Mastering Physics Solutions Chapter 17 Phases and Phase Changes
Chapter 17 Phases and Phase Changes Q.1CQ
At the beginning of a typical airline flight you are instructed about the proper use of oxygen masks that will fall from the ceiling if the cabin pressure suddenly drops. You are advised that the oxygen masks are working properly, even if the bags do not fully inflate. In fact, the bags expand to their fullest if cabin pressure is lost at high altitude, but expand only partially if the plane is at low altitude. Explain.
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Chapter 17 Phases and Phase Changes Q.1P
(a) Is the number of molecules in one mole of N2 greater than, less than, or equal to the number of molecules in one mole of O2? (b) Is the mass of one mole of N2 greater than, less than, or equal to the mass of one mole of O2?
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Chapter 17 Phases and Phase Changes Q.2CQ
How is the air pressure in a tightly sealed house affected by operating the furnace? Explain.
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Chapter 17 Phases and Phase Changes Q.2P
Is the number of atoms in one mole of helium greater than, less than, or equal to the number of atoms in one mole of oxygen? Helium consists of individual atoms. He. and oxygen is a diatomic gas. 02
Solution:
Helium is a monoatomic gas while oxygen is a diatomic gas Therefore, the total number of atoms in one mole of oxygen gas is equal to twice the number of atoms in one mole of helium Hence, the total number of atoms in one mole of helium gas is less than the total number of atoms in one mole of oxygen
Chapter 17 Phases and Phase Changes Q.3CQ
The average speed of air molecules in your room is on the order of the speed of sound. What is their average velocity?
Solution:
Since the velocity is accounts both it speed and direction of motion, so the average velocity of air molecules in the room will be Izerol as the molecules move randomly in all directions.
Chapter 17 Phases and Phase Changes Q.3P
If you put a helium-filled balloon in the refrigerator, (a) will its volume increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Lowering the temperature of an ideal gas at constant pressure results in a reduced volume.
II. The same amount of gas is in the balloon; therefore, its volume remains the same.
III. The balloon can expand more in the cool air of the refrigerator, giving an increased volume.
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Chapter 17 Phases and Phase Changes Q.4CQ
Is it possible to change both the pressure and thevolume of an ideal gas without changing the average kinetic energy of its molecules? If your answer is no, explain why not. If your answer is yes, give a specific example.
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Chapter 17 Phases and Phase Changes Q.4P
Two containers hold ideal gases at the same temperature. Container A has twice the volume and half the number of molecules as container B. What is the ratio PA/PB where PA is the pressure in container A and PB is the pressure in container B?
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Chapter 17 Phases and Phase Changes Q.5CQ
Is it possible to change both the pressure and thevolume of an ideal gas without changing the average kinetic energy of its molecules? If your answer is no, explain why not. If your answer is yes, give a specific example.
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Chapter 17 Phases and Phase Changes Q.5P
Standard temperature and pressure (STP) is defined as a temperature of 0°C and a pressure of 101.3 kPa. Whatis the volume occupied by one mole of an ideal gas at STP?
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Chapter 17 Phases and Phase Changes Q.6CQ
A camping stove just barely boils water on a mountaintop. When the stove is used at sea level, will it be able to boil water? Explain your answer.
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Chapter 17 Phases and Phase Changes Q.6P
After emptying her lungs, a person inhales 4.1 L of air at 0.0 °C and holds her breath. How much does the volume of the air increase as it warms to her body temperature of 37 °C?
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Chapter 17 Phases and Phase Changes Q.7CQ
An autoclave is a device used to sterilize medical instruments. It is essentially a pressure cooker that heats the instruments in water under high pressure. This ensures that the sterilization process occurs at temperatures greater than the normal boiling point of water. Explain why the autoclave produces such high temperatures.
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Chapter 17 Phases and Phase Changes Q.7P
In the morning, when the temperature is 286 K, a bicyclist finds that the absolute pressure in his tires is 501 kPa. That afternoon he finds that the pressure in the tires has increased to 554 kPa. Ignoring expansion of the tires, find the afternoon temperature.
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Chapter 17 Phases and Phase Changes Q.8CQ
As the temperature of ice is increased, it changes first tinto a liquid and then into a vapor. On the other hand, dry ice, which is solid carbon dioxide, changes directly from a solid to a vapor as its temperature is increased. How might one produce liquid carbon dioxide?
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Chapter 17 Phases and Phase Changes Q.8P
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Chapter 17 Phases and Phase Changes Q.9CQ
Isopropyl alcohol is sometimes rubbed onto a patient’s arms and legs to lower their body temperature. Why is this effective?
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Chapter 17 Phases and Phase Changes Q.9P
Amount of Helium in a Blimp The Goodyear blimp Spirit of Akron is 62.6 m long and contains 7023 m3 of helium. When the temperature of the helium is 285 K, its absolute pressure is 112 kPa. Find the mass of the helium in the blimp.
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Chapter 17 Phases and Phase Changes Q.10CQ
If you toss an ice cube into a swimming pool, is the water in the pool now at 0°C? Explain.
Solution:
The ice cube has an assured mass, which will engage a certain amount of heat from the water in the pool. The ice cube melt and water will come to a temperature equilibrium determined by the total mass of water and the total energy in the system.
