A free neutron (i.e., a neutron on its own rather than in a nucleus) is not a stable particle. Its average lifetime is 15 min, after which it decays into a proton, an electron, and an antineutrino. Use the energy- time uncertainty principle [Eq. (28-5)] and the relationship between mass and rest energy to estimate the inherent uncertainty in the mass of a free neutron. Compare with the average neutron mass of 1.67 × 10−27 kg. (Although the uncertainty in the neutron's mass is far too small to be measured, unstable particles with extremely short lifetimes have marked variation in their measured masses.)
> For a more realistic estimate of the maximum coefficient of performance of a heat pump, assume that a heat pump takes in heat from the outdoors at 10°C below the ambient outdoor temperature, to account for the temperature difference across its heat excha
> It is often argued that the head is the most important part of the body to cover when out in cold weather. Estimate the total energy loss by radiation if a person's head is uncovered for 15 min on a very cold, −15°C day, assuming he is bald, his skin tem
> A manometer using oil (density 0.90 g/cm3) as a fluid is connected to an air tank. Suddenly the pressure in the tank increases by 7.4 mmHg. (a) By how much does the fluid level rise in the side of the manometer that is open to the atmosphere? (b) What
> Estimate the entropy change of 850 g of water when it is heated from 20.0°C to 50.0°C. [Hint: Assume that the heat flows into the water at an average temperature of 35.0°C.]
> A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 320 km from Athens in the direction 20.0° north of east. The pilot heads directly for Sparta and flies at an airspeed of 160 km/h. After flying for 2.0 h, the pilot expec
> A student in a lecture hall has 0.25 m2 of skin (arms, hands, and head) exposed. The skin is at 34°C and has an emissivity of 0.97. The temperature of the room is 20°C (air, walls, ceiling, and floor all at the same temperature). (a) At what rate does t
> (a) What is the entropy change of 1.00 mol of H2O when it changes from ice to water at 0.0°C? (b) If the ice is in contact with an environment at a temperature of 10.0°C, what is the entropy change of the universe when the ice melts?
> A student wants to lose some weight. He knows that rigorous aerobic activity uses about 700 kcal/h (2900 kJ/h) and that it takes about 2000 kcal per day (8400 kJ) just to support necessary biological functions, including keeping the body warm. He decides
> An object moves in a circle. Is the total work done on the object by external forces necessarily zero? Explain.
> On a hot day, you are in a sealed, insulated room. The room contains a refrigerator, operated by an electric motor. The motor does work at the rate of 250 W when it is running. The refrigerator removes heat from the food storage space at a rate of 450 W
> A person of surface area 1.80 m2 is lying out in the sunlight to get a tan. If the intensity of the incident sunlight is 7.00 × 102 W/m2, at what rate must heat be lost by the person in order to maintain a constant body temperature? (Assume the effective
> Suppose you inhale 0.50 L of air initially at 20°C and 100 kPa pressure. While holding your breath, this air is warmed at constant pressure to 37°C. Treating the air as an ideal diatomic gas, how much heat flows from the body into the air?
> A sphere with a diameter of 80 cm is initially at a temperature of 250°C. If the intensity of the radiation detected at a distance of 2.0 m from the sphere's center is 102 W/m2, what is the emissivity of the sphere?
> An experiment to determine the specific heat of a gas (Chapter 14) makes use of a water manometer attached to a flask. Initially the two columns of water are even. Atmospheric pressure is 1.0 × 105 Pa. After heating the gas, the water levels
> A balloon contains 160 L of nitrogen gas at 25°C and 1.0 atm. How much energy must be added to raise the temperature of the nitrogen to 45°C while allowing the balloon to expand at atmospheric pressure?
> Six wood stoves have total surface areas A and surface temperatures T as given. Rank them in order of the power radiated, from greatest to least. Assume they all have the same emissivity. (a) A = 1.00 m2, T = 227°C (b) A = 1.01 m2, T = 227°C (c) A = 1.0
> The coefficient of static friction between a brick and a wooden board is 0.40, and the coefficient of kinetic friction between the brick and board is 0.30. You place the brick on the board and slowly lift one end of the board off the ground until the bri
> Suppose you mix 4.0 mol of a monatomic ideal gas at 20.0°C and 3.0 mol of another monatomic ideal gas at 30.0°C. If the mixture is allowed to reach equilibrium, what is the final temperature of the mixture? [Hint: Use energy conservation.]
