Answer: The heat of volcanoes and natural hot springs

Problem 1E On a cold day, why does a metal doorknob feel colder than the wooden door?

Problem 1P In lab, Will burns a 0.6-g peanut beneath 50 g of water, which increases in temperature from 22°C to 50°C. The amount of heat absorbed by the water can be found with the equation Q = cm ? T, where Q is the amount of heat, c the specific heat of water, m the mass of water, and ? T the change in the water’s temperature. a. Assuming that 40% of the heat released makes its way to the water, show that the food value of the peanut is 3500 calories, or 3.5 Calories. ________________ b. What is the food value in calories per gram? In Calories per gram?

Problem 1RQ What is the role of “loose” electrons in heat conductors?

Problem 2E What is the explanation for feather beds being warm?

Problem 2P Radioactive decay of granite and other rocks in Earth’s interior provides sufficient energy to keep the interior molten, to heat lava, and to provide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. Show that a 500°C increase in temperature for a thermally insulated chunk of granite takes about 13.3 million years. (Assume that the specific heat capacity c of granite is 800 J/kg·C°. Use the equation Q = cm? T)

Problem 2RQ If you touch the metal sides inside of an oven with a bare hand, you’re in trouble. But hold your hand briefly in the oven air and you’re okay. What does this tell you about the relative conductivities of metal and air?

Problem 3E Wrap a fur coat around a thermometer. Will the temperature rise?

Problem 3P In a 25°C room, hot coffee in a vacuum flask cools from 75°C to 50°C in 8 hours. Explain why you predict that its temperature after another 8 hours will be 37.5°C.

Problem 3RQ Explain why a firewalker can step quickly without harm on red-hot coals with bare feet.

Problem 4E If 70°F air feels warm and comfortable to us, why does 70°F water feel cool when we swim in it?

At a certain location, the solar power per unit area reaching Earth’s surface is 200 \(\mathrm{~W} / \mathrm{m}^{2}\), averaged over a 24-hour day. If the average power requirement in your home is 3 kW and you can convert solar power to electric power with 10% efficiency, how large a collector area will you need to meet all your household energy requirements from solar energy? (Will a collector fit in your yard or on your roof?)

Problem 4RQ Why are such materials as wood, fur, feathers, and even snow good insulators?

Problem 5P In lab you submerge 100 g of 40°C iron nails in 100 g of 20°C water (the specific heat of iron is 0.12 cal/g°C.) (a) Equate the heat gained by the water to the heat lost by the nails and show that the final temperature of the water becomes 22.1°C. (b) Your lab partner is surprised by the result and says that since the masses of iron and water are equal, the final water temperature should lie closer to 30°C, half-way between. What is your explanation?

Problem 5E At what common temperature will a block of wood and a block of metal both feel neither hot nor cold to the touch?

Problem 5RQ Does a good insulator prevent heat from escaping, or does it simply slow its passage?

Problem 6E If you hold one end of a piece of metal against a piece of ice, the end in your hand soon becomes cold. Does cold flow from the ice to your hand? Explain.

Problem 6RQ What happens to the volume of air as it rises? What happens to its temperature?

Problem 7E What is the purpose of a layer of copper or aluminum on the bottom of stainless steel cookware?

Problem 7RQ When an air molecule is hit by an approaching faster-moving molecule, does its rebound speed increase or decrease? How about when it hits a receding molecule?

Problem 8E In terms of physics, why do restaurants serve baked potatoes wrapped in aluminum foil?

Problem 8RQ How are the speeds of molecules of air affected when the air is compressed by the action of a tire pump?

Problem 9E Wood is a better insulator than glass, yet fiberglass is commonly used as an insulator in wooden buildings. Explain.

Problem 9RQ How are the speeds of molecules of air affected when the air rapidly expands?

Problem 10E Many tongues have been injured by licking a piece of metal on a very cold day. Why would no harm result if a clean piece of wood were licked on the same day?

Why is Millie’s hand not burned when she holds it above the escape valve of the pressure cooker (Figure 16.8)?

