# dm 3. dm 3 ) b Find the buoyant force (noste) on the stone when immersed in water. B = r f Vg)

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1 CHAPTER 9 1 Archimedes Law The magnitude of the buoyant force always equals the weight of the fluid displaced by the object Noste nesteessä on yhtä suuri kuin syrjäytetyn nestemäärän paino. Hpätee myös kaasuihinl 2 Mass of a stone is 37 kg. Density of the stone is 2.9 kg dm 3. a Find the mass of displaced water. (r w 1 kg dm 3 ) b Find the buoyant force (noste) on the stone when immersed in water. B r f Vg) ( r m V and m s 37; r stone 2.9; r water 1; g 9.81; V m r stone 37 kg 2.9 kg dm dm m w r water V 1 kg µ dm 3 dm3 º kg B r water µ V µ g º 125 N Kiven tilavuus syrjäytetyn veden tilavuus g 9.81; r 2900; m 37 V m r 37 kg 2900 kg m m Noste on syrjäytetyn vesimäärän paino: (Huom: koska m r V, kaava B r V g on itse asiassa sama kuin B m g, missä m on syrjäytetyn veden massa) g 9.81; r 1000; V ; B r V g 1000 kg º N m 3 * m3 * 9.81 m s 2 4 Water is to be pumped to the top of the Empire State Building, which is 366 m high. What gauge pressure (hydrostaattinen paine) is needed in the water line at the base of the building to raise the water to this height? r water 1000; g 9.81; h 366; p r water g h º 3.59 * 10 6 Pa CHAPTER A rectangular steel plate with dimensions of 30 cm 25 cm is heated from 20 C to 220 C. What is its change in area? (Coefficient of linear expansion for steel is /C.)

2 change in area? (Coefficient of linear expansion for steel is a cm 2 b cm 2 c. 3.3 cm 2 d. 6.6 cm 2 /C.) DA 2 a A 0 Dt DA 2 I11 * 10-6 M H30 * 25L cm 2 H220-20L º 3.3 cm 2 6. What happens to a given mass of water as it is cooled from 4 C to zero? a. expands b. contracts c. vaporizes d. neither expands, contracts, nor vaporizes Water exceptionally expands in the interval from 4 C to 0 C 7. A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.5 atm. What is the gas temperature? (R L atm/mol K or R 8.31 J/mol K), ideal gas T p V n R a K b K c. 965 K d. 609 K I12.5 µ µ 10 5 M I2 µ 10-3 M 0.5 µ K pv nrt 8 Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the molecular mass of nitrogen is 28, how many grams of nitrogen are present? In m M M a b. 56 c. 42 d. 112 m n * M 2 mol * 28 g mol 56 g 9 Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the gas temperature is 298 K, and the pressure is N ë m 2, what is the volume? (R 8.31 J/mol K) ideal gas pv nrt a m 3 b m 3 c m 3 d m 3 p V n R T V n R T p 2 * 8.31 * * m 3 10 Two moles of an ideal gas at 3.0 atm and 10 C are heated up to 150 C. If the volume is held constant during this heating, what is the final pressure? ideal gas p 1 V p 2 V T 2

3 p 1 V a. 4.5 atm b. 1.8 atm c atm d. 1.0 atm p 2 V T 2 p 1 3; ; T ; volume constant Ø it cancels out. p 1 p 2 T 2 p 2 p 1 * T 2 º 4.48 atm 11 A steel sphere sits on top of an aluminum ring. The steel sphere (a /C ) has a diameter of cm at 0 C. The aluminum ring (a /C ) has an inside diameter of cm at 0 C. Closest to which temperature given will the sphere just fall through the ring? (make an equation where final lenghts are equal: L 01 + a 1 L 01 Dt L 02 + a 2 L 02 Dt, Solve Dt.) a. 462 C b. 208 C c. 116 C d C a st 1.1 * 10-5 ; a Al 2.4 * 10-5 ; d Al ; d st 0.04; d st + a st * d st * Dt d Al + a Al * d Al * Dt µ 10-7 Dt µ 10-7 Dt Dt º 116 C g of water in a 2.0-L pressure vessel is heated to 500 C. What is the pressure inside the container? (R L atm/mol K, one mole of water has a mass of 18 grams) ideal gas pv nrt a. 7.9 atm b. 16 atm c. 24 atm d. 32 atm m 9; V 2; M 18; n m ; R 0.082; T ; M p n * R * T V º 15.8 atm º 16 atm CHAPTER A 10-kg piece of aluminum (which has a specific heat of 900 J/kg C) is warmed so that its temperature increases by 5.0 C. How much heat was transferred into it? heat Iwarming a substancem Q m c Dt a J b J