> Wien studied the spectral distribution of many radiating bodies to finally discover a simple relation between wavelength and intensity. Use the limited data shown in Fig. 14.17 to find the constant predicted by Wien for the product of wavelength of maxim
> On a day when the temperature is 19°C, a 0.15 kg baseball is dropped from the top of a 24 m tower. After the ball hits the ground, bounces a few times, and comes to rest, approximately how much has the entropy of the universe increased?
> If a blackbody is radiating at T = 1650 K, at what wavelength is the maximum intensity?
> An electron is confined to a one-dimensional box of length L. When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy 0.20 eV. (a) What is the ground-state energy (in electron-volts) of the elec
> (a) How many moles of gas are used in this engine? (b) Calculate the heat flow into or out of the gas in steps AB and CA. (c) Calculate the work done by the gas during each step.
> A brick wall with thermal conductivity κ = 1.3 W/(m·K) is covered completely with a sheet of foam of the same thickness as the brick, but with κ = 0.025 W/(m·K). How is the rate at which heat is conducted through the wall changed by the addition of the f
> UV light with a wavelength of 180 nm is incident on a metal and electrons are ejected. Instead of determining the maximum kinetic energy of the electrons with a stopping potential, the maximum kinetic energy is determined by injecting the electrons into
> Many species cool themselves by sweating, because as the sweat evaporates, heat is transferred to the surroundings. A human exercising strenuously has an evaporative heat loss rate of about 650 W. If a person exercises strenuously for 30.0 min, how much
> Five walls of a house have different surface areas, insulation materials, and insulation thicknesses. Rank them in order of the rate of heat flow through the wall, greatest to smallest. Assume the same indoor and outdoor temperatures for each wall. (a) a
> If the temperature surrounding the sunbather in Problem 78 is greater than the normal body temperature of 37°C and the air is still, so that radiation, conduction, and convection play no part in cooling the body, how much water (in liters per hour) from
> A woman of mass 51 kg is standing in an elevator. (a) If the elevator floor pushes up on her feet with a force of 408 N, what is the acceleration of the elevator? (b) If the elevator maintains constant acceleration and is moving at 1.5 m/s as it passes
> One cross-country skier is wearing a down jacket that is 2.0 cm thick. The thermal conductivity of goose down is 0.025 W/(m·K). Her companion on the ski outing is wearing a wool jacket that is 0.50 cm thick. The thermal conductivity of wool is 0.040 W/(m
> A 10.0 g iron bullet with a speed of 4.00 × 102 m/s and a temperature of 20.0°C is stopped in a 0.500 kg block of wood, also at 20.0°C, which is fixed in place. (a) At first all of the bullet's kinetic energy goes into the internal energy of the bullet.
> Find the temperature drop across the epidermis (the outer layer of skin) under these conditions: the rate of heat flow via conduction through a 10.0 cm2 area of the epidermis is 50 mW; the epidermis is 2.00 mm thick and has thermal conductivity 0.45 W/(m
> Five ice cubes, each with a mass of 22.0 g and at a temperature of−50.0°C, are placed in an insulating container. How much heat will it take to change the ice cubes completely into steam?
> A hiker is wearing wool clothing of 0.50 cm thickness to keep warm. Her skin temperature is 35°C and the outside temperature is 4.0°C. Her body surface area is 1.2 m2. (a) If the thermal conductivity of wool is 0.040 W/(m·K), what is the rate of heat co
> When a roller coaster takes a sharp turn to the right, it feels as if you are pushed toward the left. Does a force push you to the left? If so, what is it? If not, why does there seem to be such a force?
> When a mercury manometer is connected to a gas main, the mercury stands 40.0 cm higher in the tube that is open to the air than in the tube connected to the gas main. A barometer at the same location reads 740 mmHg. Determine the absolute pressure of the
> While camping, some students decide to make hot chocolate by heating water with a solar heater that focuses sunlight onto a small area. Sunlight falls on their solar heater, of area 1.5 m2, with an intensity of 750 W/m2. How long will it take 1.0 L of wa
> A copper rod has one end in ice at a temperature of 0°C, the other in boiling water. The length and diameter of the rod are 1.00 m and 2.00 cm, respectively. At what rate in grams per hour does the ice melt? Assume no heat flows out the sides of the rod.