Chapter 17 Phases and Phase Changes Q.10P
A compressed-air tank holds 0.500 m3 of air at a temperature of 285 K and a pressure of 880 kPa. What volume would the air occupy if it were released into the atmosphere, where the pressure is 101 kPa and the temperature is 303 K?
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Chapter 17 Phases and Phase Changes Q.11CQ
A drop of water on a kitchen counter evaporates in a matter of minutes. However, only a relatively small fraction of the molecules in the drop move rapidly enough to escape through the drop’s surface. Why, then, does the entire drop evaporate rather than just a small fraction of it?
Solution:
Evaporation is the process of revolving from liquid into vapor. Evaporation of water from the kitchen’s surface, the relative fraction of the molecules drips quickly. They take energy from their surroundings (which have enough temperature) from the drop of water. Then, the next molecules come up, occupy the same level, and repeat the above process. In this way, all of the water evaporates in a matter of minutes from the surface of the kitchen. Hence, entire drop evaporates rather than just a small fraction of it.
Chapter 17 Phases and Phase Changes Q.11P
A typical region of interstellar space may contain 106 atoms per cubic meter (primarily hydrogen) at a temperature of 100 K. What is the pressure of this gas?
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Chapter 17 Phases and Phase Changes Q.12
CE Four ideal gases have the following pressures, P,volumes, V, and mole numbers, n: gas A, P = 100 kPa, V = 1 m3, n = 10 mol; gas B, P = 200 kPa, V = 2 m3, n = 20 mol; gas C, P = 50 kPa, V = 1 m3, n = 50 mol;gas D,P = 50 kPa, V = 4 m3 n = 5 mol. Rank these gases in order of increasing temperature. Indicate ties where appropriate.
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Chapter 17 Phases and Phase Changes Q.13P
A balloon contains 3.7 liters of nitrogen gas at a temperature of 87 K and a pressure of 101 kPa. If the temperature of the gas0 is allowed to increase to 24 °C and the pressure remains constant, what volume will the gas occupy?
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Chapter 17 Phases and Phase Changes Q.14P
A balloon is filled with helium at a pressure of 2.4 × 105 Pa. The balloon is at a temperature of 18 °C and has a radius of 0.25 m. (a) How many helium atoms are contained in the balloon? (b) Suppose we double the number of helium atoms in the balloon, keeping the pressure and the temperature fixed. By what factor does the radius of the balloon increase? Explain.
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Chapter 17 Phases and Phase Changes Q.15P
A gas has a temperature of 310 K and a pressure of 101 kPa. (a) Find the volume occupied by 1.25 mol of this gas, assuming it is ideal, (b) Assuming the gas molecules can be approximated as small spheres of diameter 2.5 × 10−10 m, determine the fraction of the volume found in part (a) that is occupied by the molecules, (c) In determining the properties of an ideal gas, we assume that molecules are pointa of zero volume. Discuss the validity of this assumption for the case considered here.
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Chapter 17 Phases and Phase Changes Q.16P
A 15-cm3 flask contains 0.460 g of a gas at a pressure of 153 kPa and a temperature of 322 K. What is the molecular mass of this gas?
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Chapter 17 Phases and Phase Changes Q.17P
The Atmosphere of Mars On Mars, the average temperature is —64°F and the average atmospheric pressure is 0.92 kPa. (a) What is the number of molecules per volume in the Martian atmosphere? (b) Is the number of molecules per volume on the Earth greater than, less than, or equal to the number per volume on Mars? Explain your reasoning, (c) Estimate the number of molecules per volume in Earth’s atmosphere.
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Chapter 17 Phases and Phase Changes Q.18P
The air inside a hot-air balloon has an average temperature of 79.2 °C. The outside air has a temperature of 20.3 °C. What is the ratio of the density of air in the balloon to the density of air in the surrounding atmosphere?
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Chapter 17 Phases and Phase Changes Q.19P
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Chapter 17 Phases and Phase Changes Q.20P
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Chapter 17 Phases and Phase Changes Q.21P
One mole of a monatomic ideal gas has an initial pressure of 210 kPa, an initial volume of 1.2 × 10−3 m3, and an initial temperature of 350 K. The gas now undergoes three separate processes: (i) a constant-temperature expansion that triples its volume; (ii) a constant-pressure compression to its initial volume; and (iii) a constant-volume increase in pressure to its initial pressure. At the end of these three processes, the gas is back at its initial pressure, volume, and temperature. Plot these processes on a pressure-versus-volume graph, showing the values of P and V at the end points of each process.
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Chapter 17 Phases and Phase Changes Q.22P
The air inyour room is composed mostly of oxygen (O2) and nitrogen (N2) molecules. The oxygen molecules are more massive than the nitrogen molecules, (a) Is the rms speed of the O2 molecules greater than, less than, or equal to the rms speed of the N2 molecules? (b) Choose the best explanation from among the following:
I. The more massive oxygen molecules have greater momentum and therefore greater speed.
II. Equal temperatures for the oxygen and nitrogen molecules imply they have equal rms speeds.
III. The temperature is the same for both molecules, and hence their average kinetic energies are equal. As a result, the more massive oxygen molecules have lower speeds.
