Homework for AP Physics B

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Homework for APB Physics Date: 1-20-2012

Key for Ch17 Test

1. (a) ½ (b) 9x2 -16y2 = 144 “hyperbola”2. (a) 79 N (b) 210 Hz3. (a) a pipe open at both ends (b) 0.786 m4. (a) 350 Hz (b) 400 kg5. 5.26 Hz6. (a) 2.25 mm (b) 4.5 mm

Chapter 11 APB Quarterly Prep

1. A child wants to pump up a bicycle tire so that its pressure is 1.2 × 105 Pa above that of atmospheric pressure. If the child uses a pump with a circular piston 0.035 m in diameter, what force must the child exert?A) 120 N B) 89 N C) 76 N D) 54 NE) 240 N

2. Using the value of atmospheric pressure at sea level, 1 × 105 Pa, estimate the total mass of the earth's atmosphere above a 5-m2 area.A) 5 × 104 kg B) 9 × 102 kg C) 2 × 10–4 kg D) 4 × 10–2 kg E) 3 × 105 kg

3. A pirate's treasure chest lies 20.0 m below the surface of the ocean. What is the magnitude of the force that acts on the rectangular top that is 0.750 m × 0.425 m?A) 980 N B) 2.39 × 103 N C) 9.48 × 104 N D) 4.71 × 105 N E) 2.00 × 106 N

4. At a location where the acceleration due to gravity is 9.807 m/s2, the atmospheric pressure is 9.891 × 104 Pa. A barometer at the same location is filled with an unknown liquid. What is the density of the unknown liquid if its height in the barometer is 1.163 m?A) 210 kg/m3 B) 4336 kg/m3 C) 5317 kg/m3 D) 8672 kg/m3 E) 9688 kg/m3

5. A woman is enjoying a tropical drink while lying on a beach. The acceleration due to gravity at her location is 9.78 m/s2. What gauge pressure must exist in the woman's mouth if she is drinking through a straw extending 0.075 m above the surface of the drink? Note: Assume the drink has a density of 1020 kg/m3.A) 850 Pa B) 750 Pa C) 1100 Pa D) 1000 Pa E) 920 Pa

6. A barometer is taken from the base to the top of a 279-m tower. Assuming the density of air is 1.29 kg/m3, what is the measured change in pressure?A) 359 Pa B) 927 Pa C) 2120 Pa D) 2730 Pa E) 3530 Pa

7. One of the largest barometers ever built was an oil-filled barometer constructed in Leicester, England in 1991. The oil had a height of 12.2 m. Assuming a pressure of 1.013 × 105 Pa, what was the density of the oil used in the barometer?A) 798 kg/m3 B) 847 kg/m3 C) 981 kg/m3 D) 1150 kg/m3 E) 1210 kg/m3

8. A force of 250 N is applied to a hydraulic jack piston that is 0.02 m in diameter. If the piston that supports the load has a diameter of 0.15 m, approximately how much mass can be lifted by the jack? Ignore any difference in height between the pistons.A) 250 kg B) 700 kg C) 1400 kg D) 2800 kg E) 5600 kg

9. A balloon inflated with helium gas (density = 0.2 kg/m3) has a volume of 6 × 10–3 m3. If the density of air is 1.3 kg/m3, what is the buoyant force exerted on the balloon?A) 0.01 N B) 0.08 N C) 0.8 N D) 1.3 N E) 7.8 N

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10. A 2-kg block displaces 10 kg of water when it is held fully immersed. The object is then tied down as shown in the figure; and it displaces 5 kg of water. What is the tension in the string?

A) 10 NB) 20 N C) 30 N D) 70 NE) 100 N

11. The density of ice is 0.92 g/cm3; and the density of seawater is 1.03 g/cm3. A large iceberg floats in Arctic waters. What fraction of the volume of the iceberg is exposed?A) 0.080 % B) 11 %C) 89 %D) 92 % E) 99 %

12-13 When a block of volume 1.00 × 10–3 m3 is hung from a spring scale as shown in Figure A, the scale reads 10.0 N. When the same block is then placed in an unknown liquid, it floats with 2/3 of its volume submerged as suggested in Figure B. The density of water is 1.00 × 103 kg/m3.

12. Determine the mass of the block.A) 1.02 kg B) 2.02 kg C) 3.02 kg D) 4.04 kg E) 9.80 kg

13. Determine the density of the unknown liquid.A) 3.03 × 103 kg/m3 B) 4.62 × 103 kg/m3 C) 6.16 × 103 kg/m3 D) 8.01 × 103 kg/m3 E) 1.57 × 104 kg/m3

14. Selena uses a garden hose to fill a bucket of water. The water enters the hose through a faucet with a 6.0-cm diameter. The speed of the water at the faucet is 5 m/s. If the faucet and the nozzle are at the same height, and the water leaves the nozzle with a speed of 20 m/s, what is the diameter of the nozzle?A) 1.5 cm B) 2.0 cm C) 3.0 cm D) 4.0 cm E) 6.0 cm

15. Water flows through a pipe of diameter 8.0 cm with a speed of 10.0 m/s. It then enters a smaller pipe of diameter 3.0 cm. What is the speed of the water as it flows through the smaller pipe?A) 1.4 m/s B) 2.8 m/s C) 27 m/s D) 54 m/s E) 71 m/s

16. Water enters a pipe of diameter 3.0 cm with a velocity of 3.0 m/s. The water encounters a constriction where its velocity is 15 m/s. What is the diameter of the constricted portion of the pipe?A) 0.44 cm B) 0.75 cm C) 1.3 cm D) 1.6 cm E) 6.7 cm

17. Elaine went to her outside faucet to fill a 0.0189-m3 bucket with water to wash her car. Water exits with a speed of 0.61 m/s. The radius of the faucet is 0.0078 m. How long does it take to fill the bucket completely?A) 9.0 s B) 17 s C) 160 s D) 280 s E) 490 s

18. A large tank is filled with water to a depth of 15 m. A spout located 10.0 m above the bottom of the tank is then opened as shown in the drawing. With what speed will water emerge from the spout?

