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Chapter 12 continued 59. Water Heater A 3.010 2 -W electric immersion heater is used to heat a cup of water, as shown in Figure 12-20. The cup is made of glass, and its mass is 3.0010 2 g. It contains 250 g of water at 15°C. How much time is needed to bring the water to the boiling point? Assume that the temperature of the cup is the same as the temperature of the water at all times and that no heat is lost to the air. Q m G C G T G m W C W T W but T G T W ,so Q (m G C G m W C W )T ((0.300 kg)(840 J/kg°C) (0.250 kg)(4180 J/kg°C))(100.0°C 15°C) 1.110 5 J Now P E Q t t ,so t Q P 1. 1105 J 3. 00102 J/s 370 s 6.1 min 60. Car Engine A 2.5010 2 -kg cast-iron car engine contains water as a coolant. Suppose that the engine’s temperature is 35.0°C when it is shut off, and the air temperature is 10.0°C. The heat given off by the engine and water in it as they cool to air temperature is 4.4010 6 J. What mass of water is used to cool the engine? Q m W C W T m i C i T Q mi mW CW Ci T T (4.410 6 J) ((2.50102 kg)(450 J/kg°C)(35.0°C 10.0°C)) (4180 J/kg°C)(35.0°C 10.0°C) 15 kg 12.2 Changes of State and the Laws of Thermodynamics page 337 Level 1 61. Years ago, a block of ice with a mass of about 20.0 kg was used daily in a home icebox. The temperature of the ice was 0.0°C when it was delivered. As it melted, how much heat did the block of ice absorb? Q mH f (20.0 kg)(3.3410 5 J/kg) 6.6810 6 J 62. A 40.0-g sample of chloroform is condensed from a vapor at 61.6°C to a liquid at 61.6°C. It liberates 9870 J of heat. What is the heat of vaporization of chloroform? Q mHv Hv 2.47105 Q 9870 J J/kg m 0.0400 kg 280 Solutions Manual Physics: Principles and Problems 250 g 15°C 3.0010 2 g 3.0010 2 W ■ Figure 12-20 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 12 continued 63. A 750-kg car moving at 23 m/s brakes to a stop. The brakes contain about 15 kg of iron, which absorbs the energy. What is the increase in temperature of the brakes? During braking, the kinetic energy of the car is converted into heat energy. So, KE C Q B 0.0, and KE C m B C B T 0.0 so, T KE C mBCB 1 2 mC (vf 2 v 2 i ) mBCB 29°C Level 2 64. How much heat is added to 10.0 g of ice at 20.0°C to convert it to steam at 120.0°C? Amount of heat needed to heat ice to 0.0°C: Q mCT (0.0100 kg)(2060 J/kg°C) 412 J (0.0°C (20.0°C)) Amount of heat to melt ice: Q mH f (0.0100 kg)(3.3410 5 J/kg) 3.3410 3 J Amount of heat to heat water to 100.0°C: Q mCT (0.0100 kg)(4180 J/kg°C) (100.0°C 0.0°C) 4.1810 3 J Amount of heat to boil water: Q mH v 1 2 (750 kg)(0.02 (23 m/s) 2 ) (15 kg)(450 J/kg°C) (0.0100 kg)(2.2610 6 J/kg) 2.2610 4 J Amount of heat to heat steam to 120.0°C: Q mCT (0.0100 kg)(2060 J/kg°C) 404 J (120.0°C 100.0°C) The total heat is 412 J 3.3410 3 J 4.1810 3 J 2.2610 4 J 404 J 3.0910 4 J 65. A 4.2-g lead bullet moving at 275 m/s strikes a steel plate and comes to a stop. If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change? Because the kinetic energy is converted to thermal energy, KE Q 0. So KE m B C B T and KE T m C B B and the mass of the bullet divides out so T 1 2 (v f 2 v i 2 ) CB 1 2 ((0.0 m/s)2 (275 m/s) 2 ) 130 J/kg°C 290°C 1 2 m B (v f 2 v i 2 ) mB C B 66. Soft Drink A soft drink from Australia is labeled “Low-Joule Cola.” The label says “100 mL yields 1.7 kJ.” The can contains 375 mL of cola. Chandra drinks the cola and then wants to offset this input of food energy by climbing stairs. How high would Chandra have to climb if she has a mass of 65.0 kg? Chandra gained (3.75)(1.7 kJ) 6.410 3 J of energy from the drink. To conserve energy, E PE 0 or 6.410 3 J mgh so, h 6.4103 J 6.410 mg 3 J (65.0 kg)(9.80 m/s2 ) 1.010 1 m, or about three flights of stairs Physics: Principles and Problems Solutions Manual 281
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