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Chapter 17 Phases and Phase Changes Q.23P
If the translational speed of molecules in an ideal gas is doubled, by what factor does the Kelvin temperature change? Explain.
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Chapter 17 Phases and Phase Changes Q.24P
A piston held at the temperature T contains a gas mixture with molecules of three different types; A, B, and C. The corresponding molecular masses are mc > m8 > mA Rank these molecular types in order of increasing (a) average kinetic energy and (b) rms speed. Indicate ties where appropriate.
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Chapter 17 Phases and Phase Changes Q.25P
The molecules in a tank of hydrogen have the same rms speed as the molecules in a tank of oxygen. State whether each of the following statements is true, false, or unknowable with the given information: (a) the pressures are the same; (b) the hydrogen is at the higher temperature; (c) the hydrogen has the higher pressure; (d) the temperatures are the same; (e) the oxygen is at the higher temperature.
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Chapter 17 Phases and Phase Changes Q.26P
At what temperature is the rms speed of H2 equal to the rms speed that O2 has at 313 K?
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Chapter 17 Phases and Phase Changes Q.27P
Suppose a planet has an atmosphere of pure ammonia at 0.0 °C. What is the rms speed of the ammonia molecules?
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Chapter 17 Phases and Phase Changes Q.28P
Three moles of oxygen gas (that is, 3.0 mol of O2) are placed in a portable container with a volume of 0.0035 m3.1f the temperature of the gas is 295 °C, find (a) the pressure of the gas and (b) the average kinetic energy of an oxygen molecule, (c) Suppose the volume of the gas is doubled, while the temperature and number of moles are held constant. By what factor do your answers to parts (a) and (b) change? Explain.
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Chapter 17 Phases and Phase Changes Q.29P
The rms speed of O2 is 1550 m/s at a given temperature, (a) Is the rms speed of H2O at this temperature greater than, less than, or equal to 1550 m/s? Explain, (b) Find the rms speed of H2Oat this temperatiue.
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Chapter 17 Phases and Phase Changes Q.30P
An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant, (a) If the number
of molecules in the gas is doubled, does the rms speed increase, decrease, or stay the same? Explain, (b) If the initial rms speed is 1300 m/s, what is the final rms speed?
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Chapter 17 Phases and Phase Changes Q.31P
What is the temperature of a gas of CO2 molecules whose rms speed is 329 m/s?
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Chapter 17 Phases and Phase Changes Q.32P
The rms speed of a sample of gas is increased by 1 %. (a) What is the percent change in the temperature of the gas? (b) What is the percent change in the pressure of the gas, assuming its volume is held constant?
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Chapter 17 Phases and Phase Changes Q.33P
Enriching Uranium In naturally occurring uranium atoms, 99.3% are 238U (atomic mass = 238 u, where u = 1.6605 × 10−27 kg) and only 0.7% are 235U (atomic mass = 235 u). Uranium-fueled reactors require an enhanced proportion of 235U. Since both isotopes of uranium have identical chemical properties, they can be separated only by methods that depend on their differing masses. One such method is gaseous diffusion, in which uranium hexafluoride (UF6) gas diffuses through a series of porous barriers. The lighter 235UFfi molecules have a slightly higher rms speed at a given temperature than the heavier 238UF6 molecules, and this allows the two isotopes to be separated. Find the ratio of the rms speeds of the two isotopes at 230 °C.
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Chapter 17 Phases and Phase Changes Q.34P
A 350-mL spherical flask contains 0.075 mol of an ideal gas at a temperature of 293 K. What is the average force exerted on the walls of the flask by a single molecule?
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Chapter 17 Phases and Phase Changes Q.35P
A brick has faces with the following dimensions: face 1 is 1 cm by 2 cm; face 2 is 2 cm by 3 cm; face 3 is 1 cm by 3 cm. On which face should the brick be placed if it is to have the smallest change in dimensions due to its own weight? Explain.
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Chapter 17 Phases and Phase Changes Q.36P
A hollow cylindrical rod (rod 1) and a solid cylindrical rod (rod 2) are made of the same material. The two rods have the same length and the same outer radius. If the same compressional force is applied to each rod, (a) is the change in length of rod 1 greater than, less than, or equal to the change in length of rod 2? (b) Choose the beat explanation from among the following:
I. The solid rod has the larger effective cross-sectional area, since the empty part of the hollow rod doesn’t resist compression. Therefore, the solid rod has the smaller change in length.
II. The rods have the same outer radius and hence the same cross-sectional area. As a result, their change in length is the same.
III. Tile walls of the hollow rod are hard and resist compression more than the uniform material in the solid rod. Therefore the hollow rod has the smaller change in length.
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Chapter 17 Phases and Phase Changes Q.37P
A rock climber hangs freely from a nylon rope that is 14 m long and has a diameter of 8.3 mm. If the rope stretches 4.6 cm, what is the mass of the climber?
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Chapter 17 Phases and Phase Changes Q.38P
To stretch a relaxed biceps muscle 2.5 cm requires a force of 25 N. Find the Young’s modulus for the muscle tissue, assuming it to be a uniform cylinder of length 0.24 m and cross-sectional area 47 cm2.