> A hotel room is in thermal equilibrium with the rooms on either side and with the hallway on a third side. The room loses heat primarily through a 1.30 cm thick glass window that has a height of 76.2 cm and a width of 156 cm. If the temperature inside th
> Your hot water tank is insulated, but not very well. To reduce heat loss, you wrap some old blankets around it. With the water at 81°C and the room at 21°C, a thermometer inserted between the outside of the original tank and your blanket reads 36°C. By w
> A locomotive pulls a train of 10 identical cars, on a track that runs east-west, with a force of 2.0 × 106 N directed east. What is the force with which the last car to the west pulls on the rest of the train?
> A satellite is placed in a noncircular orbit about Earth. The farthest point of its orbit (apogee) is 4.0 Earth radii from the center of Earth, while its nearest point (perigee) is 2.0 Earth radii from Earth’s center. If we define the gravitational poten
> A 75 kg block of ice at 0.0°C breaks off from a glacier, slides along the frictionless ice to the ground from a height of 2.43 m, and then slides along a horizontal surface consisting of gravel and dirt. Find how much of the mass of the ice is melted by
> Boiling water in an aluminum pan is being converted to steam at a rate of 10.0 g/s. The flat bottom of the pan has an area of 325 cm2 and the pan's thickness is 3.00 mm. If 27.0% of all heat that is transferred to the pan from the flame beneath it is los
> A 60.0 g piece of ice slides 5.00 m down an icy roof inclined at 27.0° to the horizontal. The magnitude of its acceleration is 4.10 m/s2. All the ice is at 0°C. How much ice melts?
> A wall that is 2.74 m high and 3.66 m long has a thickness composed of 1.00 cm of wood plus 3.00 cm of insulation (with the thermal conductivity approximately of wool). The inside of the wall is 23.0°C and the outside of the wall is at −5.00°C. (a) What
> At the surface of a freshwater lake the pressure is 105 kPa. (a) What is the pressure increase in going 35.0 m below the surface? (b) What is the approximate pressure decrease in going 35 m above the surface? Air at 20°C has density of 1.20 kg/m3.
> Two aluminum blocks are in thermal contact. (a) Are the blocks necessarily in physical contact? Explain. (b) If they have the same temperature, do they necessarily have the same internal energy? Explain. (c) If their internal energies are not equal, i
> A copper rod of length 0.50 m and cross-sectional area 6.0 × 10−2 cm2 is connected to an iron rod with the same cross section and length 0.25 m. One end of the copper is immersed in boiling water and the other end is at the
> A 3.0 L container of nitrogen gas (N2) and a 5.0 L container of oxygen gas (O2) are both at 20°C and 1.0 atm. (a) Which gas has the larger rms speed? Explain. (b) At what temperature will oxygen gas have the same rms speed as nitrogen when the nitrogen
> Given a slab of material with area 1.0 m2 and thickness 2.0 × 10−2 m, (a) what is the thermal resistance if the material is asbestos? (b) What is the thermal resistance if the material is iron? (c) What is the thermal resistance if the material is copp
> A star's spectrum emits more radiation with a wavelength of 700.0 nm than with any other wavelength. (a) What is the surface temperature of the star? (b) If the star's radius is 7.20 × 108 m, what power does it radiate? (c) If the star is 9.78 ly from
> To pass a physical fitness test, Marcella must run 1.00 km at an average speed of 3.33 m/s. She runs the first 0.500 km at an average of 4.20 m/s. What should be her average speed over the remaining 0.500 km in order to finish with an overall average spe
> A metal rod with a diameter of 2.30 cm and length of 1.10 m has one end immersed in ice at 32.0°F and the other end in boiling water at 212°F. If the ice melts at a rate of 1.32 g every 175 s, what is the thermal conductivity of this metal? What metal co
> A 20.0 g lead bullet leaves a rifle at a temperature of 47.0°C and travels at a speed of 5.00 × 102 m/s until it hits a 6.0 kg block of ice at 0°C that is initially at rest on a frictionless surface. The bullet becomes embedded in the ice. (a) How fast
> (a) What thickness of cork would have the same R-factor as a 1.0 cm thick stagnant air pocket? (b) What thickness of tin would be required for the same R-factor?
> What is the average pressure on the soles of the feet of a standing 90.0 kg person due to the contact force with the floor? Each foot has a surface area of 0.020 m2.
> It requires 17.10 kJ to melt 1.00 × 102 g of urethane [CO2(NH2)C2H5] at 48.7°C. What is the latent heat of fusion of urethane in kJ/mol?
