Solved: (a) Estimate the total power radiated into space

Problem 24P A 30-g ice cube at its melting point is dropped into an insulated container of liquid nitrogen. How much nitrogen evaporates if it is at its boiling point of 77 K and has a latent heat of vaporization of 200kJ/kg? Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point.

Problem 25P A cube of ice is taken from the freezer at ?8.5°C and placed in a 95-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0°C. The final situation is observed to be all water at 17.0°C. What was the mass of the ice cube?

Problem 27P In a hot day’s race, a bicyclist consumes 8.0 L of water over the span of four hours. Making the approximation that all of the cyclist’s energy goes into evaporating this water as sweat, how much energy in kcal did the rider use during the ride? (Since the efficiency of the rider is only about 20%, most of the energy consumed does go to heat, so our approximation is not far off.)

Problem 28P What mass of steam at 100°C must be added to 1.00 kg of ice at 0°C to yield liquid water at 20°C?

Problem 1Q What happens to the work done on a jar of orange juice when it is vigorously shaken?

Problem 2Q When a hot object warms a cooler object, does temperature flow between them? Are the temperature changes of the two objects equal? Explain.

Problem 3Q (a) If two objects of different temperatures are placed in contact, will heat naturally flow from the object with higher internal energy to the object with lower internal energy? (b) Is it possible for heat to flow even if the internal energies of the two objects are the same? Explain.

Problem 4Q In warm regions where tropical plants grow but the temperature may drop below freezing a few times in the winter, the destruction of sensitive plants due to freezing can be reduced by watering them in the evening. Explain.

Problem 5Q The specific heat of water is quite large. Explain why this fact makes water particularly good for heating systems (that is. hot-water radiators).

Problem 6Q Why does water in a metal canteen stay cooler if the cloth jacket surrounding the canteen is kept moist?

Explain why water cools (its temperature drops) when it evaporates, using the concepts of latent heat and internal energy.

(II) Samples of copper, aluminum, and water experience the same temperature rise when they absorb the same amount of heat. What is the ratio of their masses? [Hint: See Table 14-1.]

Problem 11Q Very high in the Earth’s atmosphere, the temperature can be 700°C. Yet an animal there would freeze to death rather than roast. Explain.

Problem 12Q Explorers on failed Arctic expeditions have survived by covering themselves with snow. Why would they do that?

Problem 13Q Why is wet sand at a beach cooler to walk on than dry sand?

Problem 14Q If you hear that an object has “high heat content," does that mean that its temperature is high? Explain.

Problem 15Q When hot-air furnaces are used to heat a house, why is it important that there be a vent for to return to the furnace? What happens if this vent is blocked by a bookcase?

Problem 16Q Ceiling fans are sometimes reversible, so that they drive the air down in one season and pull it up in another season. Explain which way you should set the fan (a) for summer, (b) for winter.

Problem 17P When a 290-g piece of iron at 180°C is placed in a 95-g aluminum calorimeter cup containing 250 g of glycerin at 10°C, the final temperature is observed to be 38°C. Estimate the specific heat of glycerin.

Problem 18Q Microprocessor chips have a “heat sink" glued on top that looks like a series of fins. Why are they shaped like that?

Problem 20Q The floor of a house on a foundation under which the air can flow is often cooler than a floor that rests directly on the ground (such as a concrete slab foundation). Explain.

Sea breezes are often encountered on sunny days at the shore of a large body of water. Explain, noting that the temperature of the land rises more rapidly than that of the nearby water.

Problem 21Q A 22°C day is warm, while a swimming pool at 22°C feels cool. Why?

Problem 22P During exercise, a person may give off 180 kcal of heat in 30min by evaporation of water from the skin. How much water has been lost?

Problem 22Q Explain why air temperature readings are always taken with the thermometer in the shade.

Problem 23Q A premature baby in an incubator can be dangerously cooled even when the air temperature in the incubator is warm. Explain.

Problem 26Q Heat loss occurs through windows by the following processes: (1) through the glass panes; (2) through the frame, particularly if it is metal; (3) ventilation around edges; and (4) radiation, (a) For the first three, what is (are) the mechanism(s): conduction, convection, or radiation? (b) Heavy curtains reduce which of these heat losses? Explain in detail.

Problem 27Q A piece of wood lying in the Sun absorbs more heat than a piece of shiny metal. Yet the metal feels hotter than the wood when you pick it up. Explain.