A) 3.1 m/s B) 9.9 m/s C) 14 m/s D) 17 m/s E) 31 m/s

19. Oil ( = 925 kg/m3) is flowing through a pipeline at a constant speed when it encounters a vertical bend in the pipe raising it 4.0 m. The cross sectional area of the pipe does not change. What is the difference in pressure (PB – PA) in the portions of the pipe before and after the rise?

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A) +2.4 × 104 Pa B) –3.6 × 104 Pa C) +5.1 × 105 Pa D) –7.2 × 105 Pa E) –1.8 × 103 Pa

20. The density of the liquid flowing through the horizontal pipe in the drawing is 1200 kg/m3. The speed of the fluid at point A is 7.5 m/s while at point B it is 11 m/s. What is the difference in pressure, PB – PA, between points B and A?

A) –1.9 × 103 Pa B) +3.8 × 103 Pa C) –2.5 × 104 Pa D) +5.0 × 104 Pa E) –3.9 × 104 Pa

21. A large vat is continually filled with a viscous liquid that flows from two equally long, cylindrical pipes, labeled A and B, onto a conveyer belt as shown in the drawing. The diameter of pipe B is 1.75 times larger than that of pipe A. What is the ratio of the average volume flow rate of the liquid exiting pipe B to that of the liquid exiting pipe A?

A) 1.87 B) 3.06 C) 1.32 D) 9.38 E) 4.33

Chapter 12 APB Quarterly Prep

1. A circular hole in an copper plate is 2.925 cm in diameter at 20.0 °C. What is the diameter of the hole if the temperature of the plate is raised to 120.0 °C? The coefficient of linear expansion of copper is 17 × 10–6/C°. A) 2.925 cm B) 2.929 cm C) 2.933 cm D) 2.957 cm E) 2.988 cm

2. The coefficient of linear expansion of a certain solid is 11 × 10–6/C°. Assuming this solid behaves like most solids, what is its coefficient of volume expansion?A) 22 × 10–6/C° B) 33 × 10–36/C° C) 33 × 10–6/C° D) 13 × 10–5/C° E) 13 × 10–4/C°

3. Zirconium tungstate is an unusual material because its volume shrinks with an increase in temperature for the temperature range 0.3 K to 1050 K (where it decomposes). In fact, the volumetric coefficient of thermal expansion is –26.4 × 10–6/K. Determine the ratio V/V0 for the above mentioned temperature range. Express your answer in percent.A) –5.28% B) –3.59% C) –2.77% D) –1.90% E) –1.04%

4. The coefficient of volumetric expansion for gold is 4.20 × 10–5/C°. The density of gold is19 300 kg/m3 at 0.0 °C. What is the density of gold at 1050 °C?A) 20 200 kg/ m3 B) 19 300 kg/m3 C) 19 000 kg/m3 D) 18 800 kg/m3 E) 18 500 kg/m3

5. A tanker ship is filled with 2.25 × 105 m3 of gasoline at a refinery in southern Texas when the temperature is 17.2 °C. When the ship arrives in New York City, the temperature is 1.3 °C. If the coefficient of volumetric expansion for gasoline is 9.50 × 10–4/C°, how much has the volume of the gasoline decreased when it is unloaded in New York?A) 1.50 × 10–2 m3 B) 66.2 m3 C) 1290 m3 D) 3400 m3 E) 1.05 × 104 m3

6. A soft drink manufacturer claims that a new diet drink is “low Joule.” The label indicates the available energy per serving is 6300 J. What is the equivalent of this energy in Calories (1 Calorie = 1000 cal)?A) 0.015 Cal B) 0.48 Cal C) 1.0 Cal D) 1.5 Cal E) 4.8 Cal

7. Two spheres, labeled A and B, have identical masses, but are made of different substances. The specific heat capacity of sphere A is 645 J/(kg · C°) and that of sphere B is 240 J/(kg · C°). The spheres are initially at 21 °C; and the same quantity of heat is added to each sphere. If the final temperature of sphere A is 74 °C, what is the approximate final temperature of sphere B?A) 160 °C B) 140 °C C) 110 °C D) 53 °C E) 39 °C

8. A 2.00-kg metal object requires 1.00 × 104 J of heat to raise its temperature from 20.0 °C to 40.0 °C. What is the

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specific heat capacity of the metal?A) 50.0 J/(kg · C°) B) 125 J/(kg · C°) C) 250 J/(kg · C°) D) 500 J/(kg · C°) E) 1.00 × 103 J/(kg · C°)

9. A 0.30-kg lead ball is heated to 90.0 °C and dropped into an ideal calorimeter containing 0.50 kg of water initially at 20.0 °C. What is the final equilibrium temperature of the lead ball? The specific heat capacity of lead is 128 J/(kg · C°); and the specific heat of water is 4186 J/(kg · C°).A) 84.8 °C B) 20.8 °C C) 21.3 °C D) 27.8 °C E) 32.1 °C

10-11 A 2.00-kg metal block slides on a rough, horizontal surface inside an insulated pipe. After sliding a distance of 500.0 m, its temperature is increased by 2.00 °C. Note: Assume that all of the heat generated by frictional heating goes into the metal block. For this metal, the specific heat capacity is 0.150 cal/(g · C°).