4 b J c J d J m 10; c 900; Dt 5; Q m c Dt º 45 kj 14. If one s hands are being warmed by holding them to one side of a flame, the predominant form of heat transfer is what process? a. conduction c. convection d. vaporization b.radiation 15. The use of fiberglass insulation in the outer walls of a building is intended to minimize heat transfer through what process? a. conduction c. convection d. vaporization a.conduction 16 How does the heat energy from the sun reach us through the vacuum of space? a. conduction c. convection d. none of the above choices are valid 17. Marc attaches a falling 500-kg object with a rope through a pulley to a paddle wheel shaft. He places the system in a well insulated tank holding 25 kg of water. When the object falls, it causes the paddle wheel to rotate and churn the water. If the object falls a vertical distance of 100 m at constant speed, what is the temperature change of the water? (the specific heat of water is J/kg C, and g 9.81 m ë s 2 ) m w * c * Dt ã m obj * h * g; a C b C c. 4.7 C d. 0.8 C m obj 500; m w 25; h 100; g 9.81; c 4186; m w * c * Dt m obj * h * g; Dt 4.69 C 18. An inventor develops a stationary cycling device by which an individual, while pedaling, can convert all of the energy expended into heat for warming water. What minimum power must be generated if 300 g water (enough for 1 cup of coffee) is to be heated in 10 min from 20 C to 95 C? (the specific heat of water is J/kg C) Equation: m c Dt Power * time a W b. 590 W c. 160 W d. 31 W

5 d. 31 W m 0.300; t 600; Dt 95-20; c 4186; Q c * m * Dt; P Q t º 157 W 19. A windowpane is half a centimeter thick and has an area of 1.0 m 2. The temperature difference between the inside and outside surfaces of the pane is 15 C. What is the rate of heat flow through this window? (Thermal conductivity for glass is 0.84 heat conduction power a J/s (W) b J/s c J/s d. 630 J/s L 0.005; A 1; Dt 15; k 0.84; P k * A * Dt L º 2520 W J s m C ). P k A T h-t c L 20. A waterfall is 145 m high. What is the increase in water temperature at the bottom of the falls if all the initial potential energy goes into heating the water? (g 9.8 m ë s 2, c w J/kg C) [ Q m c Dt m g h ] a C b C c C d C Heat gained by water is equal to relased potential energy of water at 145 m higher IE p m g hm c w 4186; m W c w DT m W * 9.81 * 145 m W c w DT m W * 9.81 * 145 DT m W * 9.81 * 145 m W c w º C 21. A solar heating system has a 25.0% conversion efficiency; the solar radiation incident on the panels is W ë m 2. What is the increase in temperature of 30.0 kg of water in a 1.00-h period by a 4.00 m 2 -area collector? Hc w J/kg C) a C b C c C d C In one hour the energy collected is, E 0.25 * 3600 s * 1000 J * J s This heats water by : m W c w DT * 4186 * DT DT º 28.7 C 22. Find the final equilibrium temperature when 10.0 g of milk at 10.0 C is added to 160 g of coffee at 90.0 C. (Assume the specific heats of coffee and milk are the same as water and neglect the heat capacity of the container.) c water 4186 J/kg ºC

6 the container.) c water 4186 J/kg ºC a C b C c C d C Coffee gives heat : m C c H90 - TL; Milk takes heat : m M c HT - 10L; Assume both have same specific heat c 4186; m Coffee 160; m Milk 10 m Coffee c H90 - TL m Milk c HT - 10L T º 85.3 C 23. The tungsten filament of a light bulb has an operating temperature of about 2100 K. If the emitting area of the filament is 1.0 cm 2, and its emissivity is 0.68, what is the power output of the light bulb? (s W ë m 2 K 4 ) radiation power P s A e T 4 a. 100 W b. 75 W c. 60 W d. 40 W T 2100; A 1 * 10-4 ; e 0.68; s * 10-8 ; P s A e T 4 º 75 W CHAPTER A system is acted on by its surroundings in such a way that it receives 50 J of heat while simultaneously doing 20 J of work. What is its net change in internal energy? (DUQ+W, Q is the heat taken by the system and W is the work done on the system.) a. 70 J b. 30 J c. zero d. -30 J Q 50; W -20; DU Q + W 30 J 25. A heat engine exhausts J of heat while performing J of useful work. What is the efficiency of the engine? W Q h - Q c a. 15% b. 33% c. 50% d. 60% Q c 3000; W 1500; eff W 1500 Q h % 26. A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K and 200 K will have what maximum efficiency? (Carnot: e c T h-t c T h )

7 a. 60% b. 50% c. 40% d. 30% T h e c T h - T c T h %, Huom Kelvinit 27. An engine absorbs 2000 J of heat from a hot reservoir and expels 750 J to a cold reservoir during each operating cycle. What is the efficiency of the engine? How much work is done during each cycle? e W Q h % W Q h - Q c J

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