The Earth cools off at night much more quickly when the weather is clear than when cloudy. Why?

Problem 29Q An "emergency blanket" is a thin shiny (metal-coated) plastic foil. Explain how it can help to keep an immobile person warm.

Problem 30Q Explain why cities situated by the ocean tend to have less extreme temperatures than inland cities at the same latitude.

Problem 34P Calculate the rate of heat flow by conduction through the windows of Example 14-8. assuming that there are strong gusty winds and the external temperature is - 5°C

To get an idea of how much thermal energy is contained in the world's oceans, estimate the heat liberated when a cube of ocean water, 1 Km on each side, is cooled by 1K. (Approximate the ocean water as pure water for this estimate.)

(I) How much heat (in joules) is required to raise the temperature of 30.0 kg of water from \(15^{\circ} \mathrm{C}\) to \(95^{\circ} \mathrm{C}\)?

(a) Find the total power radiated into space by the Sun, assuming it to be a perfect emitter at \(T=5500 \mathrm{~K}\). The Sun's radius is \(7.0 \times 10^{8} \mathrm{~m}\). (b) From this, determine the power per unit area arriving at the Earth, \(1.5 \times 10^{11} \mathrm{~m}\) away (Fig. ). Equation Transcription: Text Transcription: T=5500 K 7.0 x 108 m 1.5 x 1011 m

Problem 2P To what temperature will 7700 J of heat raise 3.0 kg of water that is initially at 10.0°C?

Problem 3P An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatt-hours? (c) Your power company charges about a dime per kilowatt-hour. How much would your energy cost per day if you bought it from the power company? Could you feed yourself on this much money per day?

A British thermal unit (Btu) is a unit of heat in the British system of units. One Btu is defined as the heat needed to raise 1 lb of water by \(1 \ \mathrm {F}^\circ\). Show that 1 Btu = 0.252 kcal = 1055 J.

Estimate the rate at which heat can be conducted from the interior of the body to the surface. As a model, assume that the thickness of tissue is 4.0 cm. that the skin is at \(34^\circ{C}\) and the interior at \(37^\circ{C}\). and that the surface area is \(1.5 \ \mathrm{m}^2\). Compare this to the measured value of about 230 W that must be dissipated by a person working lightly. This clearly shows the necessity of convective cooling by the blood.

Problem 5P A water heater can generate 32,000 kJ/h. How much water can it heat from 15°C to 50°C per hour?

Problem 6P A small immersion heater is rated at 350 W. Estimate how long it will take to heat a cup of soup (assume this is 250 mL of water) from 20°C to 60°C.

Problem 7P How many kilocalories are generated when the brakes are used to bring a 1200-kg car to rest from a speed of 95 km/h?

Problem 7Q Explain why burns caused by steam on the skin are often more severe than burns caused by water at 100°C.

An automobile cooling system holds 16 L of water. How much heat does it absorb if its temperature rises from \(20^\circ {C}\) to \(90^\circ {C}\)?

Problem 63GP What will be the final result when equal masses of ice at 0°C and steam at 100°C are mixed together?

Problem 9P What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 5.1 kg of the metal from 18.0°C to 31.5°C?

Problem 9Q Will potatoes cook faster if the water is boiling faster?

Does an ordinary electric fan cool the air? Why or why not? If not, why use it?

Problem 11P A 35-g glass thermometer reads 21.6°C before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 39.2°C. What was the original temperature of the water?

Problem 12P What will be the equilibrium temperature when a 245-g block of copper at 285°C is placed in a 145-g aluminum calorimeter cup containing 825 g of water at 12.0°C?

(II) A hot iron horseshoe (mass \(=0.40 \mathrm{~kg}\) ), just forged (Fig. 14-16), is dropped into \(1.35 \mathrm{~L}\) of water in a \(0.30-\mathrm{kg}\) iron pot initially at \(20.0^{\circ} \mathrm{C}\). If the final equilibrium temperature is \(25.0^{\circ} \mathrm{C}\), estimate the initial temperature of the hot horseshoe.

(II) A 215-g sample of a substance is heated to \(330^{\circ} \mathrm{C}\) and then plunged into a 105-g aluminum calorimeter cup containing \(165 \mathrm{~g}\) of water and a \(17 \mathrm{~g}\) glass thermometer at \(12.5^{\circ} \mathrm{C}\). The final temperature is \(35.0^{\circ} \mathrm{C}\). What is the specific heat of the substance? (Assume no water boils away.)