10. How much work does the force of friction do on the block?A) zero joules B) 300 J C) –300 J D) 2510 J E) –2510 J

11. What is the coefficient of sliding friction between the block and the surface?A) zero B) 0.061 C) 0.100 D) 0.256 E) 0.299

12. A 2.0-g sample of steam at 100 °C loses 1140 calories of heat. What is the resulting temperature of the sample?A) 60 °C B) 70 °C C) 80 °C D) 96 °C E) 99 °C

13. What is the minimum amount of energy required to completely melt a 7.25-kg lead brick which has a starting temperature of 18.0 °C? The melting point of lead is 328 °C. The specific heat capacity of lead is 128 J/(kg · C°); and its latent heat of fusion is 23 200 J/kg.A) 1.20 × 105 J B) 1.68 × 105 J C) 2.88 × 105 J D) 4.56 × 105 J E) 7.44 × 105 J

14. A thermos bottle contains 3.0 kg of water and 2.0 kg of ice in thermal equilibrium at 0 °C. How much heat is required to bring the system to thermal equilibrium at 50 °C?A) 1.05 × 106 J B) 1.30 × 106 J C) 1.72 × 106 J D) 2.26 × 106 J E) 1.13 × 107 J

15. Ryan places 0.150 kg of boiling water in a thermos bottle. How many kilograms of ice at –12.0 °C must Ryan add to the thermos so that the equilibrium temperature of the water is 75.0 °C?A) 0.0233 kg B) 0.0265 kg C) 0.0436 kg D) 0.0713 kg E) 0.625 kg

16. Determine the latent heat of vaporization of unknown substance X in kcal/g if 4.0 g of boiling liquid X are completely vaporized in 1.2 hours by an input of 15 kcal/h into the system by an energy source.A) 4.5 kcal/g B) 1.5 kcal/g C) 2.7 kcal/g D) 3.0 kcal/g E) 5.9 kcal/g

17-19 A 0.0500-kg lead bullet of volume 5.00 × 10–6 m3 at 20.0 °C hits a block that is made of an ideal thermal insulator and comes to rest at its center. At that time, the temperature of the bullet is 327 °C. Use the following information for lead:

coefficient of linear expansion: = 2.0 × 10–5/C° specific heat capacity: c = 128 J/(kg · C°)

latent heat of fusion: Lf = 23 200 J/kg melting point: Tmelt = 327 °C

17. How much heat was needed to raise the bullet to its final temperature?A) 963 J B) 1960 J C) 3640 J D) 3880 J E) 4440 J

18. What is the volume of the bullet when it comes to rest?A) 5.00 × 10–6 m3 B) 5.01 × 10–6 m3 C) 5.03 × 10–6 m3 D) 5.07 × 10–6 m3 E) 5.09 × 10–6 m3

19. What additional heat would be needed to melt the bullet?

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A) 420 J B) 628 J C) 837 J D) 1160 J E) 2010 J

20. The graph shows the equilibrium vapor pressure versus temperature for a certain liquid and its vapor within an open container. If the container is at sea level, at approximately what temperature will the liquid boil?

A) 50 °C B) 65 °C C) 75 °C D) 85 °C E) 100 °C

21. Given the following information, determine the relative humidity at 15 °C.partial pressure of water at 15 °C = 1230 Papartial pressure of water at the dew point, 15 °C = 1710 Pa

A) 39.0 % B) 47.9 % C) 50.8 % D) 64.1 % E) 71.9 %

Chapter 13 APB Quarterly Prep

1. The ends of a cylindrical steel rod are maintained at two different temperatures. The rod conducts heat from one end to the other at a rate of 10 cal/s. At what rate would a steel rod twice as long and twice the diameter conduct heat between the same two temperatures?A) 5 cal/s B) 10 cal/s C) 20 cal/s D) 40 cal/s E) 80 cal/s

2. At what rate is heat lost through a 1.5 m × 3.0 m rectangular glass windowpane that is 0.4 cm thick when the inside temperature is 22 °C and the outside temperature is 6.0 °C? The thermal conductivity for the glass is 0.75 W/(m · C°).A) 560 W B) 1800 W C) 7200 W D) 3600 W E) 13 500 W

3. Two cylindrical steel rods A and B have radii of 0.02 m and 0.04 m, respectively. The two steel rods conduct the same amount of heat per unit time for the same temperature differences between their two ends. What is the ratio of the lengths of the rods, LA/LB?A) 0.25 B) 0.50 C) 1.00 D) 2.00 E) 4.00

4. A cabin has a 0.159-m thick wooden floor [k = 0.141 W/(m · C°)] with an area of 13.4 m2. A roaring fire keeps the interior of the cabin at a comfortable 18.0 °C while the air temperature in the crawl space below the cabin is –16.4 °C. What is the rate of heat conduction through the wooden floor?A) 19 J/s B) 138 J/s C) 264 J/s D) 408 J/s E) 459 J/s

5. A granite wall has a thickness of 0.50 m and a thermal conductivity of 2.1 W/(m · C°). The temperature on one face of the wall is 5.2 °C and 20.0 °C on the opposite face. How much heat is transferred in one hour through each square meter of the granite wall?A) 2.2 × 105 J/m2 B) 1.7 × 105 J/m2 C) 7.4 × 104 J/m2 D) 1.1 × 106 J/m2 E) 62 J/m2

6. On a cold winter day, the outside temperature is –5.0 °C while the interior of a well-insulated garage is maintained at 20.0 °C by an electric heater. Assume the walls have a total area of 75 m2, a thickness of 0.15 m, and a thermal conductivity of 0.042 W/(m · C°). What is the cost to heat the garage for six hours at these temperatures if the cost of electricity is $ 0.11/kWh? Note: 1 kWh = 3.6 × 106 J.A) $ 0.18 B) $ 0.44 C) $ 0.61 D) $ 0.35 E) $ 1.09

7. Heat is conducted by two cylindrical rods, one carbon and one aluminum, with identical cross-sectional area and length. The temperature difference between the ends of each rod is the same. Carbon has a thermal conductivity of 1100 J/(s m C°) and that of aluminum is 240 J/(s m C°). What percentage of the total energy transferred by the

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two rods each second is conducted by the silver rod?A) 64 % B) 18 % C) 30 % D) 46 % E) 82 %

8. In an experiment to determine the thermal conductivity of a bar of a new alloy, one end of the bar is maintained at 0.0 °C and the other end at 100.0 °C. The bar has a cross-sectional area of 1.0 cm2 and a length of 15 cm. If the rate of heat conduction through the bar is 34 W, what is the thermal conductivity of the bar?A) 34 W/(m · C°) B) 360 W/(m · C°) C) 160 W/(m · C°) D) 510 W/(m · C°) E) 0.029 W/(m · C°)

9. Two identical solid spheres have the same temperature. One of the spheres is cut into two identical pieces. These two hemispheres are then separated. The intact sphere radiates an energy Q during a given time interval. During the same interval, the two hemispheres radiate a total energy Q. What is the ratio Q/Q?A) 2.0 B) 0.50 C) 4.0 D) 1.5 E) 0.25

10. Which one of the following statements concerning the Stefan-Boltzmann equation is true?A) This equation applies only to perfect radiators. B) This equation applies only to perfect absorbers.C) This equation is valid with any temperature units.D) This equation describes the transport of thermal energy by conduction.E) The equation can be used to calculate the power absorbed by any surface.