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Chapter 17 Phases and Phase Changes Q.39P
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Chapter 17 Phases and Phase Changes Q.40P
The Marianas Trench The deepest place in all the oceans is the Marianas Trench, where the depth is 10.9 Km and the pressure is 1.10 × 108 Pa. If acopper ball 15.0 cm in diameter is taken to the bottom of the trench, by how much does its volume decrease?
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Chapter 17 Phases and Phase Changes Q.41P
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Chapter 17 Phases and Phase Changes Q.42P
A steel wire 4.7 m long stretches0.11 cm when it is given a tension of 360 N. (a) What is the diameter of the wire? (b) If it is desired that the stretch be less than 0.11 cm, should its diameter be increased or decreased? Explain.
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Chapter 17 Phases and Phase Changes Q.43P
Spiderweb An orb weaver spider with a mass of 0.26 g hangs vertically by one of its threads. The thread has a Young’s modulus of 4.7 × 109N/m2 and a radius of 9.8 × 10−6 m. (a) What is the fractional increase inthe thread’s length caused by the spider? (b) Suppose a 76-kg person hangs verticallyfrom a nylon rope. What radius must the rope haveif its fractional increase in length is to be the same as that of the spider’s thread?
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Chapter 17 Phases and Phase Changes Q.44P
Two rods of equal length (0.55 m.) and diameter (1.7 cm) arc placed end to end. One rod is aluminum, the other is brass. If a compressive force of 8400 N is applied to the rods, (a) how much does their combined length decrease? (b) Which of the rods changes its length by the greatest amount? Explain.
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Chapter 17 Phases and Phase Changes Q.45P
A piano wire 0.82 m long and 0.93 mm in diameter is fixed on one end. The other end is wrapped around a timing peg 3.5 mm in diameter. Initially the* wire, whose Young’s modulus is 2.4 × 1010 N/m2, has a tension of 14 N. Find the tension in the wire after the tuning peg has been turned through one complete revolution.
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Chapter 17 Phases and Phase Changes Q.46P
The formation of ice from water is accompanied by which of the following: (a) an absorption of heat by the water; (b) an increase in tempera ture; (c) a decrease in volume; (d) a removal of heat from the water; (e) a decrease in temperature?
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Chapter 17 Phases and Phase Changes Q.47P
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Chapter 17 Phases and Phase Changes Q.48P
Using the vapor-pressure curve given m Figure 17-26, find the temperature at which water boils when the pressure is 1.5 kPa.
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Chapter 17 Phases and Phase Changes Q.49P
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Chapter 17 Phases and Phase Changes Q.50P
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Chapter 17 Phases and Phase Changes Q.51P
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Chapter 17 Phases and Phase Changes Q.52P
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Chapter 17 Phases and Phase Changes Q.53P
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Chapter 17 Phases and Phase Changes Q.54P
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Chapter 17 Phases and Phase Changes Q.55P
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Chapter 17 Phases and Phase Changes Q.56P
CE Four liquids are at their freezing temperature. Heat is now removed from each of the liquids until it becomes completely solidified. The amount of heat that must be removed, Q, and the mass, m, of each of the liquids are as follows: liquid A, Q = 33,500 J, m = 0.100 kg; liquid B, Q = 166,000J, m = 0.500 kg; liquid Ç, Q = 31,500 J, m = 0.250 kg; liquid D, Q = 5400J, m = 0.0500 kg. Rank these liquids in order of increasing latent heat of fusion. Indicate ties where appropriate.
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Chapter 17 Phases and Phase Changes Q.57P
How much heat must be removed from 0.96 kg of water at 0 °C to make ice cubes at 0 °C?
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Chapter 17 Phases and Phase Changes Q.58P
A heat transfer of 9.5 × 10s J is required to convert a block of ice at −15 °C to water at 15 °C. What was the mass of the block of ice?
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Chapter 17 Phases and Phase Changes Q.59P
How much heat must be added to 1.75 kg of copper to change ‘ it from a solid at 1358 K to a liquid at 1358 K?
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Chapter 17 Phases and Phase Changes Q.60P
IP A 1.1-kg block of ice is initially at a temperature of −50 °C. (a) If 5.2 × 105 J of heat are added to the ice, what is the final temperature of the system? Find the amount of ice, if any, that remains, (b) Suppose the amount of heat added to the ice block is doubled. By what factor must the mass of the ice be increased if the system is to have the same final temperature? Explain.
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Chapter 17 Phases and Phase Changes Q.61P
Referring to the previous problem, suppose the amount ‘ of heat added to the block of ice is reduced by a factor of 2 to 2.6 × 105 J. Note that this amount of heat is still sufficient to melt at ieast some of the ice. (a) Do you expect the temperature increase in this case to be one-half that found in the previous problem? Explain, (b) What is the final temperature of the system in this case? Find the amount of ice, if any, that remains.
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Chapter 17 Phases and Phase Changes Q.62P
Figure 17-21 shows a temperature-versus-heat plot for 1.000 kg of water, (a) Calculate the heat corresponding to the points A, B, C, and D. (b) Calculate the slope of the line from point B to point C. Show that this slope is equal to 1/c, where c is the specific heat of liquid water.
