Water
1 teaspoon
1 teaspoon
Wine
1 2
1.1 You have a glass of water and a glass of wine, as shown in the fi gure. You perform the fol-lowing processes. (1) transfer 1 teaspoon of water to the glass of wine and mix thoroughly; then (2) transfer 1 teaspoon of this contaminated wine to the water. Now both the water and the wine are contaminated. Which of the following is true? Explain. Hint: it may be useful to consider this problem in terms of an extensive property.
(a) The volume of water contaminating the wine is greater than the volume of wine contaminating the water.
(b) The volume of water contaminating the wine is equal to the volume of wine contaminating the water.
(c) The volume of wine contaminating the water is greater than the volume of water contaminating the wine.
1.2 You have a jar of 90 nickels and a jar of 90 pennies. You perform the following processes.
(1) Transfer 10 nickels to the jar of pennies and mix thoroughly; then (2) transfer 10 coins from the contaminated pennies back to the jar with nickels. Which of the following is true? Explain.
(a) The amount of pennies in the jar of mostly nickels is greater than the amount of nickels in the jar of mostly pennies.
(b) The amount of pennies in the jar of mostly nickels is the equal to the amount of nickels in the jar of mostly pennies.
(c) The amount of nickels in the jar of mostly pennies is greater than the amount of pennies in the jar of mostly nickels.
1.3 Shown in the following fi gure is a process from which Species A is isothermally compressed from 0.5 bar and 300 K to 1 bar. The insets of each state, which are of equal volume, contain a
“molecular view” of species A.
A
A A
A
A A A
A
A Molecular view
Molecular view Ideal gas A
T1 = 300 K P1 = 0.5 bar
State 1 State 2
Process
T1 = 300 K P2 = 1 bar
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32 ► Chapter 1. Measured Thermodynamic Properties and Other Basic Concepts
Molecular view Molecular view
T1 = 300 K
P2 = 1 bar P1 = 5 bar
valve
1.4 Go to the teaching or research labs at your university and determine three ways temperature is measured and three ways pressure is measured.
1.5 Consider a binary mixture of a light gas a with mass ma and a heavy gas b with mass mb at temperature T. How does the mean-square velocity of the two species compare? Which species, on average, moves faster?
1.6 Consider the system sketched below:
Next consider the open system shown in the following fi gure. Species A fl ows steadily through the system and expands through the valve from an inlet state at 5 bar and 300 K to an exit state at 1 bar.
You may assume Species A acts as an ideal gas. In analogy to the closed system depicted earlier, the equal volume insets are shown in this fi gure. Fill in the corresponding “molecular views” of Species A. Explain your answer.
Large reservoir of boiling water
(100° C)
Cu Block
Large reservoir of ice water
(0° C)
(a) After a short time, is this system in equilibrium?
(b) After a long time?
(c) After a very long time?
1.7 Consider a tightly capped water bottle containing two phases with a small amount of liquid water and saturated air. If the bottle is left in the sun on a hot day and the temperature increases, what happens to the amount of water in the liquid? Explain.
1.8 A rigid, sealed container initially contains pure water at 100°C. Some of the water is in the liquid phase, and some is in the vapor phase (i.e., as steam). Air is then injected into the system in an isothermal process at constant volume. What happens?
1.9 Using language a high school student could understand, explain the difference between satu-ration pressure and vapor pressure.
1.10 This question addresses the two piston-cylinder assemblies depicted on the left of Figure 1.8 that illustrate the concept of saturation pressure. The piston on the right is at twice the pressure of the system on the left; however, if you count molecules of species a, there are less than twice the number on the right (i.e., the number does not increase directly proportional to temperature). Is this a mistake? Explain.
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1.9 Problems ◄ 33 1.11 Sometimes a lid to a pot used for cooking fi ts “too well” and can be diffi cult to remove after the pot cools down. Why do you think this is happening?
1.12 I thoroughly infl ated a bag of soccer balls last summer. However, when I brought them out to play this winter, they all were underinfl ated. Discuss the possible reasons.
1.13 Relative humidity is defi ned as the ratio of the mass of water in air divided by the mass of water at saturation. Compare the water content in the air on a day on which the temperature is 10°C with 90% relative humidity to a day at 30°C and 50% relative humidity. Which day has higher water content?
1.14 When a system contains regions that differ in physical structure or chemical composition, an overall value can be assigned to its properties. Consider the system, system 1, shown below. It contains na molecules in state a and nb molecules in state b.
(a) Develop an expression for the extensive volume V1 in terms of na, nb, and the volumes of each homogeneous region Va and Vb.
(b) Develop an expression for the intensive molar volume v1 in terms of na, nb and the molar volumes of each homogeneous region va and vb.
(c) Generalize the result of part (a) to come up with an expression for any extensive prop-erty K1 in terms of na, nb, and the extensive properties Ka and Kb.
(d) Generalize the result of part (b) to come up with an expression for the intensive form of the property in part (c), k1, in terms of na, nb, and the intensive properties ka and kb.