11. Which one of the following statements concerning emissivity is false?A) The emissivity is 1.0 for a perfect radiator. B) The emissivity is 1.0 for a perfect absorber.C) Emissivity depends on the condition of the surface.D) Emissivity is a dimensionless quantity. E) Emissivity depends on the surface area of the object.12. A hot metal ball is hung in an oven that is maintained at 700 K; and it cools. When the temperature of the ball is 950 K, it is losing heat at a rate of 0.15 J/min. At what rate will the ball lose heat when the ball reaches 820 K? Assume that the emissivity of the ball and its surface area do not change appreciably with temperature.A) 0.1 J/min B) 0.007 J/min C) 0.08 J/min D) 0.06 J/min E) 0.04 J/min

13. Assume that the sun is a sphere of radius 6.96 × 108 m and that its surface temperature is 5.8 × 103 K. If the sun radiates at a rate of 3.90 × 1026 W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?A) 5.6 × 107 W/m2 B) 6.4 × 107 W/m2 C) 5.6 × 1017 W/m2 D) 12.8 × 107 W/m2 E) 25.6 × 107 W/m2

14. A blue supergiant star has a radius of 7.4 × 1010 m. The spherical surface behaves as a blackbody radiator. If the surface temperature is 2.4 × 104 K, what is the rate at which energy is radiated from the star?A) 1.2 × 103 J/s B) 9.4 × 1019 J/s C) 2.0 × 1023 J/s D) 8.2 × 1032 J/s E) 1.3 × 1033 J/s

15. Assuming a filament in a 100 W light bulb acts like a perfect blackbody, what is the temperature of the hottest portion of the filament if it has a surface area of 6.3 × 10–5 m2? The Stefan-Boltzmann constant is 5.67 × 10–8 W/(m2 · K2).A) 130 K B) 1100 K C) 2300 K D) 5800 K E) 30 000 K

16. A person steps out of the shower and dries off. The person's skin with an emissivity of 0.70 has a total area of 1.2 m2 and a temperature of 33 °C. What is the net rate at which energy is lost to the room through radiation by the naked person if the room temperature is 24 °C?A) 0.041 W B) 25 W C) 81 W D) 67 W E) 47 W

17. The power radiated by a distant star is 6.2 × 1027 W. The radius of the star, which may be considered a perfect radiator, is 1.06 × 1010 m. Determine the surface temperature of the star.A) 2970 K B) 4630 K C) 7440 K D) 8710 K E) 9970 K

18. A beaker of water is placed on a Bunsen burner. As the lower layers of water are heated, they become less dense and rise. This permits cooler layers to move downward and be heated. Eventually, the water boils. Which method(s) of heat transfer is (are) primarily responsible for boiling the sample?A) conduction B) convection C) radiationD) both conduction and radiation E) both conduction and convection

19-20 Two kilograms of ice at 0.0 °C are placed in a sealed glass container [k = 0.80 W/(m · C°)]. The container is

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then placed in a room that is maintained at 30.0 °C. The top cover is a thermal insulator and all other sides of the container are exposed to room air. The surface area of the container is 6.53 × 10–2 m2; and its glass walls are 0.0050 m thick.

19. How much heat is required to melt the ice?A) 16 J B) 1080 J C) 1.6 × 105 J D) 6.7 × 105 J E) 4.5 × 106 J

20. Approximately, how long does it take all of the ice to melt?A) 4.7 min B) 7.8 min C) 18 min D) 36 min E) 2.7 h

Chapter 14 APB Quarterly Prep

1. A sample of a monatomic ideal gas is originally at 20 °C. What is the final temperature of the gas if the pressure is doubled and volume is reduced to one-fourth its initial value?A) 900 °C B) 10 °C C) 80 °C D) 130 °C E) 260 °C

2. An ideal gas at 0 °C is contained within a rigid vessel. The temperature of the gas is increased by 1 C°. What is Pf/Pi, the ratio of the final to initial pressure?A) 273/274 B) 274/273 C) ½ D) 1/10 E) 1/273

3. Helium gas at 20 °C is confined within a rigid vessel. The gas is then heated until its pressure is doubled. What is the final temperature of the gas?A) 10 °C B) 20 °C C) 40 °C D) 313 °C E) 586 °C

4. Neon gas at 305 K is confined within a constant volume at a pressure P1. If the gas has a pressure P2 when it is cooled to 125 K, what is the ratio of P2 to P1?A) 0.410 B) 0.639 C) 0.717 D) 1.56 E) 2.44

5. In the space between two stars, the temperature of a gas cloud is 12 K; and the density of the gas is 1.2 × 10–8

atom/m3. What is the absolute pressure of the gas?A) 2.0 × 10–30 Pa B) 1.2 × 10–28 Pa C) 2.0 × 10–17 Pa D) 1.2 × 10–6 Pa E) 1.4 × 10–4 Pa

6. An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?A) 9.117 × 105 Pa B) 6.447 × 105 Pa C) 4.559 × 105 Pa D) 3.102 × 105 Pa E) 1.823 × 106 Pa

7. Heat is supplied to a sample of a monatomic ideal gas at 40 °C. It is observed that the gas expands until its volume and pressure are doubled. What is the final temperature of the gas?A) 10 °C B) 20 °C C) 40 °C D) 980 °C E) 1600 °C