Problem 15P How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water initially at 8.0°C? Assume that the part of the pot which is heated with the water is made of 360 g of aluminum, and that no water boils away.

Problem 16P Estimate the Calorie content of 75 g of candy from the following measurements. A 15-g sample of the candy is allowed to dry before putting it in a bomb calorimeter. The aluminum bomb has a mass of 0.725 kg and is placed in 2.00 kg of water contained in an aluminum calorimeter cup of mass 0.624 kg. The initial temperature of the mixture is 15.0°C, and its temperature after ignition is 53.5°C.

Problem 17Q Down sleeping bags and parkas are often specified as so many inches or centimeters of loft, the actual thickness of the garment when it is fluffed up. Explain.

The 1.20-kg head of a hammer has a speed of 6.5 m/s just before it strikes a nail (Fig. 14–17) and is brought to rest. Estimate the temperature rise of a 14-g iron nail generated by 10 such hammer blows done in quick succession. Assume the nail absorbs all the energy.

(II) A \(0.095-\mathrm{kg}\) aluminium sphere is dropped from the roof of a \(45-\mathrm{m}\)-high building. If 65% of the thermal energy produced when it hits the ground is absorbed by the sphere, what is its temperature increase?

(II) The heat capacity, C, of an object is defined as the amount of heat needed to raise its temperature by \(1 \mathrm{C}^{\circ}\). Thus, to raise the temperature by \(\Delta T\) requires heat Q given by \(Q=C \Delta T\). (a) Write the heat capacity C in terms of the specific heat, c, of the material. (b) What is the heat capacity of \(1.0 \mathrm{~kg}\) of water? (c) Of \(25 \mathrm{~kg}\) of water?

Problem 21P How much heat is needed to melt 16.50 kg of silver that is initially at 20°C?

Problem 23P If 2.80 × 105 J of energy is supplied to a flask of liquid oxygen at ?183°C, how much oxygen can evaporate?

Why is the liner of a thermos bottle silvered (Fig. 14–15), and why does it have a vacuum between its two walls?

Problem 25Q Imagine you have a wall that is very well insulated—it has a very high thermal resistance, R1.Now you place a window in the wall that has a relatively low R-value, R2. What has happened to the overall R-value of the wall plus window, compared to R1 and R2 ? [Hint: The temperature difference across the wall is still the same everywhere.]

Problem 26P An iron boiler of mass 230 kg contains 830 kg of water at 18°C. A heater supplies energy at the rate of 52,000 kJ/h. How long does it take for the water (a) to reach the boiling point, and (b) to all have changed to steam?

Problem 29P The specific heat of mercury is 138 J/kg·C°. Determine the latent heat of fusion of mercury using the following calorimeter data: 1.00 kg of solid Hg at its melting point of ?39.0°C is placed in a 0.620-kg aluminum calorimeter with 0.400 kg of water at 12.80°C; the resulting equilibrium temperature is 5.06°C.

Problem 30P A 70-g bullet traveling at 250 m/s penetrates a block of ice at 0°C and comes to rest within the ice. Assuming that the temperature of the bullet doesn’t change appreciably, how much ice is melted as a result of the collision?

Problem 31P A 54.0-kg ice-skater moving at 6.4 m/s glides to a stop. Assuming the ice is at 0°C and that 50% of the heat generated by friction is absorbed by the ice, how much ice melts?

Problem 32P At a crime scene, the forensic investigator notes that the 8.2-g lead bullet that was stopped in a doorframe apparently melted completely on impact. Assuming the bullet was fired at room temperature (20°C), what does the investigator calculate as the minimum muzzle velocity of the gun?

Problem 33P One end of a 33-cm-long aluminum rod with a diameter of 2.0 cm is kept at 460°C, and the other is immersed in water at 22°C. Calculate the heat conduction rate along the rod.

(I) (a) How much power is radiated by a tungsten sphere (emissivity e=0.35 ) of radius \(22 \mathrm{~cm}\) at a temperature of \(25^{\circ} \mathrm{C}\) ? (b) If the sphere is enclosed in a room whose walls are kept at \(-5^{\circ} \mathrm{C}\), what is the net flow rate of energy out of the sphere?