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Chapter 17 Phases and Phase Changes Q.63P
Suppose the 1.000 kg of water in Figure 17-21 starts at point A at time zero. Heat is added to this system at the rate of 12,250 J/s. How long does it take for the system to reach (a) point B, (b) point C, and (c) point D? (d) Describe the physical state of the system at time t = 63.00 s.
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Chapter 17 Phases and Phase Changes Q.64P
Figure 17-22 shows a temperature-versus-heat plot for 0.550 kg of water, (a) Calculate the slope of the line from point A to point B. Show that the slope is equal to “1/mc, where c is the specific heat of ice. (b) Calculate the slope of the line from point C to point D. Show that the slope is equal to 1/mc, where c is the specific heat of liquid water.
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Chapter 17 Phases and Phase Changes Q.65P
In Conceptual Checkpoint 17-5 we pointed out that steam can cause more serious burns than water at the same temperature. Here we examine this effect quantitatively, noting that flesh becomes badly damaged when its temperature reaches 50.0 °C. (a) Calculate the heat released as 12.5 g of liquid water at 100 °C is cooled to 50.0 °C. (b) Calculate the heat released when 12.5 g of steam at 100 °C is condensed and cooled to 50.0 °C. (c) Find the mass of flesh that can be heated from 37,0 °C (normal body temperature) to 50.0 °C for the cases considered in parts (a) and (b). (The average specific heat of flesh is 3500J/kg · K.)
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Chapter 17 Phases and Phase Changes Q.66P
When you go out to your car one cold whiter morning you discover a 0.58-cm-tliick layer of ice on the windshield, which has an area of 1.6 m2. Tf the temperature of the ice is −2.0 °C, and its density is 917 kg/m3 find the heat required to melt all the ice.
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Chapter 17 Phases and Phase Changes Q.67P
A large punch bowl holds 3.99 kg of lemonade (which is essentially water) at 20.5 °C. A 0.0550-kg ice cube at -10.2 °C is placed in the lemonade. What is the final tempera ture of the system, and the amount of ice (if any) remaining? Ignore any heat exchange with the bowl or the surroundings.
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Chapter 17 Phases and Phase Changes Q.68P
A 155-g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to −196 °C. The cylinder is immediately placed in an insulated cup containing 80.0 g of water at 15.0 °C. What is the equilibrium temperature of this system? If your answer is 0 °C, determine the amount of water thathas frozen. The average specific heat of aluminum over this temperature range is 653 J/(kg · K).
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Chapter 17 Phases and Phase Changes Q.69P
An 825-g iron block is heated to 352 °C and placed in an insulated container (of negligible heat capacity) containing 40.0 g of water at 20.0 °C. What is the equilibrium tempera hare of this system? If your answer is 100 °C, determine the amount of water that has vaporized. The average specific heat of iron over this temperature range is 560 J/(kg · K).
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Chapter 17 Phases and Phase Changes Q.70P
IP A 35-g ice cube at 0.0 °C is added to 110 g of water in a 62-g aluminum cup. The cup and the water have an initial temperature of 23 °C. (a) Find the equilibrium temperature of the cup and its contents, (b) Suppose the aluminum cup is replaced with one of equal mass made from silver. Is the equilibrium temperature with the silver cup greater than, less than, or the same as with the aluminum cup? Explain.
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Chapter 17 Phases and Phase Changes Q.71P
A 48-g block of copper at-12 °C is added to 110 g of water in a 75-g aluminum cup. The cup and the water have an initial temperature of 4.1 °C. (a) Find the equilibrium temperature of the cup and its contents, (b) What mass of ice, if any, is present when the system reaches equilibrium?
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Chapter 17 Phases and Phase Changes Q.72P
A 0.075-kg ice cube at 0.0 °C is dropped into a Styrofoam cup holding 0.33 kg of water at 1.4 °C. (a) Find the final temperature of the system and the amount of ice (if any) remaining. Assume the cup and the surroundings can be ignored, (b) Find the initial temperature of the water that would be enough to jus/ barely melt all of the ice.
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Chapter 17 Phases and Phase Changes Q.73P
To help keep her barn warm on cold days, a farmer stores 865 kg of warm water in the barn. How many hours would a 2.00-kilowatt electric heater have to operate to provide the same amount of heat as is given off by the water as it cools from 20.0 °C to 0 °C and then freezes at 0 °C?
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Chapter 17 Phases and Phase Changes Q.74GP
Plastic bubble wrap is used as a protective packing material. Ts the bubble wrap more effective on a cold day or on a warm day? Explain.
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Chapter 17 Phases and Phase Changes Q.75GP
Two adjacent rooms in a hotel are equal in size and connected by an open door. Room 1 is warmer than room 2. Which room contains more air? Explain.
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Chapter 17 Phases and Phase Changes Q.76GP
As you go up in altitude, do you expect the ratio of oxygen to nitrogen in the atmosphere to increase, decrease; or stay the same? Explain.