8. An ideal gas with a fixed number of molecules is maintained at a constant pressure. At 30.0 °C, the volume of the gas is 1.25 m3. What is the volume of the gas when the temperature is increased to 150.0 °C?A) 0.90 m3 B) 1.50 m3 C) 1.75 m3 D) 2.45 m3 E) 6.25 m3

9. The temperature of a monatomic ideal gas with a mass per mole of 0.00750 kg/mol is 298 K. The absolute pressure of the gas is 1.65 × 105 Pa when its volume is 1.21 × 10–3 m3. What is the mass of the gas?A) 9.11 × 10–5 kg B) 2.18 × 10–4 kg C) 4.22 × 10–4 kgD) 6.04 × 10–4 kg E) 2.27 × 10–3 kg

10. An ideal gas is contained in a vessel with a moveable piston. Initially, the gas has a volume of 0.024 m3, an absolute pressure of 1.8 atm, and a temperature of 35.0 °C. The pressure is 0.90 atm when the volume of the container is decreased to 0.012 m3. What is the final temperature of the gas?A) 77 K B) 85 K C) 170 K D) 154 K E) 282 K

11. At what temperature would one mole of molecular nitrogen (N2) have 7.0 × 103 J of translational kinetic energy? Note: the atomic mass of N is 14 u.A) 130 °C B) 290 °C C) 480 °C D) 560 °C E) 720 °C

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12. A five-liter tank contains 2.00 moles of oxygen gas, O2, at 40 °C. What pressure is exerted on the sides of the tank by the oxygen molecules?A) 83.3 Pa B) 4.01 × 103 Pa C) 1.33 × 105 Pa D) 4.01 × 105 Pa E) 1.04 × 106 Pa

13. A 7.50 × 10–3-m3 bottle contains 0.0200 kg of oxygen gas, O2, at 77.0 °C. What is the pressure exerted on the inner walls of the flask by the oxygen gas? Note: the atomic mass of O is 15.9994 u.A) 8.42 × 104 Pa B) 1.45 × 105 Pa C) 2.43 × 105 Pa D) 4.86 × 105 Pa E) 1.46 × 106 Pa

14. Consider two ideal gases, A and B, at the same temperature. The rms speed of the molecules of gas A is twice that of gas B. How does the molecular mass of A compare to that of B?A) The molecular mass of A is twice that of B. B) The molecular mass of A is one half that of B.C) The molecular mass of A is 1.4 times that of B. D) The molecular mass of A is one fourth that of B.E) The molecular mass of A is four times that of B.

15. A canister containing 115 kg of an ideal gas has a volume of 6.5 m3. If the gas exerts a pressure of 4.0 × 105 Pa, what is the rms speed of the molecules?A) 260 m/s B) 180 m/s C) 310 m/s D) 390 m/s E) 420 m/s

16. A flask contains 1.00 mole of oxygen gas, O2, at 0.00 °C and 1.013 × 105 Pa. What is the rms speed of the molecules? Note: the atomic mass of O is 16 u.A) 230 m/s B) 460 m/s C) 651 m/s D) 920 m/s E) 1302 m/s

17. A tank contains 135 moles of the monatomic gas argon at a temperature of 15.3 °C. How much energy must be added to the gas to increase its temperature to 45.0 °C?A) 2.50 × 103 J B) 3.33 × 104 J C) 5.00 × 104 J D) 5.70 × 105 J E) 7.50 × 106 J

18. Calculate the rms speed of the carbon dioxide molecules in the air if the temperature is 15.0 °C. Note: The mass of the carbon dioxide molecule is 44.01 u.A) 316 m/s B) 469 m/s C) 378 m/s D) 404 m/s E) 511 m/s

19. What is the internal energy of 1.75 kg of helium (atomic mass = 4.00260 u) with a temperature of 100 °C?A) 4.65 × 103 J B) 5.44 × 105 J C) 2.03 × 106 J D) 8.16 × 106 J E) 1.22 × 107 J

20. A concentration difference of a certain solute of 1.0 × 10–2 kg/m3 is maintained between the ends of a tube with a length of 3.5 m and a cross-sectional area of 0.25 m2. When 0.0040 g of the solute is introduced to the tube, it takes 350 minutes for this solute to diffuse through the solvent to the opposite end of the tube. What is the diffusion constant for the solute?A) 2.7 × 10–7 m2/s B) 4.5 × 10–9 m2/s C) 7.5 × 10–10 m2/s D) 6.3 × 10–8 m2/s E) 1.1 × 10–11 m2/s

Chapter 15 APB Quarterly Prep

1. Rick spends four hours researching on the internet and does 1090 J of work. In the process, his internal energy decreases by 2190 J. Determine the value of Q, including the algebraic sign.A) –1100 J B) +1100 J C) –2190 J D) +3280 J E) –3280 J

2. When the gas enclosed beneath the piston shown in the figure receives 2170 J of heat, Q, from its surroundings, it performs 2840 J of work in raising the piston. What is the change in the internal energy of the gas?

A) +670 J B) –670 J C) –5010 J D) +5010 J E) zero joules

3. A system containing an ideal gas at a constant pressure of 1.42 × 105 Pa gains 2320 J of heat. During the process, the internal energy of the system increases by 2540 J. What is the change in volume of the gas?A) +1.55 × 10–3 m3 B) –1.55 × 10–3 m3 C) +2.36 × 10–3 m3 D) –2.36 × 10–3 m3 E) zero m3

4. A container is divided into two chambers that are separated by a valve. The left chamber contains one mole of a

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monatomic ideal gas. The right chamber is evacuated. At some instant, the valve is opened and the gas rushes freely into the right chamber. Which one of the following statements concerning this process is true?

A) Work is done by the gas. B) The temperature of the gas decreases.C) The change in the entropy of the gas is zero. D) The walls of the containing vessel must get colder.E) The change in the internal energy of the gas is zero.

5. A thermally isolated sample of an ideal gas at a fixed temperature is confined to one half of a container by an impermeable membrane. The other half of the container is evacuated. The membrane is then pierced and the gas is allowed to expand freely and to double its volume as shown. Which one of the following statements is true concerning this situation?

