–80** Reconsider Prob. 14–79. Using appropriate software, develop a general solution to the problem in which the input variables may be supplied and parametric studies performed. For each set of input variables for which the pressure is atmospheric, show the process on the psychrometric chart.
**14–81** Repeat Pr... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**FIGURE P14–79**",
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} |
- **14–89C** What is evaporative cooling? Will it work in humid climates?
- **14–90C** During evaporation from a water body to air, under what conditions will the latent heat of vaporization be equal to the heat transfer from the air?
- **14–91C** Does an evaporation process have to involve heat transfer? Describe a pr... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Evaporative Cooling**",
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**14–97**C Two unsaturated airstreams are mixed adiabatically. It is observed that some moisture condenses during the mixing process. Under what conditions will this be the case?
**14–98**C Consider the adiabatic mixing of two airstreams. Does the state of the mixture on the psychrometric chart have to be on the stra... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Adiabatic Mixing of Airstreams**",
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**14–106C** How does a natural-draft wet cooling tower work?
**14–107C** What is a spray pond? How does its performance compare to the performance of a wet cooling tower?
**14–108** The cooling water from the condenser of a power plant enters a wet cooling tower at 40°C at a rate of 90 kg/s. The water is cooled to ... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Wet Cooling Towers**",
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... |
**14–114** The air in a room is at 1 atm, 32°C, and 60 percent relative humidity. Determine (*a*) the specific humidity, (*b*) the enthalpy, in kJ/kg dry air, (*c*) the wet-bulb temperature, (*d*) the dew-point temperature, and (*e*) the specific volume of the air, in m3 /kg dry air. Use the psychrometric chart.
**14... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Review Problems**",
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**14–129E** Reconsider Prob. 14–128E. The relative humidity of the air in a home is to be restored to 60 percent by evaporating 60°F water into the air. How much heat, in Btu, is required to do this in a home of 16,000 ft3 volume?
**14–130** Air enters a cooling section at 97 kPa, 35°C, and 30 percent relative humidi... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**FIGURE P14–128E**",
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**14–134** An automobile air conditioner uses refrigerant-134a as the cooling fluid. The evaporator operates at 100 kPa gage and the condenser operates at 1.5 MPa gage. The compressor requires a power input of 6 kW and has an isentropic efficiency of 85 percent. Atmospheric air at 25°C and 60 percent relative humidity ... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**FIGURE P14-133**",
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} |
**14–141** A room contains 65 kg of dry air and 0.43 kg of water vapor at 25°C and 90 kPa total pressure. The relative humidity of air in the room is
(a) 29.9% (b) 35.2% (c) 41.5% (d) 60.0% (e) 66.2%
**14–142** A 40-m³ room contains air at 30°C and a total pressure of 90 kPa with a relative humidity of 75 percent. ... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Fundamentals of Engineering (FE) Exam Problems**",
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**14–151** Identify the major sources of heat gain in your house in summer, and propose ways of minimizing them and thus reducing the cooling load.
**14–152** The air-conditioning needs of a large building can be met by a single central system or by several individual window units. Considering that both approaches ar... | {
"Header 1": "EXAMPLE 14-10 Cooling of a Power Plant by a Cooling Tower",
"Header 3": "**Design and Essay Problems**",
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**I** n the preceding chapters we limited our consideration to nonreacting systems—systems whose chemical composition remains unchanged during a process. This was the case even with mixing processes during which a homogeneous mixture is formed from two or more fluids without the occurrence of any chemical reactions. In... | {
"Header 1": "**CHEMICAL REACTIONS** 15",
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} |
Any material that can be burned to release thermal energy is called a **fuel**. Most familiar fuels consist primarily of hydrogen and carbon. They are called **hydrocarbon fuels** and are denoted by the general formula $C_nH_m$ . Hydrocarbon fuels exist in all phases, some examples being coal, gasoline, and natural ga... | {
"Header 1": "**CHEMICAL REACTIONS** 15",
"Header 3": "15-1 • FUELS AND COMBUSTION",
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} |
The mass (and number of atoms) of each element is conserved during a chemical reaction.
processes, the moisture in the air and the H2O that forms during combustion can also be treated as an inert gas, like nitrogen. At very high temperatures, however, some water vapor dissociates into H2 and O2 as well as into H, O, ... | {
"Header 1": "**CHEMICAL REACTIONS** 15",
"Header 3": "**FIGURE 15–4**",
"token_count": 973,
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One kmol of octane ( $C_8H_{18}$ ) is burned with air that contains 20 kmol of $O_2$ , as shown in Fig. 15–6. Assuming the products contain only $CO_2$ , $H_2O$ , $O_2$ , and $N_2$ , determine the mole number of each gas in the products and the air–fuel ratio for this combustion process.
**SOLUTION** The amount ... | {
"Header 1": "**CHEMICAL REACTIONS** 15",
"Header 3": "**■ EXAMPLE 15-1** Balancing the Combustion Equation",
"token_count": 841,
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} |
It is often instructive to study the combustion of a fuel by assuming that the combustion is complete. A combustion process is **complete** if all the carbon in the fuel burns to $CO_2$ , all the hydrogen burns to $H_2O$ , and all the sulfur (if any) burns to $SO_2$ . That is, all the combustible components of a fue... | {
"Header 1": "15-2 • THEORETICAL AND ACTUAL COMBUSTION PROCESSES",
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Coal from Pennsylvania which has an ultimate analysis (by mass) of 84.36 percent C, 1.89 percent $H_2$ , 4.40 percent $O_2$ , 0.63 percent $N_2$ , 0.89 percent S, and 7.83 percent ash (noncombustibles) is burned with a theoretical amount of air (Fig. 15–10). Disregarding the ash content, determine the mole fractions... | {
"Header 1": "Before After 100 kPa 25°C Gas sample including CO<sub>2</sub> 1 liter $y_{CO_2} = \\frac{V_{CO_2}}{V} = \\frac{0.1}{1} = 0.1$",
"Header 3": "**EXAMPLE 15-2** Combustion of Coal with Theoretical Air",
"token_count": 1803,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_engineer... |
A certain natural gas has the following volumetric analysis: 72 percent CH<sub>4</sub>, 9 percent H<sub>2</sub>, 14 percent N<sub>2</sub>, 2 percent O<sub>2</sub>, and 3 percent CO<sub>2</sub>. This gas is now burned with the stoichiometric amount of air that enters the combustion chamber at 20°C, 1 atm, and 80 percent... | {
"Header 1": "Before After 100 kPa 25°C Gas sample including CO<sub>2</sub> 1 liter $y_{CO_2} = \\frac{V_{CO_2}}{V} = \\frac{0.1}{1} = 0.1$",
"Header 3": "**■ EXAMPLE 15-3** Combustion of a Gaseous Fuel with Moist Air",
"token_count": 1455,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdfcoffee.com_en... |
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