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Chapter 17 Phases and Phase Changes Q.77GP
Suppose the Celsius temperature of an ideal gas is doubled from 100 °C to 200 °C. (a) Docs the average kinetic energy of the molecules in this gas increase by a factor-that is greater than, less than, or equal to 2? (b) Choose the best explanation from among the following:
I. Changing the temperature from 100 °C to 200 °C goes beyond the boiling point, which will increase the kinetic energy by more than a factor of 2.
II. The average kinetic energy is directly proportional to the temperature, so doubling the temperature doubles the kinetic energy.
III. Doubling the Celsius temperature from 100 °C to 200 °C changes the Kelvin temperature from 373.15 K to 473.15 K, which is an increase oF less than a factor of 2.
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Chapter 17 Phases and Phase Changes Q.78GP
Suppose the absolute temperature of an ideal gas is doubled from 100 K to 200 K. (a) Does the average speed of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2? (b) Choose the beat explanation from among the following:
I. Doubling the Kelvin temperature doubles the average kinetic energy, but this implies an increase in the average speed by a factor of , which is less than 2.
II. The Kelvin temperature is the one we use in the ideal-gas law, and therefore doubling it also doubles the average speed of the molecules.
III. The change in average speed depends on the mass of the molecules in the gas, and hence doubling the Kelvin temperature generally results in an increase in speed that is greater than a factor of 2.
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Chapter 17 Phases and Phase Changes Q.79GP
Largest Raindrops Atmospheric scientists studying clouds in the Marshall Islands have observed what they believe to be the world’s largest raindrops, with a radius of 0.52 cm. Flow many molecules are in these monster drops?
Solution:
Mass of rain drop = m
Chapter 17 Phases and Phase Changes Q.80GP
Coolin: Computers Researchers arc developing “heat exchangers” for laptop computers that take heat from the laptop—to keep it from being damaged by overheating—and use it to vaporize methanol. Given that 5100 J of heat is removed from the laptop when 4.6 g of methanol is vaporized, what is the latent heat of vaporization for methanol?
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Chapter 17 Phases and Phase Changes Q.81GP
Scuba Tanks In scuba diving circles, “an 80” refers to a scuba tank tha t holds 80 cubic feet öf ah’, a standard amount for recreational diving. Given that a scuba tank is a cylinder 2 feet long and half a foot in diameter, determine (a) the volume of a tank arid (b) the pressure in a tank when 80 cubic feet of air is compressed into its relatively small volume, (c) What is the mass of air ina tank that holds 80 cubic feet of air. Assume the temperature is 21 “C and that the walls of the tank are of negligible thickness.
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Chapter 17 Phases and Phase Changes Q.82GP
A reaction vessel contains 8.06 g of H; and 64.0 g of O2 at a temperature of 125 °C and a pressure of 101 kPa. (a) What is the volume of the vessel? (b) The hydrogen and oxygen are now ignited by a spark, initiating the reaction 2 H2 + O2 → 2 H2O. This reaction consumes all the hydrogenand oxygen in the vessel. What is the pressure of the resulting water vapor when i t returns to its initial temperature of 125 °C?
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Chapter 17 Phases and Phase Changes Q.83GP
A bicycle tire with a radius of 0.68 m has a gauge pressure of 42 lb/in2. Treating the tire as a hollow hoop with a cross-sectional area of 0.0028 m2, find the number of air molecules in the tire when its temperature is 24 °C.
Solution:
Chapter 17 Phases and Phase Changes Q.84GP
Peter catches a 4.8-kg striped bass on a fishing line 0.54 mm in diameter and begins to reel it in. He fishes from a pier well above the water, and his fish hangs vertically from the line out of the water. The fishing line has a Young’s modulus of 5.1 × 109 N/m2. (a) What is the fractional increase in length of the fishing line if the fish is at rest? (b) What is the fractional increase in the fishing line’s length when the fish is pulled upward with a constant speed of 1.5 m/s? (c) What is the fractional increase in the fishing line’s length when the fish is pulled upward with a constant acceleration of 1.5 m/s2?
Solution:
Chapter 17 Phases and Phase Changes Q.85GP
You use a steel socket wrench 28 cm long to loosen a rusty bolt, applying a force F at the end of the handle. The handle undergoes a shear deformation of 0.11 mm. (a) If the crosssectional area of the handle is 2.3 cm2, what is the magnitude of the applied force F? (b) If the cross-sectional area of the handle is doubled, by what factor does the shear deformation change? Explain.
Solution:
Chapter 17 Phases and Phase Changes Q.86GP
A steel ball (density = 7860 kg/m3) with a diameter of 6.4 cm is lied to an aluminum wire 82 cm long and 2.5 mm in diameter The ball is whirled about in a vertical circle with a tangential speed of 7.8 m/s at the top of the circle and 9.3 m/s at the bottom of the circle. Find the amount of stretch in the wire (a) at the top and (b) at the bottom of the circle.
Solution:
Chapter 17 Phases and Phase Changes Q.87GP
Solution:
Chapter 17 Phases and Phase Changes Q.88GP
Five molecules have the following speeds: 221 m/s, 301 m/s, 412 m/s, 44.0 m/s, and 182 m/s. (a) Find vav for these molecules, (b) Do you expect (v)av to be greater than, less than, or equal to (vav)2? Explain, (c) Calculate (02)av and comment on your results, (d) Calculate Orms and compare with vav.