A) The process is reversible. B) This is an isothermal process. C) The entropy of the gas decreases.D) The internal energy of the gas must decrease. E) The temperature of the gas decreases to one-half of its original value.

6-8 5.00 kg of liquid water is heated to 100.0 °C in a closed system. At this temperature, the density of liquid water is 958 kg/m3. The pressure is maintained at atmospheric pressure of 1.01 × 105 Pa. A moveable piston of negligible weight rests on the surface of the water. The water is then converted to steam by adding an additional amount of heat to the system. When all of the water is converted, the final volume of the steam is 8.50 m3. The latent heat of vaporization of water is 2.26 × 106 J/kg.

6 How much work is done by this closed system during this isothermal process?A) 8.37 J B) 4.20 × 103 J C) 1.21 × 104 J D) 8.58 × 105 J E) 1.94 × 106 J

7. How much heat is added to the system in the isothermal process of converting all of the water into steam?A) 2.17 × 103 J B) 1.70 × 104 J C) 4.52 × 105 J D) 3.78 × 106 J E) 1.13 × 107 J

8. What is the change in the internal energy during this isothermal process?A) zero joules B) 1.28 × 104 J C) 4.40 × 105 J D) 2.93 × 106 J E) 1.04 × 107 J9 - 11 An ideal monatomic gas expands isobarically from state A to state B. It is then compressed isothermally from state B to state C and finally cooled at constant volume until it returns to its initial state A.

9. What is the temperature of the gas when it is in state B?A) 437 K B) 573 K C) 927 K D) 1200 K E) 1473 K

10. How much work is done by the gas in expanding isobarically from A to B?A) 1 × 103 J B) 2 × 103 J C) 3 × 103 J D) 4 × 103 J E) 5 × 103 J

11. How much work is done on the gas in going from B to C?A) 2.5 × 106 J B) 5.5 × 106 J C) 4.5 × 106 J D) 6.5 × 106 J E) 8.0 × 106 J

12. The ratio of the molar specific heat capacity at constant pressure to that at constant volume, , for diatomic hydrogen gas is 7/5. In an adiabatic compression, the gas, originally at atmospheric pressure, is compressed from an

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original volume of 0.30 m3 to 0.10 m3. What is the final pressure of the gas?A) 2.0 × 105 Pa B) 2.7 × 105 Pa C) 3.1 × 105 Pa D) 3.8 × 105 Pa E) 4.7 × 105 Pa

13. Determine the quantity of heat added to 2.8 moles of the ideal gas argon if the temperature increases from 75 °C to 225 °C during an isobaric process. Note: The molar specific heats of argon are CV = 3.0 cal/K·mol and CP = 5.0 cal/K·mol.A) 2600 cal B) 2100 cal C) 1600 cal D) 1100 cal E) 750 cal

14. What change in temperature occurs when 1600 J of heat are removed from 3.0 moles of monatomic gas under constant pressure?A) –8.1 K B) –12 K C) –15 K D) –26 K E) –38 K

15. An engine is used to lift a 2700-kg truck to a height of 3.0 m at constant speed. In the lifting process, the engine received 4.18 × 105 J of heat from the fuel burned in its interior. What is the efficiency of the engine?A) 0.19 B) 0.24 C) 0.29 D) 0.34 E) 0.39

16-18 A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 105 J of heat is removed from the hot reservoir and 5.0 × 104 J of work is performed.

16 Determine the Carnot efficiency of this engine.A) 0.15 B) 0.34 C) 0.50 D) 0.67 E) 0.81

17. What is the actual efficiency of this engine?A) 0.15 B) 0.34 C) 0.50 D) 0.67 E) 0.81

18. Determine the change in entropy of the cold reservoir.A) –1.0 × 102 J/K B) +1.0 × 102 J/K C) –1.8 × 102 J/K D) +1.8 × 102 J/K E) –2.0 × 102 J/K19. If the coefficient of performance for a refrigerator is 5.0 and 72 J of work are done on the system, how much heat is rejected to the room?A) 390 J B) 430 J C) 360 J D) 310 J E) 530 J

20. A 1.00-kg sample of steam at 100.0 °C condenses to water at 100.0 °C. What is the entropy change of the sample if the heat of vaporization of water is 2.26 × 106 J/kg?A) –6.06 × 103 J/K B) +6.06 × 103 J/K C) –2.26 × 104 J/K D) +2.26 × 104 J/K E) zero J/K

Chapter 16 Preparation for Quarterly Test APB Physics

1. The speed of sound in a certain metal block is 2.00 × 103 m/s. The graph shows the amplitude (in meters) of a wave traveling through the block versus time (in milliseconds). What is the wavelength of this wave?

A) 0.5 m B) 1.5 m C) 3.0 m D) 4.0 m E) 6.0 m

2. Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 8.0 seconds. When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. Determine the speed of the waves.A) 2.5 m/s B) 1.3 m/s C) 5.0 m/s D) 0.65 m/s E) 0.75 m/s

3. What is the wavelength of a wave with a speed of 9.0 m/s and a period of 0.33 s?A) 0.33 m B) 1.5 m C) 3.0 m D) 13 mE) 27 m

4. A certain string on a piano is tuned to produce middle C (f = 261.63 Hz) by carefully adjusting the tension in the string. For a fixed wavelength, what is the frequency when this tension is tripled?A) 87.21 Hz B) 151.05 Hz C) 370.00 Hz D) 453.16 Hz E) 784.89 Hz

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5. A steel wire of mass 0.400 kg and length 0.640 m supports a 102-kg block. The wire is struck exactly at its midpoint causing a small displacement. How long does it take the peak of this displacement to reach the top of the wire?

A) 2.00 × 10–3 s B) 4.00 × 10–3 s C) 6.00 × 10–3 s D) 8.00 × 10–3 s E) 1.60 × 10–2 s

6. A wave is traveling at 35 m/s on a string with a linear density of 0.082 kg/m. What is the tension in the string?A) 0.28 N B) 0.56 N C) 2.5 N D) 5.0 N E) 10 N

7. A transverse periodic wave described by the expression

sin 22 10

x ty

(where y and x are in meters and t is in seconds) is established on a string. Which one of the following statements concerning this wave is false?A) The wave is traveling in the negative x direction. B) The amplitude is 1.0 m.C) The frequency of the wave is 0.10 Hz. D) The wavelength of this wave is 2.0 m.E) The wave travels with speed 5.0 m/s.