Problem 36P Heat conduction to skin. Suppose 200 W of heat flows by conduction from the blood capillaries beneath the skin to the body’s surface area of 1.5 m2. If the temperature difference is 0.50 C°, estimate the average distance of capillaries below the skin surface.

Problem 37P Two rooms, each a cube 4.0 m per side, share a 12-cm-thick brick wall. Because of a number of 100-W lightbulbs in one room, the air is at 30°C, while in the other room it is at 10°C. How many of the 100-W bulbs are needed to maintain the temperature difference across the wall?

(II) How long does it take the Sun to melt a block of ice at \(0^\circ{C}\) with a flat horizontal area \(1.0 \ \mathrm {m}^2\) and thickness 1.0 cm? Assume that the Sun’s rays make an angle of \(30^\circ\) with the vertical and that the emissivity of ice is 0.050.

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 14–18). The copper end is placed in a furnace maintained at a constant temperature of 250°C. The aluminum end is placed in an ice bath held at constant temperature of 0.0°C. Calculate the temperature at the point where the two rods are joined.

(II) (a) Using the solar constant, estimate the rate at which the whole Earth receives energy from the Sun. (b) Assume the Earth radiates an equal amount back into space (that is, the Earth is in equilibrium). Then, assuming the Earth is a perfect emitter (e = 1.0), estimate its average surface temperature.

Problem 41P A 100-W lightbulb generates 95 W of heat, which is dissipated through a glass bulb that has a radius of 3.0 cm and is 1.0 mm thick. What is the difference in temperature between the inner and outer surfaces of the glass?

Suppose the insulating qualities of the wall of a house come mainly from a 4.0-in. layer of brick and an R-19 layer of insulation, as shown in Fig. 14–19. What is the total rate of heat loss through such a wall, if its total area is \(240~ \mathrm{ft}^2\) and the temperature difference across it is \(12 ~\mathrm F^\circ \)?

Problem 44P Approximately how long should it take 11.0 kg of ice at 0°C to melt when it is placed in a carefully sealed Styrofoam ice chest of dimensions 25 cm × 35 cm × 55 cm whose walls are 1.5 cm thick? Assume that the conductivity of Styrofoam is double that of air and that the outside temperature is 32°C.

(III) A double-glazed window has two panes of glass separated by an air space, Fig. Show that the rate of heat flow through such a window by conduction is given by \(\frac{Q}{t}=\frac{A\left(T_{2}-T_{1}\right)}{l_{1} / k_{1}+l_{2} / k_{2}+l_{3} / k_{3}}\) where \(k_{1}, k_{2}, \text { and } k_{3}\) are the thermal conductivities for glass, air, and glass, respectively. (b) Generalize this expression for any number of materials placed next to one another. Equation Transcription: Text Transcription: Q over t=A(T_2 - T_1) over l_1/k_1 + l_2/k_2 + l_3/k_3 k_1,k_2, and k_3

Problem 45GP A soft-drink can contains about 0.20 kg of liquid at 5°C. Drinking this liquid can actually consume some of the fat in the body, since energy is needed to warm the water to body temperature (37°C). How many food Calories should the drink have so that it is in perfect balance with the heat needed to warm the liquid?

If coal gives off \(30 \mathrm{MJ} / \mathrm{kg}\) when it is burned, how much coal would be needed to heat a house that requires \(2.0 \times 10^5 \mathrm{MJ}\) for the whole winter? Assume that 30% of the heat is lost up the chimney.

Problem 48GP A 15-g lead bullet is tested by firing it into a fixed block of wood with a mass of 1.05 kg. The block and imbedded bullet together absorb all the heat generated. After thermal equilibrium has been reached, the system has a temperature rise measured as 0.020 C°. Estimate the entering speed of the bullet.

Problem 50GP During light activity, a 70-kg person may generate 200kcal/h. Assuming that 20% of this goes into useful work and the other 80% is converted to heat, calculate the temperature rise of the body after 1.00 h if none of this heat were transferred to the environment.

Problem 51GP A 340-kg marble boulder rolls off the top of a cliff and falls a vertical height of 140 m before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in the rock.

Problem 52GP A 2.3-kg lead ball is dropped into a 2.5-L insulated pail of water initially at 20.0°C. If the final temperature of the water-lead combination is 28.0°C, what was the initial temperature of the lead ball?