State b
System 1
State a
+ =
Va
Vb
na na
nb nb
1.15 Consider two systems of ideal gases. System I consists of pure gas A at a given pressure and temperature. System II contains a mixture of gases A and B at the same temperature and pressure.
If the molecular weight of gas B is larger than gas A, how does the molar density 1mol/cm32 of system I compare to system II?
1.16 Consider two systems of ideal gases. System I consists of pure gas A at a given pressure and temperature. System II contains a mixture of gases A and B at the same temperature and pressure.
If the molecular weight of gas B is larger than gas A, how does the mass density 1g/cm32 of system I compare to system II?
1.17 You can breathe in approximately 2 L of air into your lungs. What volume of helium do you think you can breathe in? Explain.
1.18 A “pressure cooker” is a device that allows food to be cooked at pressures that are higher than atmospheric pressure. Explain why this device changes how your food is cooked.
1.19 The ideal gas model is one example of an equation of state. Why do you think it is termed an equation of state?
1.20 Consider a system containing water in the following states. What phases are present?
(a) P5 10 3bar4; T 5 170 3°C4 (b) v^ 5 3 3m3/kg4; T5 70 3°C4 (c) P5 60 3bar4; v^ 5 0.05 3m3/kg4 (d) P5 5 3bar4; s 5 7.0592 3kJ/1kg K2 4
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34 ► Chapter 1. Measured Thermodynamic Properties and Other Basic Concepts
Numerical Problems
1.21 Estimate the speed at which the average oxygen molecule is moving in the room that you are in.
1.22 The Reamur temperature scale uses the normal freezing and boiling points of water to defi ne 0°and 80°, respectively. What is the value of room temperature (22°C) on the Reamur scale?
1.23 At what temperature does water boil on the top of Mount Everest, elevation z5 8848 m?
Recall that the dependence of pressure with altitude is given by:
P5 Patm exp ¢2 MWgz RT ≤
where, Patm is atmospheric pressure, g is the gravitational acceleration, and MW is the molecular weight of the gas.
1.24 Water is cooled in a rigid closed container from the critical point to 10 bar. Determine the quality of the fi nal state.
1.25 Using linear interpolation, estimate the specifi c volume of water under the following condi-tions using data from the steam tables:
(a) P5 1.9 3MPa4; T 5 2503°C4 (b) P5 1.9 3MPa4; T 5 3003°C4 (c) P5 1.9 3MPa4; T 5 2703°C4
Look up the specifi c volumes of water that correspond to cases (a), (b), and (c) on the website http://webbook.nist.gov/chemistry/fl uid/ and report their values. Comment on the agreement between the two sources.
1.26 Determine the mass of 1 L of saturated liquid water at 25°C. How do you think this value compares to the mass of 1L of subcooled liquid water at 25°C and atmospheric pressure?
1.27 Determine the temperature, quality, and internal energy of 5 kg of water in a rigid container of volume 1 m3 at a pressure of 2 bar.
1.28 A rigid container of volume 1 m3 contains saturated water at 1 MPa. If the quality is 0.10, what is the volume occupied by the vapor?
1.29 Use the data in the steam tables to plot the vapor–liquid dome on a Pv diagram. It is useful to plot v on a log scale.
1.30 Calculate the volume of water using the ideal gas model under the following conditions.
Then report the percent error when compared to the values reported in the steam tables.
(a) P5 1.01 3bar4; T 5 100 3°C4 (b) P5 1 3bar4; T 5 500 3°C4 (c) P5 100 3bar4; T 5 500 3°C4 (d) P5 100 3bar4; T 5 1000 3°C4
1.31 How many moles of air are in the room in which you are sitting? What is its mass?
1.32 Consider a gas at 20°C and 1 bar. The molecules may be considered to be hard spheres with a diameter of 3 Å. Estimate the percentage of the available volume they occupy.
1.33 You want to keep your house dry enough so that water does not condense on your walls at night. If the temperature gets down to 40°F at night, what is the maximum allowable density of water in the room during the day when the room is at 70°F?
1.34 Consider a rigid, thick-walled tube that is fi lled with H2O liquid and vapor at 0.1 MPa. After it is sealed, it is heated so that it passes through its critical point. What fraction of the mass in the tube is liquid?
1.35 As best as you can, estimate the specifi c volume of water at each of the following conditions.
Justify your answer.
(a) 2 bar and 200°C (b) 2 bar and 100°C
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1.9 Problems ◄ 35 1.36 A rigid container contains 1 kg of water at 90°C. If 200 g of the water are in the liquid phase and the rest is vapor, determine the pressure in the tank and the volume of the tank.
1.37 40 g of water are sealed in a 10 L container at 300°C. As accurately as you can, determine the pressure of the container.
1.38 A rigid container of 100 L contains saturated water at 100°C. The water is heated, and it reaches the critical point. Determine the initial mass of water in the tank and its quality.
1.39 A piston-cylinder assembly contains 0.5 kg of water at 50°C and 500 kPa. It is then isobari-cally heated until all the water is vaporized. What is the fi nal temperature and volume?
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C H A P T E R
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