8. A wave has an amplitude of 0.35 m, a frequency of 1.05 × 106 Hz, and travels in the positive x direction at the speed of light, 3.00 × 108 m/s. Which one of the following equations correctly represents this wave?A) y = 0.35 sin (6.60 × 106t – 0.022x) B) y = 0.35 sin (6.60 × 106t + 0.022x)C) y = 0.35 sin (286t – 1.05 × 106x) D) y = 0.35 sin (286t + 1.05 × 106x)E) y = 0.35 sin (1.05 × 106t + 3.00 × 108x)

9. A transverse wave is traveling in the –x direction on a string that has a linear density of 0.011 kg/m. The tension in the string is 7.4 N. The amplitude of the wave is 0.017 m; and its wavelength is 1.5 m. Which one of the following is the correct equation for the displacement of a particle from its equilibrium position?A) y = (0.017 m) sin[(84 Hz)t + (4.2 m–1)x] B) y = (0.017 m) sin[(110 Hz)t + (4.2 m–1)x]C) y = (4.2 m) sin[(84 Hz)t + (59 m–1)x] D) y = (4.2 m) sin[(110 Hz)t – (59 m–1)x]E) y = (0.017 m) sin[(110 Hz)t – (8.4 m–1)x]

10. A transverse periodic wave on a string with a linear density of 0.200 kg/m is described by the following equation: y = 0.08 sin(469t – 28.0x), where x and y are in meters and t is in seconds. What is the tension in the string?A) 3.99 N B) 32.5 N C) 56.1 N D) 65.8 N E) 79.6 N

11. A bell is ringing inside of a sealed glass jar that is connected to a vacuum pump. Initially, the jar is filled with air. What does one hear as the air is slowly removed from the jar by the pump?A) The sound intensity from the bell gradually decreases.B) The frequency of the sound from the bell gradually increases.C) The frequency of the sound from the bell gradually decreases.D) The speed of the sound from the bell gradually increases.E) The intensity of the sound from the bell does not change.

12. A stationary railroad whistle is sounded. An echo is heard 5.0 seconds later by the train's engineer. If the speed of sound is 343 m/s, how far away is the reflecting surface?A) 68 mB) 140 m C) 860 m D) 1700 m E) 2000 m

13. The speed of sound in fresh water at 293 K is 1482 m/s. At what temperature is the speed of sound in helium gas the same as that of fresh water at 293 K? Helium is considered a monatomic ideal gas ( = 1.67 and atomic mass = 4.003 u).A) 313 K B) 377 K C) 442 K D) 525 K E) 633 K

14. Two fans are watching a baseball game from different positions. One fan is located directly behind home plate, 18.3 m from the batter. The other fan is located in the centerfield bleachers, 127 m from the batter. Both fans observe

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the batter strike the ball at the same time (because the speed of light is about a million times faster than that of sound), but the fan behind home plate hears the sound first. What is the time difference between hearing the sound at the two locations? Use 345 m/s as the speed of sound.A) 0.316 s B) 0.368 s C) 3.17 s D) 1.89 s E) 0.053 s

15. Two children setup a “telephone” by placing a long, slender aluminum (Y = 6.9 × 1010 N/m2) rod that has a length of 6.1-m between their two houses. To communicate, a child taps a coded message on one end. How long do the sound waves take to reach the other end? Note: the density of aluminum is 2700 kg/m3.A) 1.2 × 10–3 s B) 2.4 × 10–7 s C) 8.0 × 10–6 s D) 6.3 × 10–5 s E) 1.1 × 10–4 s

16. Castor oil has a density of 956 kg/m3. If the speed of sound in castor oil is 1474 m/s, what is its adiabatic bulk modulus?A) 1.77 × 109 N/m2 B) 2.08 × 109 N/m2 C) 5.71 × 109 N/m2 D) 8.90 × 109 N/m2

E) 9.22 × 109 N/m2

17. A physics student is asked to determine the length of a long, slender, copper bar by measuring the time required for a sound pulse to travel the length of the bar. The Young's modulus of copper is 1.1 × 1011 N/m2; and its density is 8890 kg/m3. The student finds that the time for the pulse to travel from one end to the other is 5.6 × 10–4 s. How long is the rod?A) 11 mB) 7.8 m C) 5.5 m D) 2.0 m E) 0.45 m

18. The speaker and two microphones shown in the figure are arranged inside a sealed container filled with neon gas. The wires from the microphones are connected to an oscilloscope (not shown). The signal from the microphones is monitored beginning at time t = 0 s when a sound pulse is emitted from the speaker. The pulse is picked up by microphone 1 at t1 = 1.150 × 10–2 s and by microphone 2 at t2 = 1.610 × 10–2 s. What is the speed of sound in neon gas?

A) 124 m/s B) 174 m/s C) 362 m/s D) 435 m/s E) 724 m/s

19. The intensity of a spherical wave 2.5 m from the source is 120 W/m2. What is the intensity at a point 9.0 m away from the source?A) 9.3 W/m2 B) 24 W/m2 C) 53 W/m2 D) 80 W/m2 E) 270 W/m2

20. A bell emits sound energy uniformly in all directions at a rate of 4.00 × 10–3 W. What is the intensity of the wave 100.0 m from the bell?A) 3.18 × 10–8 W/m2 B) 3.14 × 10–7 W/m2 C) 5.02 × 10–2 W/m2 D) 5.02 × 102 W/m2

E) 6.28 × 107 W/m2

21. How far must one stand from a 5-mW point sound source if the intensity at that location is at the hearing threshold? Assume the sound waves travel to the listener without being disturbed.A) 500 m B) 1 kmC) 2 kmD) 4 kmE) 20 km