Problem 11E Visit a snow-covered cemetery and note that the snow does not slope upward against the grave-stones. Instead, it forms depressions, as shown. Can you think of a reason for this?

Problem 11RQ Why does the direction of coastal winds change from day to night?

Problem 12E Why are mittens warmer than gloves on a cold day?

Problem 12RQ In what form does radiant energy travel?

Problem 13E If you were caught in freezing weather with only your own body heat as a source, would you be warmer in an Arctic igloo or in a wooden shack? Defend your answer.

Relatively speaking, do high-frequency waves have long wavelengths or short wavelengths?

Problem 14E Wood conducts heat very poorly—it has a very low conductivity. Does wood still have a low conductivity if it is hot? Could you quickly and safely grasp the wooden handle of a pan from a hot oven with your bare hand? Although the pan handle is hot, is much heat conducted from it to your hand if grasped briefly? Why would it be a poor idea to do the same with an iron handle? Explain.

Problem 14RQ How does the frequency of radiant energy relate to the absolute temperature of the radiating source?

Problem 15E Does wood have a low conductivity if it is very hot—that is, in the stage of smoldering, red-hot coals? Could you safely walk across a bed of red-hot wooden coals with bare feet? Although the coals are hot, does much heat conduct from them to your feet if you step quickly? Could you do the same on red-hot iron coals? Explain. (Caution: Coals can stick to your feet, so—OUCH!—don’t try it!)

Problem 15RQ What is terrestrial radiation?

Problem 16E Is it possible for heat to flow between two objects with the same internal energy? Can heat flow from an object with less internal energy to one with more internal energy? Defend your answers.

Problem 16RQ Cite a primary difference between waves of solar radiation and waves of terrestrial radiation.

Problem 17E When two cups of hot chocolate, one at 50°C and the other at 60°C, are poured into a bowl, why will the temperature of the mixture be between 50°C and 60°C?

Problem 17RQ Since all objects emit energy to their surroundings, why don’t the temperatures of all objects continuously decrease?

Problem 18E Why is it incorrect to say that, when a hot object warms a cold object, temperature flows between them?

Problem 18RQ What determines whether an object is a net absorber or a net emitter of radiant energy at a given time?

Problem 19E Why is it incorrect to say that, when a hot object warms a cold one, the increase in temperature of the cold one is equal to the decrease in temperature of the hot one? When is this statement correct?

Problem 19RQ Which will normally warm faster—a black pot of cold water or a silvered pot of cold water? Explain.

A friend says that the molecules in a mixture of gas in thermal equilibrium have the same average kinetic energy. Do you agree or disagree? Explain.

Problem 20RQ Can an object be both a good absorber and a good reflector at the same time? Why, or why not?

Problem 21E Your friend states that the average speed of all hydrogen and nitrogen molecules in a gas is the same. Do you agree or disagree, and why?

Problem 21RQ Why does the pupil of the eye appear black?

Problem 22E Why would you not expect all the molecules of air in your room to have the same average speed?

Problem 22RQ What happens to the temperature of something that radiates energy without absorbing the same amount in return?

Problem 23E In a mixture of hydrogen and oxygen gases at the same temperature, which molecules move faster? Why?

Problem 23RQ An object radiating energy at night is in contact with the relatively warm Earth. How does its conductivity affect whether or not it becomes appreciably colder than the air?

One container is filled with argon gas and the other with krypton gas. If both gases have the same temperature, in which container are the atoms moving faster? Why?

Problem 24RQ Which will undergo the greater rate of cooling—a red-hot poker in a warm oven or a red-hot poker in a cold room (or do both cool at the same rate)?

Problem 25E Which atoms, on average, move slower in a mixture, U-238 or U-235? How would this affect diffusion through a porous membrane of otherwise identical gases made from these isotopes?

Does Newton’s law of cooling apply to warming as well as to cooling?

Problem 26E Solid uranium can be converted chemically to uranium fluoride, UF6, which can be cooked up into a dense vapor that diffuses through a porous barrier. Which is likely to diffuse at a greater rate, a gas with isotope U-235 or U-238?

Problem 26RQ What would be the consequence of completely eliminating the greenhouse effect?