> Compute the heat of fusion of a substance from these data: 31.15 kJ will change 0.500 kg of the solid at 21°C to liquid at 327°C, the melting point. The specific heat of the solid is 0.129 kJ/(kg·K).
> A stainless steel saucepan, with a base that is made of 0.350 cm thick steel [ κ = 46.0 W/(m·K)] fused to a 0.150 cm thickness of copper [κ = 401 W/(m·K)], sits on a ceramic heating element at 104.00°C. The diameter of the pan is 18.0 cm, and it contains
> You are given 250 g of coffee (same specific heat as water) at 80.0°C (too hot to drink). In order to cool this to 60.0°C, how much ice (at 0.0°C) must be added? Ignore the heat capacity of the cup and heat exchanges with the surroundings.
> Explain why the force of gravity due to Earth does not pull the Moon in closer and closer on an inward spiral until it hits Earth’s surface.
> The inner vessel of a calorimeter contains 2.50 × 102 g of tetrachloromethane, CCl4, at 40.00°C. The vessel is surrounded by 2.00 kg of water at 18.00°C. After a time, the CCl4 and the water reach the equilibrium temperature of 18.54°C. What is the speci
> A phase diagram is shown. Starting at point A, follow the dashed line to point E and consider what happens to the substance represented by this diagram as its pressure and temperature are changed. (a) Explain what happens for each line segment, AB, BC,
> A rocket is launched from rest. After 8.0 min, it is 160 km above Earth’s surface and is moving at a speed of 7.6 km/s. Assuming the rocket moves up in a straight line, what are its (a) average velocity and (b) average acceleration?
> On a hot summer day, Daphne is off to the park for a picnic. She puts 0.10 kg of ice at 0°C in a thermos and then adds tea initially at 25°C. How much tea will just melt all the ice?
> A dog loses a lot of heat through panting. The air rushing over the upper respiratory tract causes evaporation and thus heat loss. A dog typically pants at a rate of around 300 pants per minute. As a rough calculation, assume that one pant causes 0.010 g
> The maximum pressure most organisms can survive is about 1000 times atmospheric pressure. Only small, simple organisms such as tadpoles and bacteria can survive such high pressures. What then is the maximum depth at which these organisms can live under t
> A piece of gold of mass 0.250 kg and at a temperature of 75.0°C is placed into a 1.500 kg copper pot containing 0.500 L of water. The pot and water are at 22.0°C before the gold is added. What is the final temperature of the water?
> A 0.360 kg piece of solid lead at 20°C is placed into an insulated container holding 0.980 kg of liquid lead at 420°C. The system comes to an equilibrium temperature with no loss of heat to the environment. Ignore the heat capacity of the container. (a)
> A 2.0 kg block of copper at 100.0°C is placed into 1.0 kg of water in a 2.0 kg iron pot. The water and the iron pot are at 25.0°C just before the copper block is placed into the pot. What is the final temperature of the water, assuming negligible heat fl
> A 75 g cube of ice at −10.0°C is placed in 0.500 kg of water at 50.0°C in an insulating container so that no heat is lost to the environment. Will the ice melt completely? What will be the final temperature of this system?
> The student from Problem 79 realizes that standing naked in a cold room will not give him the desired weight loss results since it is much less efficient than simply exercising. So he decides to “burn” calories through conduction. He fills the bathtub wi
> (a) How much ice at −10.0°C must be placed in 0.250 kg of water at 25.0°C to cool the water to 0°C and melt all of the ice? (b) If half that amount of ice is placed in the water, what is the final temperature of the water?
> Before the discovery of the neutron, one theory of the nucleus proposed that the nucleus contains protons and electrons. For example, the helium-4 nucleus would contain 4 protons and 2 electrons instead of—as we now know to be true—2 protons and 2 neutro
> A blacksmith heats a 0.38 kg piece of iron to 498°C in his forge. After shaping it into a decorative design, he places it into a bucket of water to cool. If the available water is at 20.0°C, what minimum amount of water must be in the bucket to cool the
> In the human nervous system, signals are transmitted along neurons as action potentials that travel at speeds of up to 100 m/s. (An action potential is a traveling influx of sodium ions through the membrane of a neuron.) The signal is passed from one neu
> A birch tree loses 618 mg of water per minute through transpiration (evaporation of water through stomatal pores). What is the rate of heat lost through transpiration?