Problem 53GP A mountain climber wears a goose down jacket 3.5 cm thick with total surface area 1.2 m2. The temperature at the surface of the clothing is ?20°C and at the skin is 34°C. Determine the rate of heat flow by conduction through the jacket (a) assuming it is dry and the thermal conductivity k is that of down, and (b) assuming the jacket is wet, so k is that of water and the jacket has matted to 0.50 cm thickness.

Problem 54GP A marathon runner has an average metabolism rate of about 950 kcal/h during a race. If the runner has a mass of 55 kg, estimate how much water she would lose to evaporation from the skin for a race that lasts 2.5 h.

Problem 56GP A house has well-insulated walls 17.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 6.5 cm thick and area 280 m2, and uncovered windows 0.65 cm thick and total area 33 m2. (a) Assuming that heat is lost only by conduction, calculate the rate at which heat must be supplied to this house to maintain its inside temperature at 23°C if the outside temperature is ?10°C. (b) If the house is initially at 10°C, estimate how much heat must be supplied to raise the temperature to 23°C within 30min. Assume that only the air needs to be heated and that its volume is 750 m3. (c) If natural gas costs $0,080 per kilogram and its heat of combustion is 5.4 × 107 J/kg, how much is the monthly cost to maintain the house as in part (a) for 24 h each day, assuming 90% of the heat produced is used to heat the house? Take the specific heat of air to be 0.24kcal/kg·C°.

Problem 57GP A 15-g lead bullet traveling at 220 m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bullet absorbs 50% of the heat generated, (a) what will be the temperature rise of the bullet? (b) If the bullet’s initial temperature was 20°C, will any of the bullet melt, and if so, how much?

Problem 58GP A leaf of area 40 cm2 and mass 4.5 × 10?4kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kg·K. (a) Estimate the rate of rise of the leaf’s temperature. (b) Calculate the temperature the leaf would reach if it lost all its heat by radiation to the surroundings at 20°C. (c) In what other ways can the heat be dissipated by the leaf?

Problem 59GP Using the result of part (a) in Problem 58, take into account radiation from the leaf to calculate how much water must be transpired (evaporated) by the leaf per hour to maintain a temperature of 35°C. Problem 58 A leaf of area 40 cm2 and mass 4.5 × 10?4kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kg·K. (a) Estimate the rate of rise of the leaf’s temperature. (b) Calculate the temperature the leaf would reach if it lost all its heat by radiation to the surroundings at 20°C. (c) In what other ways can the heat be dissipated by the leaf?

Problem 60GP An iron meteorite melts when it enters the Earth’s atmosphere. If its initial temperature was ?125°C outside of Earth’s atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earth’s atmosphere.

Problem 61GP The temperature within the Earth’s crust increases about 1.0 C° for each 30 m of depth. The thermal conductivity of the crust is 0.80W/C° m. (a) Determine the heat transferred from the interior to the surface for the entire Earth in 1 day. (b) Compare this heat to the amount of energy incident on the Earth in 1 day due to radiation from the Sun.

In a typical game of squash (Fig. 14–22), two people hit a soft rubber ball at a wall until they are about to drop due to dehydration and exhaustion. Assume that the ball hits the wall at a velocity of \(22 \mathrm{~m} / \mathrm{s}\) and bounces back with a velocity of \(12 \mathrm{~m} / \mathrm{s}\), and that the kinetic energy lost in the process heats the ball. What will be the temperature increase of the ball after one bounce? (The specific heat of rubber is about \(1200 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{C}^{\circ}\).) Equation Transcription: Text Transcription: 22 m/s 12 m/s 1200 J/kgC°

In a cold environment, a person can lose heat by conduction and radiation at a rate of about 200 W. Estimate how long it would take for the body temperature to drop from \(36.6^\circ \mathrm C\) to \(35.6^\circ \mathrm C\) if metabolism were nearly to stop. Assume a mass of 70 kg. (See Table 14–1.)

Problem 65GP After a hot shower and dishwashing, there is “no hot water” left in the 50-gal (185-L) water heater. This suggests that the tank has emptied and refilled with water at roughly 10°C. (a) How much energy does it take to reheat the water to 50°C? (b) How long would it take if the heater output is 9500 W?

Problem 66GP The temperature of the glass surface of a 60-W lightbulb is 65°C when the room temperature is 18°C. Estimate the temperature of a 150-W lightbulb with a glass bulb the same size. Consider only radiation, and assume that 90% of the energy is emitted as heat.