22. During a typical workday (eight hours), the average sound intensity arriving at Larry's ear is 1.8 × 10–5 W/m2. If the area of Larry's ear through which the sound passes is 2.1 × 10–3 m2, what is the total energy entering each of Larry's ears during the workday?A) 1.8 × 10–5 J B) 2.2 × 10–4 J C) 7.4 × 10–4 J D) 1.1 × 10–3 J E) 4.1 × 10–3 J

23. Two boys are whispering in the library. The radiated sound power from one boy's mouth is 1.2 × 10–9 W; and it spreads out uniformly in all directions. What is the minimum distance the boys must be away from the librarian so that she will not be able to hear them? The threshold of hearing for the librarian is 1.00 × 10–12 W/m2.A) 100 m B) 35 mC) 23 mD) 16 mE) 9.8 m

24. The decibel level of a jackhammer is 125 dB relative to the threshold of hearing. Determine the sound intensity produced by the jackhammer.A) 1.0 W/m2 B) 3.2 W/m2 C) 4.8 W/m2 D) 12 W/m2 E) 88 W/m2

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25. When one person was talking in a small room, the sound intensity level was 60 dB everywhere within the room. Then, there were 14 people talking in similar manner simultaneously in the room, what was the resulting sound intensity level?A) 60 dB B) 79 dB C) 71 dB D) 64 dB E) 69 dB

26. At a distance of 5.0 m from a point sound source, the sound intensity level is 110 dB. At what distance is the intensity level 95 dB?A) 5.0 m B) 7.1 m C) 14 mD) 28 mE) 42 m

27. The decibel level of a jackhammer is 130 dB relative to the threshold of hearing. Determine the decibel level if three jackhammers operate side by side.A) 65 dB B) 130 dB C) 133 dB D) 148 dB E) 260 dB

28. According to US government regulations, the maximum sound intensity level in the workplace is 90.0 dB. Within one factory, 32 identical machines produce a sound intensity level of 92.0 dB. How many machines must be removed to bring the factory into compliance with the regulation?A) 2 B) 8 C) 12 D) 16 E) 24

29. A train moving at a constant speed is passing a stationary observer on a platform. On one of the train cars, a flute player is continually playing the note known as concert A (f = 440 Hz). After the flute has passed, the observer hears the sound with a frequency of 415 Hz. What is the speed of the train? The speed of sound in air is 343 m/s.A) 7.3 m/s B) 12 m/s C) 21 m/s D) 37 m/s E) 42 m/s

30. A car moving at 35 m/s approaches a stationary whistle that emits a 220 Hz sound. The speed of sound is 343 m/s. What is the speed of the sound relative to the driver of the car?A) 300 m/s B) 308 m/s C) 340 m/s D) 365 m/s E) 378 m/s

31. A car moving at 35 m/s approaches a stationary whistle that emits a 220 Hz sound. The speed of sound is 343 m/s. What is the frequency of sound heard by the driver of the car?A) 198 Hz B) 220 Hz C) 245 Hz D) 282 Hz E) 340 Hz

32. A source moving through water at 10.0 m/s generates water waves with a frequency of 5.0 Hz. The speed of these water waves relative to the water surface is 20.0 m/s. The source approaches an observer who is at rest in the water. What wavelength would be measured for these waves by the stationary observer?A) 1.0 m B) 2.0 m C) 4.0 m D) 6.0 m E) 8.0 m

33. Two golf carts have horns that emit sound with a frequency of 394 Hz. The golf carts are traveling toward one another, each traveling with a speed of 9.5 m/s with respect to the ground. If one of the drivers sounds her horn, what frequency does the other driver hear? The speed of sound at the golf course is 345 m/s.A) 378 Hz B) 394 Hz C) 408 Hz D) 416 Hz E) 424 Hz

34. Two motorcycles are traveling in opposite directions at the same speed when one of the cyclists blasts his horn, which has frequency of 544 Hz. The other cyclist hears the frequency as 522 Hz. If the speed of sound in air is 344 m/s, what is the speed of the motorcycles?A) 5.90 m/s B) 7.24 m/s C) 8.19 m/s D) 10.0 m/s E) 11.6 m/s

35. A loudspeaker at the base of a cliff emits a pure tone of frequency 3000.0 Hz. A man jumps from rest from the top of the cliff and safely falls into a net below. How far has the man fallen at the instant he hears the frequency of the tone as 3218.0 Hz? The speed of sound is 343 m/s.

A) 12.2 m B) 15.3 m C) 31.7 m D) 46.8 m E) 61.0 m

36-38 The diagram shows the various positions of a child in motion on a swing. Somewhere in front of the child a stationary whistle is blowing.

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36. At which position(s) will the child hear the highest frequency for the sound from the whistle?A) at both A and D B) at B when moving toward A C) at B when moving toward CD) at C when moving toward B E) at C when moving toward D

37. At which position(s) will the child hear the lowest frequency for the sound from the whistle?A) at both A and D B) at B when moving toward A C) at B when moving toward CD) at C when moving toward B E) at C when moving toward D

38. At which position(s) will the child hear the same frequency as that heard by a stationary observer standing next to the whistle?A) at both A and D B) at B when moving toward A C) at B when moving toward CD) at C when moving toward B E) at C when moving toward D

39-42 The car in the drawing is moving to the left at 35 m/s. The car's horn continuously emits a 2.20 × 102 Hz sound. The figure also shows the first two regions of compression of the emitted sound waves. The speed of sound is 343 m/s.

39. How far does the car move in one period of the sound emitted from the horn?A) 0.08 m B) 0.16 m C) 8 m D) 16 mE) 35 m

40. How far has the initial compression traveled when the second compression is emitted?A) 0.77 m B) 1.56 m C) 7.7 m D) 15.5 m E) 35 m

41. What is the wavelength of the sound in the direction of motion of the car?A) 1.40 m B) 1.56 m C) 1.70 m D) 1.93 m E) 35 m

42. What is the frequency heard by a stationary observer standing in front of the car?A) 9.7 Hz B) 176 Hz C) 200 Hz D) 219 Hz E) 245 Hz

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