> A container has a large cylindrical lower part with a long thin cylindrical neck open at the top. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 5.00 m2. The height of the lower part of the c
> An x-ray photon with wavelength 6.00 pm collides with a free electron initially at rest. What is the maximum possible kinetic energy acquired by the electron?
> One end of a cylindrical iron rod of length 1.00 m and of radius 1.30 cm is placed in the blacksmith's fire and reaches a temperature of 327°C. If the other end of the rod is being held in your hand (37°C), what is the rate of heat flow along the rod? Th
> If a leaf is to maintain a temperature of 40°C (reasonable for a leaf), it must lose 250 W/m2 by transpiration (evaporative heat loss). Note that the leaf also loses heat by radiation, but we will ignore this. How much water is lost after 1 h through tra
> A spring of force constant k = 8.4 × 103 N/m is compressed by 0.10 m. It is placed into a vessel containing 1.0 kg of water and then released. Assuming all the energy from the spring goes into heating the water, find the change in temperature of the wate
> The graph shows the change in temperature as heat is supplied to a certain mass of ice initially at −80.0°C. What is the mass of the ice?
> A 0.500 kg slab of granite is heated so that its temperature increases by 7.40°C. The amount of heat supplied to the granite is 2.93 kJ. Based on this information, what is the specific heat of granite?
> Repeat Problem 41 without ignoring the temperature change of the glass. The glass has a mass of 350 g and the specific heat of the glass is 0.837 kJ/(kg·K). By what percentage does the answer change from the answer for Problem 41?
> Two 62 g ice cubes are dropped into 186 g of water in a glass. If the water is initially at a temperature of 24°C and the ice is at −15°C, what is the final temperature of the drink?
> Tina is going to make iced tea by first brewing hot tea, then adding ice until the tea cools. How much ice, at a temperature of −10.0°C, should be added to a 2.00 × 10−4 m3 glass of tea at 95.0°C to cool the tea to 10.0°C? Ignore the temperature change o
> A flywheel (a massive disk) rotates with constant angular acceleration. For a point on the rim of the flywheel, is the tangential acceleration component constant? Is the radial acceleration component constant?
> Imagine a trip where you drive along an east-west highway at 80.0 km/h for 45.0 min and then you turn onto a highway that runs 38.0° north of east and travel at 60.0 km/h for 30.0 min. (a) What is your average velocity for the trip? (b) What is your av
> A sperm whale can reach depths of 2500 m below the surface of the ocean. What is the pressure on the whale’s skin at that depth, assuming that the density of seawater is constant from the surface to that depth?
> A wall consists of a layer of wood outside and a layer of insulation inside. The temperatures inside and outside the wall are +22°C and −18°C; the temperature at the wood/insulation boundary is −8.0°C. By what factor would the heat loss through the wall
> What mass of water at 25.0°C added to a Styrofoam cup containing two 50.0 g ice cubes from a freezer at −15.0°C will result in a final temperature of 5.0°C for the drink?
> A hand pump is being used to inflate a bicycle tire that has a gauge pressure of 40.0 lb/in2. If the pump is a cylinder of length 18.0 in. with a cross-sectional area of 3.00 in.2, how far down must the piston be pushed before air will flow into the tire
> In plants, water diffuses out through small openings known as stomatal pores. If D = 2.4 × 10−5 m2/s for water vapor in air, and the length of the pores is 2.5 × 10−5 m, how long does it take for a water molecule to diffuse out through the pore?
> Ten students take a test and get the following scores: 83, 62, 81, 77, 68, 92, 88, 83, 72, and 75. What are the average value, the rms value, and the most probable value, respectively, of these test scores?
> Platelet cells in blood play an essential role in the formation of clots and exist in normal human blood at the level of about 200 000 per cubic millimeter. In order to illustrate that diffusion alone is not responsible for transporting platelets, consid
> An iron cannonball of radius 0.08 m has a cavity of radius 0.05 m that is to be filled with gunpowder. If the measurements were made at a temperature of 22°C, how much extra volume of gunpowder, if any, will be required to fill 500 cannonballs when the t
> Your friend is 3.0 m away from you in a room. There are no significant air currents. She opens a bottle of perfume, and you first smell it 20 s later. How long would it have taken for you to smell it if she had been 6.0 m away instead?
> The volume of air taken in by a warm-blooded vertebrate in the Andes Mountains is 210 L/day at standard temperature and pressure (i.e., 0°C and 1 atm). If the air in the lungs is at 39°C, under a pressure of 450 mm Hg, and we assume that the vertebrate t