Problem 27E What would be the consequence of completely eliminating the greenhouse effect?

In what way does glass act like a one-way valve for a conventional greenhouse? Does the atmosphere play the same role?

Problem 28E In a still room, smoke from a candle will sometimes rise only so far, not reaching the ceiling. Explain why.

Problem 28RQ How much radiant energy from the Sun, on average, reaches each square meter at the top of Earth’s atmosphere each second?

Problem 29E Soaring birds and glider pilots can remain aloft for hours without expending power. How do they do it?

Problem 29RQ What is the function of a photovoltaic cell?

Problem 30E Why does helium, released into the atmosphere, eventually disappear into space?

Problem 30RQ Cite three ways in which a Thermos bottle inhibits heat transfer.

Problem 31E Ice cubes float in a glass of iced tea. Why would cooling be less if the cubes were instead on the bottom of the drink?

Problem 32E Release a single molecule in an evacuated region and it will fall as fast as, and no differently from, a baseball released in the same region. Explain.

Problem 34E What does the high specific heat of water have to do with convection currents in the air at the seashore?

Problem 35E If we warm a volume of air, it expands. Does it then follow that if we expand a volume of air, it warms? Explain.

Problem 36E Ceiling fans can make you feel cooler in a warm room. Do ceiling fans reduce room temperature?

Problem 38E A snow-making machine used for ski areas blows a mixture of compressed air and water through a nozzle. The temperature of the mixture may initially be well above the freezing temperature of water, yet crystals of snow are formed as the mixture is ejected from the nozzle. Explain how this happens.

Problem 39E In which form of heat transfer is a medium not required?

Problem 40E Why does a good emitter of heat radiation appear black at room temperature?

Problem 41E Since energy is radiated by all objects, why can’t we see them in the dark?

Problem 43E From the rules that a good absorber of radiation is a good radiator and a good reflector is a poor absorber, state a rule relating the reflecting and radiating properties of a surface.

A number of bodies at different temperatures placed in a closed room share radiant energy and ultimately reach a common temperature. Would this thermal equilibrium be possible if good absorbers were poor emitters and poor absorbers were good emitters? Explain.

Problem 44E The heat of volcanoes and natural hot springs comes from trace amounts of radioactive minerals in common rock in Earth’s interior. Why isn’t the same kind of rock at Earth’s surface warm to the touch?

Problem 45E Even though metal is a good conductor, frost can be seen on parked cars in the early morning even when the air temperature is above freezing. Provide an explanation.

Problem 46E When there is morning frost on the grass in an open park, why is frost unlikely to be found on the ground directly beneath park benches?

Problem 47E Why is whitewash sometimes applied to the glass of florists’ greenhouses in the summer?

Problem 48E On a very cold sunny day, you wear a black coat and a transparent plastic coat. Which coat should be worn on the outside for maximum warmth?

Problem 49E If the composition of the upper atmosphere were changed so that it permitted a greater amount of terrestrial radiation to escape, what effect would this have on Earth’s climate?

Problem 50E Is it important to convert temperatures to the Kelvin scale when we use Newton’s law of cooling? Why or why not?

Problem 51E Why is the insulation in an attic commonly thicker than the insulation in the walls of a house?

Problem 52E Suppose that, at a restaurant, you are served coffee before you are ready to drink it. In order that it be hottest when you are ready for it, should you add cream to the coffee right away or wait until you are ready to drink it?

Problem 53E If you wish to save fuel and you’re going to leave your warm house for a half hour or so on a very cold day, should you turn your thermostat down a few degrees, turn it off altogether, or let it remain at the room temperature you desire?

Problem 54E If you wish to save fuel and you’re going to leave your cool house for a half hour or so on a very hot day, should you turn your air-conditioning thermostat up a bit, turn it off altogether, or let it remain at the room temperature you desire?

As more energy from fossil fuels and other fuels is released on Earth, the overall temperature of Earth tends to rise. How does temperature equilibrium explain why Earth’s temperature cannot rise indefinitely?

Make up a multiple-choice question that would test a classmate’s understanding of the distinction between conduction and convection. Make another in which the term radiation is the correct answer.