Solution:
Chapter 17 Phases and Phase Changes Q.89GP
(a) Find the amount of heat that must be extracted from 1.5 kg of steam at 110 °C to convert it to ice at 0.0 “C. (b) What speed would this 1 -5-kg block of ice have if its translational kinetic energy were equal to the thermal energy calculated in part (a)?
Solution:
Chapter 17 Phases and Phase Changes Q.90GP
When water freezes into ice it expands in volume by 9.05%. Suppose a volume of water is in a household water pipe or a cavity in a rock. If the water freezes, what pressure must be exerted on it to keep its volume from expanding? (If the pipe or rock cannot supply this pressure, the pipe will burst and the rock will split.)
Solution:
Chapter 17 Phases and Phase Changes Q.91GP
Suppose the 0.550 kg of ice in Figure 17-22 starts at point A. How much ice is left in the system after (a) 5.00 × 104J, (b) 1.00 × 105T, and (c) 1.50 × 105J of heat are added to the system?
Solution:
Chapter 17 Phases and Phase Changes Q.92GP
Students on a spring break picnic bring a cooler that contains 5.1 kg of ice at 0.0 aC. The cooler has walls that are 3.8 cm thick and are made of Styrofoam, which has a thermal conductivity of 0.030 W/(m · C°). The surface area of the cooler is 1.5 m2, and it rests in the shade where the air temperature is 21 °C. (a) Find the rate at which heat flows into the cooler, (b) How long does it take for the ice in the cooler to melt?
Solution:
Chapter 17 Phases and Phase Changes Q.93GP
A 5.5-kg block of ice a t −1.5 “C slides on a horizontal surface with a coefficient of kinetic friction equal to 0.062. The initial speed of the block is 6.9 m/s and its final speed is 5.5 m/s. Assuming that all the energy dissipated by kinetic friction goes into melting a small mass m of the ice, and tha t the rest of the ice block remains at −1.5 °C, determine the value of m.
Solution:
Chapter 17 Phases and Phase Changes Q.94GP
Solution:
Chapter 17 Phases and Phase Changes Q.95PP
The American naturalist Charles William Beebe (1877-1962) set a world record in 1934 when he and Otis Barton (1899-1992) made a dive to a depth of 923 m below the surface of the ocean. The dive was made just 10 miles from Nonsuch Island, off the coast of Bermuda, in a device known as the bathysphere, designed and built by Barton. The bathysphere was basically a steel sphere 4.75 ft in diameter with three small ports made of fused quartz. Lowered in to the ocean on a steel cable whose radius was 1.85 cm, the bathysphere also carried bottles of oxygen, chemicals to absorb carbon dioxide, and a telephone line to the surface.
Charles William Beebe (left) and Otis Barton with the bathysphere in 1934. Beebe was fascinated by the new forms of life he and Barton encountered on their numerous dives. At one point he saw a “creature, several feet long, dart toward the window, turn sideways and—explode. At the flash, which was so strong that it illumined my face … I saw the great red shrimp and the outpouring fluid of flame.” No wonder he considered the ocean depths to be “a world as strange as that of Mars.”
The dives were not without their risks, however. It was not uncommon, for example, to have the bathysphere return to the surface partially filled with water after a window seal failed. On one deep dive, water began to steamrapidly into the sphere. Beebe quickly called to the surface and asked—not to be raised quickly—but to be lowered more rapidly, in the hope that increasing water pressure would force the leaking window into its seals to stop the leak. It worked, showing that Beebe was not only an exceptional naturalist, but also a cool-headed scientist with a good knowledge of basic physics!
What pressure did the bathysphere experience at its record depth?
A. 9.37 atm
B. 89.6 atm
C. 91.9 atm
D. 92.9 atm
Solution:
Chapter 17 Phases and Phase Changes Q.96PP
The American naturalist Charles William Beebe (1877-1962) set a world record in 1934 when he and Otis Barton (1899-1992) made a dive to a depth of 923 m below the surface of the ocean. The dive was made just 10 miles from Nonsuch Island, off the coast of Bermuda, in a device known as the bathysphere, designed and built by Barton. The bathysphere was basically a steel sphere 4.75 ft in diameter with three small ports made of fused quartz. Lowered in to the ocean on a steel cable whose radius was 1.85 cm, the bathysphere also carried bottles of oxygen, chemicals to absorb carbon dioxide, and a telephone line to the surface.
Charles William Beebe (left) and Otis Barton with the bathysphere in 1934.
Beebe was fascinated by the new forms of life he and Barton encountered on their numerous dives. At one point he saw a “creature, several feet long, dart toward the window, turn sideways and—explode. At the flash, which was so strong that it illumined my face … I saw the great red shrimp and the outpouring fluid of flame.” No wonder he considered the ocean depths to be “a world as strange as that of Mars.”
The dives were not without their risks, however. It was not uncommon, for example, to have the bathysphere return to the surface partially filled with water after a window seal failed. On one deep dive, water began to steamrapidly into the sphere. Beebe quickly called to the surface and asked—not to be raised quickly—but to be lowered more rapidly, in the hope that increasing water pressure would force the leaking window into its seals to stop the leak. It worked, showing that Beebe was not only an exceptional naturalist, but also a cool-headed scientist with a good knowledge of basic physics!
