1. A large tank, open at the top, 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 2. Elaine went to her outside faucet to fill a 0.0189-m 3 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) 162 s D) 287 s E) 491 s 3. 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) 1.34 cm D) 1.67 cm E) 6.70 cm Use the following to answer question 4: A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is 2.0 kg. Its volume is 5.0 m 3. The density of air is 1.3 kg/m 3. Page 1
4. What is the magnitude of the initial acceleration of the balloon? A) zero m/s 2 B) 9.8 m/s 2 C) 10.9 m/s 2 D) 22.1 m/s 2 E) 43.6 m/s 2 5. In a car lift, compressed air with a gauge pressure of 4.0 10 5 Pa is used to raise a piston with a circular cross-sectional area. If the radius of the piston is 0.17 m, what is the maximum mass that can be raised using this piston? A) 530 kg B) 3700 kg C) 9800 kg D) 22 000 kg E) 41 000 kg 6. 150 kg of boiling water is in a thermos bottle. How many grams of ice at 12.0 C must be added to the thermos so that the equilibrium temperature of the water is 75.0 C? A) 23.3 B) 26.5 C) 43.6 D) 71.3 E) 62.5 7. 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 Page 2
8. 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) 163 C B) 142 C C) 117 C D) 53 C E) 39 C 9. An aluminum tank of volume 0.0300 m 3 is filled to the top with mercury at 20.0 C. The tank is placed inside a chamber with an interior temperature of 70.0 C. The coefficient of volume expansion for mercury is 1.82 10 4 /C ; and the coefficient of volume expansion of aluminum is 69.0 10 6 /C. After the tank and its contents reach thermal equilibrium with the interior of the chamber, how much mercury has spilled? A) 2.52 10 5 m 3 B) 6.60 10 5 m 3 C) 1.69 10 4 m 3 D) 1.92 10 4 m 3 E) 2.00 10 4 m 3 10. A metal rod 40.0000-cm long at 55.0 C is heated to 85.0 C. The length of the rod is then measured to be 40.0264 cm. What is the coefficient of linear expansion of the metal? A) 13 10 6 /C B) 22 10 6 /C C) 44 10 6 /C D) 53 10 6 /C E) 71 10 6 /C 11. The power radiated by a distant star is 6.2 10 27 W. The radius of the star, which may be considered a perfect radiator, is 1.06 10 10 m. Determine the surface temperature of the star. A) 2970 K B) 4630 K C) 7440 K D) 8710 K E) 9970 K Page 3
12. If a beaker of water is placed under a broiler so that the heating coil is above the beaker. It is observed that only the surface layer boils. The water at the bottom of the beaker remains close to the initial temperature of the water. Which of the following statements is the most reasonable conclusion to be drawn from these observations? A) Water is a poor conductor of heat. B) The sample must contain impurities. C) Water is easily heated by radiation. D) Water exhibits anomalous thermal behavior. E) The molecular motion in the sample is not random. 13. 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 14. A person steps out of the shower and dries off. The person's skin with an emissivity of 0.60 has a total area of 1.1 m 2 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 14 C? A) 74 W B) 25 W C) 81 W D) 67 W 15. How much heat (in kilo-calories) would have to be removed from 400 grams of steam at 230 o C to convert it to 400 grams of ice at -50 o C? A) 128 B) 324 C) 416 D) 571 Page 4
16. A hot metal ball at 700 K is radiating 800 joules of IR each second. If it were cooled to 400 K, at what rate (in J/s) would it be radiating energy? A) 234 B) 201 C) 158 D) 85 17. At standard temperature and pressure, carbon dioxide has a density of 1.98 kg/m 3. What volume does 1.70 kg of carbon dioxide occupy at standard temperature and pressure? A) 0.43 m 3 B) 0.86 m 3 C) 1.7 m 3 D) 2.3 m 3 E) 4.8 m 3 18. How much force does the atmosphere exert on one side of a vertical wall 4.00-m high and 10.0-m long? A) 2 10 3 N B) 1 10 5 N C) 4 10 5 N D) 4 10 6 N 19. On a cold winter day, the outside temperature is 5.0 C while the interior garage is maintained at 20.0 C by an electric heater. Assume the walls have a total area of 75 m 2, a thickness of 0.15 m, and a thermal conductivity of 0.042 J/(s-m C ). What is the cost (in cents) to heat the garage for six hours at these temperatures if the cost of electricity is 11 cents per kilowatt-hour (kw-hr)? Note: 1 kw-hr = 3.6 10 6 J. A) 18 B) 44 C) 61 D) 35 E) 99 Page 5
20. A room's wall consists of a layer of insulation 0.07 m thick, whose thermal conductivity is 0.09 J/s-m-C o, and a layer of concrete 0.12 m thick. The concrete's thermal conductivity is 1.1 J/s-m-C o. If the air is the room is maintained at a constant 20 o C, and the air on the other side of the wall is at a constant -10 o C, how many joules of thermal energy will be lost each second through the wall? A) 21.9 B) 33.8 C) 46.2 D) 51.8 Page 6
Answer Key 1. B 2. C 3. C 4. D 5. B 6. A 7. B 8. A 9. C 10. B 11. A 12. A 13. C 14. A 15. B 16. D 17. B 18. D 19. D 20. B Page 7