Quick QuizzesAnswers to Even Numbered Conceptual QuestionsAnswers to Even Numbered ProblemsProblem SolutionsChapter 11 Energy in Thermal Processes Quick Quizzes 1. (a) Water, glass, iron. Because it has the highest specific heat()4186 J kg C⋅° , water has the smallest change in temperature. Glass is next ()837 J kg C⋅° , and iron ()448 J kg C⋅° is last. (b) Iron, glass, water. For a given temperature increase, the energy transfer by heat is proportional to the specific heat. 2. (b). The slopes are proportional to the reciprocal of the specific heat, so larger specific heat results in a smaller slope, meaning more energy to achieve a given change in temperature. 3. (c). The blanket acts as a thermal insulator, slowing the transfer of energy by heat from the air into the cube. 4. (b). The rate of energy transfer by conduction through a rod is proportional to the difference in the temperatures of the ends of the rod. When the rods are in parallel, each rod experiences the full difference in the temperatures of the two regions. If the rods are connected in series, neither rod will experience the full temperature difference between the two regions, and hence neither will conduct energy as rapidly as it did in the parallel connection. 5. (a) 4. The From Stefan’s law, the power radiated from an object at absolute temperature T is proportional to the surface area of that object. Star A has twice the radius and four times the surface area of star B. (b) 16. From Stefan’s law, the power radiated from an object having surface area A is proportional to the fourth power of the absolute temperature. Thus, ()()444AB B22 16Ae T AeTσσ===PBP. (c) 64. When star A has both twice the radius and twice the absolute temperature of star B, the ratio of the radiated powers is ()()()()()()()()24244AABB24AAA42424BBB BBBB412222 6441RTRTAeTAeT RTRTσπσσσπ== = =PP= 401402 CHAPTER 11 Answers to Even Numbered Conceptual Questions 2. In winter the produce is protected from freezing. The specific heat of Earth is so high that soil freezes only to a depth of a few inches in temperate regions. Throughout the year the temperature will stay nearly constant day and night. Factors to be considered are the insulating properties of the soil, the absence of a path for energy to be radiated away from or to the vegetables, and the hindrance of the formation of convection currents in the small, enclosed space. 4. The high thermal capacity of the barrel of water and its high heat of fusion mean that a large amount of energy would have to leak out of the cellar before the water and produce froze solid. Evaporation of the water keeps the relative humidity high to protect foodstuffs from drying out. 6. Yes, if you know the specific heat of zinc and copper, you can determine the relative fraction of each by heating a known weight of pennies to a specific initial temperature, say 100° C, then dump them into a known quantity of water, at say 20° C. The equation for conservation of energy will be ()()()Cu Zn1 c 100 C 20 Cpennies water watermxc x TmcT⋅+− °−= −° The equilibrium temperature, T, and the masses will be measured. The specific heats are known, so the fraction of metal that is copper, x, can be computed. 8. Convection is the dominant energy transfer process involved in the cooling of the bridge surface. Air currents can flow freely around all parts of the bridge, making convection particularly effective. 10. The black car absorbs more of the incoming energy from the Sun than does the white car, making it more likely to cook the egg. 12. Keep them dry. The air pockets in the pad conduct energy slowly. Wet pads absorb some energy in warming up themselves, but the pot would still be hot and the water would quickly conduct a lot of energy to your hand. 14. Write ()()()1C 1Cwater water air airVcρ°= °mc , to find ()()()()3331000 kg 4186 J kg C3.2 10 m1.3 kg m 1000 J kg Cwater waterair airmcVcρ⋅°== =×⋅° 16. (c). The ice and the liquid water have the same mass and both undergo a 5°C rise in temperature, but the ice requires less energy to accomplish this. Thus, the specific heat, ()cQmT=∆, of ice is less than that of the liquid water.Energy in Thermal Processes 403 Answers to Even Numbered Problems 2. 166 C° 4. 0.152 mm 6. 1.17 calories 8. 0.105°C 10. (a) (b) The remaining energy is absorbed by the surface on which the block slides. 9.9 C−3×10 °12. 467 pellets 14. copper wins, 89.7°C to 89.8°C 16. 1.7 kg 18. 47°C 20. 49 kJ 22. 0.12 MJ 24. 11.1 W 26. 0.33kg of water evaporated, 0.066 or 6.6% 28. 3403 cm /hr30. (a) 0°C, with 24 g of ice left (b) 8.2°C 32. 339 m d 34. (a) 0.50 kW into the house (b) 1.7 kW out of the house 36. 22.22 10 W/m C−×⋅°°38. (a) 52 W (b) 1.9 kW, 37 times greater 40. 27.2 10 W/m C−×⋅42. 263.77 10 W×44. 31.8 10 C×°404 CHAPTER 11 46. 91°C 48. 1.83 h 50. 14.1 h 52. approximately 0.9 kg or 1 L 54. 45°C 56. (a) 75.0°C (b) 36 kJ 58. (a) 25.8°C (b) No, the mass cancels. 60. (a) 2.0 kW (b) 4.5°C 62. 28 L 64. 28°C 66. (a) 2.03 kW (b) 27.78 ft h Btu⋅ 68. (a) 0.457 kg or more (b) The test samples and the inner surface of the insulation can be preheated to 37.0°Ç as the box is assembled. Then, nothing changes in temperature during the test period and the masses of the test samples and insulation make no difference.Energy in Thermal Processes 405 Problem Solutions 11.1 We assume that all the gravitational potential energy given up by the water is converted into internal energy and goes into raising the temperature of the water. Then, (gPE Q mc T∆==∆) or 00TT QmcT m=+ =+gh m0cT ghc=+ gives ()()()29.80 m s 50.0 m10.0 C 10.1°C4186 J kg °CT =°+ =⋅ 11.2 From ()Qm , the final temperature is cT=∆()()()()00-3400 cal 4.186 J 1 cal20 C 166 C50.0 10 kg 230 J kg CQTTmc=+ =°+ = °×⋅°TT=+∆ 11.3 The mass of water involved is ()31133kg10 4.00 10 m 4.00 10 kgmmVρ== × = ×14 (a) ()()()()14 184.00 10 kg 4 186 J kg C 1.00 C 1.67 10 JcT=∆= × ⋅° °= ×Qm (b) The power input is 91 000 MW 1.00 10 J s==×√ , so, 18971 yr1.67 10 J53.1 yr1.00 10 J s 3.156 10 sQt×== =××√ 11.4 The change in temperature of the rod is ()()41.00 10 J31.7 C0.350 kg 900 J kg CQTmc×∆= = = °°( and the change in the length is )()( )( )016224 10 C 20.0 cm 31.7 C 1.52 10 cm