How much did the volume of the bathysphere decrease as it was lowered to its record depth? (For simplicity, treat the bathysphere as a solid metal sphere.)
A. 9.0 × 10−5 m3
B. 9.2 × 10”5 m3
C. 1.1 × 10−4 m3
D. 3.8 × 10−4 m3
Solution:
Chapter 17 Phases and Phase Changes Q.97PP
The American naturalist Charles William Beebe (1877-1962) set a world record in 1934 when he and Otis Barton (1899-1992) made a dive to a depth of 923 m below the surface of the ocean. The dive was made just 10 miles from Nonsuch Island, off the coast of Bermuda, in a device known as the bathysphere, designed and built by Barton. The bathysphere was basically a steel sphere 4.75 ft in diameter with three small ports made of fused quartz. Lowered in to the ocean on a steel cable whose radius was 1.85 cm, the bathysphere also carried bottles of oxygen, chemicals to absorb carbon dioxide, and a telephone line to the surface.
Charles William Beebe (left) and Otis Barton with the bathysphere in 1934.
Beebe was fascinated by the new forms of life he and Barton encountered on their numerous dives. At one point he saw a “creature, several feet long, dart toward the window, turn sideways and—explode. At the flash, which was so strong that it illumined my face … I saw the great red shrimp and the outpouring fluid of flame.” No wonder he considered the ocean depths to be “a world as strange as that of Mars.”
The dives were not without their risks, however. It was not uncommon, for example, to have the bathysphere return to the surface partially filled with water after a window seal failed. On one deep dive, water began to steamrapidly into the sphere. Beebe quickly called to the surface and asked—not to be raised quickly—but to be lowered more rapidly, in the hope that increasing water pressure would force the leaking window into its seals to stop the leak. It worked, showing that Beebe was not only an exceptional naturalist, but also a cool-headed scientist with a good knowledge of basic physics!
How much did the volume of the bathysphere decrease as it was lowered to its record depth? (For simplicity, treat the bathysphere as a solid metal sphere.)
A. 9.0 × 10−5 m3
B. 9.2 × 10”5 m3
C. 1.1 × 10−4 m3
D. 3.8 × 10−4 m3
Solution:
Chapter 17 Phases and Phase Changes Q.98PP
The American naturalist Charles William Beebe (1877-1962) set a world record in 1934 when he and Otis Barton (1899-1992) made a dive to a depth of 923 m below the surface of the ocean. The dive was made just 10 miles from Nonsuch Island, off the coast of Bermuda, in a device known as the bathysphere, designed and built by Barton. The bathysphere was basically a steel sphere 4.75 ft in diameter with three small ports made of fused quartz. Lowered in to the ocean on a steel cable whose radius was 1.85 cm, the bathysphere also carried bottles of oxygen, chemicals to absorb carbon dioxide, and a telephone line to the surface.
Charles William Beebe (left) and Otis Barton with the bathysphere in 1934. Beebe was fascinated by the new forms of life he and Barton encountered on their numerous dives. At one point he saw a “creature, several feet long, dart toward the window, turn sideways and—explode. At the flash, which was so strong that it illumined my face … I saw the great red shrimp and the outpouring fluid of flame.” No wonder he considered the ocean depths to be “a world as strange as that of Mars.”
The dives were not without their risks, however. It was not uncommon, for example, to have the bathysphere return to the surface partially filled with water after a window seal failed. On one deep dive, water began to steamrapidly into the sphere. Beebe quickly called to the surface and asked—not to be raised quickly—but to be lowered more rapidly, in the hope that increasing water pressure would force the leaking window into its seals to stop the leak. It worked, showing that Beebe was not only an exceptional naturalist, but also a cool-headed scientist with a good knowledge of basic physics!
Suppose the bathysphere and its occupants had a combined mass of 12,700 kg. How much did the cable stretch when the bathysphere was at a depth of 923 m? (Neglect the weight of the cable itself, but include the effects of the bathysphere’s buoyancy.)
A. 47 cm
B. 48 cm
C. 52 cm
D. 53 cm
Solution:
Chapter 17 Phases and Phase Changes Q.99IP
(a) Find the final temperature of the system if two 0.0450-kg ice cubes are added to the warm lemonade. The temperature of the ice is 0 °C; the temperature and mass of the warm lemonade are 20.0 °C and 3.95 kg, respectively. (b) How many 0.0450-kg ice cubes at 0 °C must be added to the original warm lemonade if the final temperature of the system is to be at least as cold as 15.0 °C?
Solution:
Chapter 17 Phases and Phase Changes Q.100IP
(a) Find the final temperature of the system if a single 0.045-kg ice cube at 0 °C is added to 2.00 kg of lemonade at 1.00 °C. (b) What initial temperature of the lemonade will be just high enough to melt all of the ice in a single ice cube and result in an equilibrium tempera ture of 0 °C? The mass of the lemonade is 2.00 kg and the temperature of the ice cube is 0 °C.
Solution:
