How much heat is needed to melt 23.50 kg of silver that is

To what temperature will 8200 J of heat raise 3.0 kg of water that is initially at 10.0C?

How much heat (in joules) is required to raise the temperature of 34.0 kg of water from 15C to 95C?

When a diver jumps into the ocean, water leaks into the gap region between the divers skin and her wetsuit, forming a water layer about 0.5 mm thick. Assuming the total surface area of the wetsuit covering the diver is about and that ocean water enters the suit at 10C and is warmed by the diver to skin temperature of 35C, estimate how much energy (in units of candy ) is required by this heating process.

An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatthours? (c) If your power company charges about 10 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 F. Show that 1 Btu = 0.252 kcal = 1056 J

How many joules and kilocalories are generated when the brakes are used to bring a 1300-kg car to rest from a speed of 95 km/h?

A water heater can generate How much water can it heat from 12C to 42C per hour?

A small immersion heater is rated at 375 W. Estimate how long it will take to heat a cup of soup (assume this is 250 mL of water) from 15C to 75C.

An automobile cooling system holds 18 L of water. How much heat does it absorb if its temperature rises from 15C to 95C?

What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 4.1 kg of the metal from 18.0C to 37.2C?

(a) How much energy is required to bring a 1.0-L pot of water at 20C to 100C? (b) For how long could this amount of energy run a 60-W lightbulb?

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 141.]

(II) How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water initially at 11°C? Assume that the part of the pot which is heated with the water is made of 280 g of aluminum and that no water boils away.

What will be the equilibrium temperature when a 265-g block of copper at 245C is placed in a 145-g aluminum calorimeter cup containing 825 g of water at 12.0C?

A 31.5-g glass thermometer reads 23.6C before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 41.8C. What was the original temperature of the water? Ignore the mass of fluid inside the glass thermometer.

A 0.40-kg iron horseshoe, just forged and very hot (Fig. 1416), is dropped into 1.25 L of water in a 0.30-kg iron pot initially at 20.0C. If the final equilibrium temperature is 25.0C, estimate the initial temperature of the hot horseshoe.

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

The heat capacity, C, of an object is defined as the amount of heat needed to raise its temperature by 1 C. Thus, to raise the temperature by requires heat Q given by (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 kg of water? (c) Of 45 kg of water?

The 1.20-kg head of a hammer has a speed of just before it strikes a nail (Fig. 1417) and is brought to rest. Estimate the temperature rise of a 14-g iron nail generated by eight such hammer blows done in quick succession. Assume the nail absorbs all the energy

A 215-g sample of a substance is heated to 330C and then plunged into a 105-g aluminum calorimeter cup containing 185 g of water and a 17-g glass thermometer at 10.5C. The final temperature is 35.0C. What is the specific heat of the substance? (Assume no water boils away.)

A 0.095-kg aluminium sphere is dropped from the roof of a 55-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?

Estimate the Calorie content of 65 g of candy from the following measurements. A 15-g sample of the candy is placed in a small aluminum container of mass 0.325 kg filled with oxygen. This container is placed in 1.75 kg of water in an aluminum calorimeter cup of mass 0.624 kg at an initial temperature of 15.0C. The oxygencandy mixture in the small container (a bomb calorimeter) is ignited, and the final temperature of the whole system is 53.5C.

Determine the energy content of 100 g of Karens fudge cookies from the following measurements. A 10-g sample of a cookie is allowed to dry before putting it in a bomb calorimeter (page 396). The aluminum bomb has a mass of 0.615 kg and is placed in 2.00 kg of water contained in an aluminum calorimeter cup of mass 0.524 kg. The initial temperature of the system is 15.0C, and its temperature after ignition is 36.0C.

If of energy is supplied to a container of liquid oxygen at how much oxygen can evaporate?

How much heat is needed to melt 23.50 kg of silver that is initially at 25C?

During exercise, a person may give off 185 kcal of heat in 25 min by evaporation of water (at 20C) from the skin. How much water has been lost? [Hint: See page 399.]

What mass of steam at 100C must be added to 1.00 kg of ice at 0C to yield liquid water at 30C?

A 28-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 Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point

High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from your body if you: (a) eat 1.0 kg of snow which your body warms to body temperature of 37C; (b) melt 1.0 kg of snow using a stove and drink the resulting 1.0 kg of water at 2C, which your body has to warm to 37C

An iron boiler of mass 180 kg contains 730 kg of water at 18C. A heater supplies energy at the rate of How long does it take for the water (a) to reach the boiling point, and (b) to all have changed to steam?

Determine the latent heat of fusion of mercury using the following calorimeter data: 1.00 kg of solid Hg at its melting point of is placed in a 0.620-kg aluminum calorimeter with 0.400 kg of water at 12.80C; the resulting equilibrium temperature is 5.06C.

At a crime scene, the forensic investigator notes that the 6.2-g lead bullet that was stopped in a doorframe apparently melted completely on impact. Assuming the bullet was shot at room temperature (20C), what does the investigator calculate as the minimum muzzle velocity of the gun?

A 64-kg ice-skater moving at glides to a stop. Assuming the ice is at 0C and that 50% of the heat generated by friction is absorbed by the ice, how much ice melts?

A cube of ice is taken from the freezer at and placed in an 85-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0C. The final situation is all water at 17.0C. What was the mass of the ice cube?

A 55-g bullet traveling at penetrates a block of ice at 0C and comes to rest within the ice. Assuming that the temperature of the bullet doesnt change appreciably, how much ice is melted as a result of the collision?

Calculate the rate of heat flow by conduction through the windows of Example 148, assuming that there are strong gusty winds and the external temperature is 5C

(I) One end of a 56-cm-long copper rod with a diameter of 2.0 cm is kept at \(460^\circ \mathrm C\), and the other is immersed in water at \(22^\circ \mathrm C\). Calculate the heat conduction rate along the rod.

(a) How much power is radiated by a tungsten sphere (emissivity ) of radius 19 cm at a temperature of 25C? (b) If the sphere is enclosed in a room whose walls are kept at what is the net flow rate of energy out of the sphere?

How long does it take the Sun to melt a block of ice at 0C with a flat horizontal area and thickness 1.0 cm? Assume that the Suns rays make an angle of 35 with the vertical and that the emissivity of ice is 0.050

Heat conduction to skin. Suppose 150 W of heat flows by conduction from the blood capillaries beneath the skin to the bodys surface area of If the temperature difference is 0.50 C, estimate the average distance of capillaries below the skin surface.

Two rooms, each a cube 4.0 m per side, share a 14-cmthick brick wall. Because of a number of 100- W lightbulbs in one room, the air is at 30C, while in the other room it is at 10C. How many of the 100- W bulbs are needed to maintain the temperature difference across the wall?

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 0.50 mm thick. What is the difference in temperature between the inner and outer surfaces of the glass?

Approximately how long should it take 8.2 kg of ice at 0C 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 34C.

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 1418). The copper end is placed in a furnace maintained at a constant temperature of 205C. The aluminum end is placed in an ice bath held at a constant temperature of 0.0C. Calculate the temperature at the point where the two rods are joined

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.1419. What is the total rate of heat loss through such a wall, if its total area is 195 ft2 and the temperature difference across it is 35 F?

A soft-drink can contains about 0.35 kg of liquid at 5C. Drinking this liquid can actually consume some of the fat in the body, since energy is needed to warm the liquid to body temperature (37C). How many food Calories should the drink have so that it is in perfect balance with the heat needed to warm the liquid (essentially water)?

(a) Estimate the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5500 K. The Sun’s radius is \(7.0 \times 10^8\ m\). (b) From this, determine the power per unit area arriving at the Earth, \(1.5 \times 10^{11}\ m\) away (Fig. 14-20).

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

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

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

During light activity, a 70-kg person may generate Assuming that 20% of this goes into useful work and the other 80% is converted to heat, estimate the temperature rise of the body after 45 min if none of this heat is transferred to the environment.

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 34C and the interior at 37C, and that the surface area is 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

A bicyclist consumes 9.0 L of water over the span of 3.5 hours during a race. Making the approximation that 80% of the cyclists energy goes into evaporating this water (at 20C) as sweat, how much energy in kcal did the rider use during the ride? [Hint: See page 399.]

If coal gives off when burned, how much coal is needed to heat a house requiring for the whole winter? Assume that 30% of the heat is lost up the chimney.

A 15-g lead bullet is tested by firing it into a fixed block of wood with a mass of 35 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 bullets entering speed

A 310-kg marble boulder rolls off the top of a cliff and falls a vertical height of 120 m before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in the rock

A 2.3-kg lead ball is placed in a 2.5-L insulated pail of water initially at 20.0C. If the final temperature of the waterlead combination is 32.0C, what was the initial temperature of the lead ball?

A microwave oven is used to heat 250 g of water. On its maximum setting, the oven can raise the temperature of the liquid water from 20C to 100C in (a) At what rate does the oven put energy into the liquid water? (b) If the power input from the oven to the water remains constant, determine how many grams of water will boil away if the oven is operated for 2 min (rather than just 1 min 45 s).

In a typical squash game (Fig. 1421), two people hit a soft rubber ball at a wall. Assume that the ball hits the wall at a velocity of and bounces back at a velocity of 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 )

The temperature within the Earths crust increases about 1.0 C for each 30 m of depth. The thermal conductivity of the crust is (a) Determine the heat transferred from the interior to the surface for the entire Earth in 1.0 h. (b) Compare this heat to the 1000 W m2 that reaches the Earths surface in 1.0 h from the Sun

An iron meteorite melts when it enters the Earths atmosphere. If its initial temperature was outside of Earths atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earths atmosphere

The temperature of the glass surface of a 75-W lightbulb is 75C when the room temperature is 18C. 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.

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 36.6C to 35.6C if metabolism were nearly to stop. Assume a mass of 65 kg. (See Table 141.)

A 12-g lead bullet traveling at passes through a thin wall and emerges at a speed of If the bullet absorbs 50% of the heat generated, (a) what will be the temperature rise of the bullet? (b) If the bullets initial temperature was 20C, will any of the bullet melt, and if so, how much?

A leaf of area \(40 \ \mathrm {cm}^2\) and mass \(4.5 \times 10^{-4} \ \mathrm {kg}\) directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of \(0.80 \ \mathrm {kcal/kg} \cdot \mathrm K\). (a) Estimate the energy absorbed per second by the leaf from the Sun, and then (b) estimate the rate of rise of the leaf’s temperature. (c) Will the temperature rise continue for hours? Why or why not? (d) Calculate the temperature the leaf would reach if it lost all its heat by radiation to the surroundings at \(24^\circ \mathrm C\). (e) In what other ways can the heat be dissipated by the leaf?

Using the result of part (a) in Problem 65, 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 35C.

After a hot shower and dishwashing, there seems to be no hot water left in the 65-gal (245-L) water heater. This suggests that the tank has emptied and refilled with water at roughly 10C. (a) How much energy does it take to reheat the water to 45C? (b) How long would it take if the heater output is 9500 W?

A house thermostat is normally set to 22C, but at night it is turned down to 16C for 9.0 h. Estimate how much more heat would be needed (state as a percentage of daily usage) if the thermostat were not turned down at night. Assume that the outside temperature averages 0C for the 9.0 h at night and 8C for the remainder of the day, and that the heat loss from the house is proportional to the temperature difference inside and out. To obtain an estimate from the data, you must make other simplifying assumptions; state what these are

Problem 1COQ A 5-kg cube of warm iron (60°C) is put in thermal contact with a 10-kg cube of cold iron (15°C). Which statement is valid? (a) Heat flows spontaneously from the warm cube to the cold cube until both cubes have the same heat content. (b) Heat flows spontaneously from the warm cube to the cold cube until both cubes have the same temperature. (c) Heat can flow spontaneously from the warm cube to the cold cube, but can also flow spontaneously from the cold cube to the warm cube. (d) Heat flows from the larger cube to the smaller one because the larger one has more internal energy.

Problem 1MCQ When you put an ice cube in a glass of warm tea, which of the following happens? (a) Cold flows from the ice cube into the tea. (b) Cold flows from the ice cube into the tea and heat flows from the tea into the ice cube. (c) Heat flows from the tea into the ice cube. (d) Neither heat nor cold flows. Only temperature flows between the ice and the tea.

Problem 1P (I) To what temperature will 8200 J of heat raise 3.0 kg of water that is initially at 10.0°C?

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

Create graphs similar to Fig. 14–5, but for lead and ethyl alcohol. Compare and contrast them with each other and with the graph for water. Are there any temperature ranges for which all three substances are liquids? All vapors? All solids? For convenience, use the specific heats given in Table 14–1 for all states of lead and ethyl alcohol.

Problem 3MCQ For objects at thermal equilibrium, which of the following is true? (a) Each is at the same temperature. (b) Each has the same internal energy. (c) Each has the same heat. (d) All of the above.

Problem 2P (I) How much heat (in joules) is required to raise the temperature of 34.0 kg of water from 15°C to 95°C?

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

(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 \((\epsilon=1.0)\), estimate its average surface temperature. [Hint: Discuss why you use area \(A=\pi r_{E}^{2}\) or \(A=4 \pi r_{E}^{2}\) in each part.] Equation transcription: Text transcription: (epsilon=1.0) A=pi r_{E}^{2} A=4 pi r{E}^{2}

Problem 3P (II) When a diver jumps into the ocean, water leaks into the gap region between the diver’s skin and her wetsuit, forming a water layer about 0.5 mm thick. Assuming the total surface area of the wetsuit covering the diver is about 1.0 m2 and that ocean water enters the suit at 10°C and is warmed by the diver to skin temperature of 35°C, estimate how much energy (in units of candy bars = 300 kcal) is required by this heating process.

(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 3SL Calculate what will happen when 1000 J of heat is added to 100 grams of (a) ice at -20oC , (b) ice at 0°C, (c) water at 10°C, (d) water at 100°C, and (e) steam at 110°C.

Problem 4MCQ Which of the following happens when a material undergoes a phase change? (a) The temperature changes. (b) The chemical composition changes. (c) Heat flows into or out of the material. (d) The molecules break apart into atoms.

Problem 4P (II) An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatt-hours? (c) If your power company charges about 10 ¢ 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?

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 4SL A house has well-insulated walls 19.5 cm thick (assume conductivity of air) and area 410 m2, a roof of wood 5.5 cm thick and area 250 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 -15°C (b) If the house is initially at 15°C, estimate how much heat must be supplied to raise the temperature to 23°C within 30 min. Assume that only the air needs to be heated and that its volume is (c) If natural gas costs $0.080 kg and its heat of combustion is 5.4 X 107 j/kg. what 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 0.24 kcal/kg/C°.

Problem 5MCQ As heat is added to water, is it possible for the temperature measured by a thermometer in the water to remain constant? (a) Yes, the water could be changing phase. (b) No, adding heat will always change the temperature. (c) Maybe; it depends on the rate at which the heat is added. (d)Maybe; it depends on the initial water temperature

Problem 5P (II) 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 F°. Show that 1 BTU = 0.252 Kcal = 1056 j.

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 6MCQ A typical thermos bottle has a thin vacuum space between the shiny inner flask (which holds a liquid) and the shiny protective outer flask, often stainless steel. The vacuum space is excellent at preventing (a) conduction. (b) convection. (c) radiation. (d) conduction and convection. (e) conduction, convection, and radiation.

Problem 6P (II) How many joules and kilocalories are generated when the brakes are used to bring a 1300-kg car to rest from a speed of 95 km/h?

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

Problem 7MCQ Heat is (a) a fluid called caloric. (b) a measure of the average kinetic energy of atoms. (c) the amount of energy transferred between objects as a result of a difference in temperature. (d) an invisible, odorless, weightless substance. (e) the total kinetic energy of an ideal gas.

Problem 7P (II) A water heater can generate 32,000 kj/h. How much water can it heat from 12°C to 42°C per hour?

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

Problem 8MCQ Radiation is emitted (a) only by glowing objects such as the Sun. (b) only by objects whose temperature is greater than the temperature of the surroundings. (c) only by objects with more caloric than their surroundings. (d) by any object not at 0 K. (e) only by objects that have a large specific heat.

Problem 8P (II) A small immersion heater is rated at 375W. Estimate how long it will take to heat a cup of soup (assume this is 250mL of water) from 15°C to 75°C.

Problem 8Q Explain why water cools (its temperature drops) when it evaporates, using the concepts of latent heat and internal energy.

Problem 9MCQ Ten grams of water is added to ten grams of ice in an insulated container. Will all of the ice melt? (a) Yes. (b) No. (c) More information is needed

Problem 9P (I) An automobile cooling system holds 18 L of water. How much heat does it absorb if its temperature rises from 15°C to 95°C?

Problem 9Q Will pasta cook faster if the water boils more vigorously? Explain.

Problem 10MCQ Two objects are made of the same material, but they have different masses and temperatures. If the objects are brought into thermal contact, which one will have the greater temperature change? (a) The one with the higher initial temperature. (b) The one with the lower initial temperature. (c) The one with the greater mass. (d) The one with the lesser mass. (e) The one with the higher specific heat. (f) Not enough information.

Problem 10P (I) What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 4.1 kg of the metal from 18.0°C to 37.2°C?

Problem 10Q 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 11MCQ It has been a hot summer, so when you arrive at a lake, you decide to go for a swim even though it is nighttime. The water is cold! The next day, you go swimming again during the hottest part of the day, and even though the air is warmer the water is still almost as cold. Why? (a) Water is fairly dense compared with many other liquids. (b)Water remains in a liquid state for a wide range of temperatures. (c) Water has a high bulk modulus. (d)Water has a high specific heat.

(II) (a) How much energy is required to bring a 1.0-L pot of water at \(20^{\circ}C\) to \(100^{\circ}C\)? (b) For how long could this amount of energy run a 60-W lightbulb?

Problem 11Q Explorers on failed Arctic expeditions have survived by covering themselves with snow. Why would they do that?

Problem 12MCQ Two equal-mass liquids, initially at the same temperature, are heated for the same time over the same stove. You measure the temperatures and find that one liquid has a higher temperature than the other. Which liquid has the higher specific heat? (a) The cooler one. (b) The hotter one. (c) Both are the same.

Problem 12P (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?

Problem 12Q Why is wet sand at a beach cooler to walk on than dry sand?

(II) How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water initially at \(11^{\circ}C\)? Assume that the part of the pot which is heated with the water is made of 280 g of aluminum, and that no water boils away.

Problem 13Q If you hear that an object has “high heat content,” does that mean that its temperature is high? Explain.

Problem 14EA Return to the Chapter-Opening Question, page 390, and answer it again now. Try to explain why you may have answered differently the first time.

Problem 14EB A pot of water is boiling on a gas stove, and then you turn up the heat. What happens? (a) The temperature of the water starts increasing. (b) There is a tiny decrease in the rate of water loss by evaporation. (c) The rate of water loss by evaporation increases. (d) There is an appreciable increase in both the rate of boiling and the temperature of the water. (e) None of these.

Which process in Example 14–6 required the greatest heat loss?

Problem 14ED How much more ice at -10° C would be needed in Example 14–7 to bring the tea down to 0°C, while just melting all the ice?

Explain why drapes in front of a window reduce heat loss from a house.

Problem 14EF Fanning yourself on a hot day cools you by (a) increasing the radiation rate of the skin; (b) increasing conductivity; (c) decreasing the mean free path of air; (d) increasing the evaporation of perspiration; (e) none of these.

Problem 14P (II) What will be the equilibrium temperature when a 265-g block of copper at 245°C is placed in a 145-g aluminum calorimeter cup containing 825 g of water at 12.0°C?

Problem 14Q When hot-air furnaces are used to heat a house, why is it important that there be a vent for air to return to the furnace? What happens if this vent is blocked by a bookcase?

Problem 15P (II) A 31.5-g glass thermometer reads 23.6°C before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 41.8°C. What was the original temperature of the water? Ignore the mass of fluid inside the glass thermometer.

Problem 15Q 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.

(II) A 0.40-kg iron horseshoe, just forged and very hot (Fig. 14–16), is dropped into 1.25 L of water in a 0.30-kg iron pot initially at \(20.0^{0} \mathrm{C}\). If the final equilibrium temperature is \(25.0^{0} \mathrm{C}\), estimate the initial temperature of the hot horseshoe. Equation transcription: Text transcription: 20.0^{0}{C} 25.0^{0}{C}

Problem 16Q Goose 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.

Problem 17P (II) 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 17Q Microprocessor chips have a “heat sink” glued on top that looks like a series of fins. Why are they shaped like that?

Problem 18P (II) The heat capacity, C, of an object is defined as the amount of heat needed to raise its temperature by 1 C°. Thus, to raise the temperature by ? T requires heat Q given by Q =C ? 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 kg of water? (c) Of 45 kg of water?

Problem 18Q 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.

(II) The 1.20-kg head of a hammer has a speed of 7.5 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 eight such hammer blows done in quick succession. Assume the nail absorbs all the energy.

Problem 19Q 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.

Problem 20P (II) A 215-g sample of a substance is heated to 330°C and then plunged into a 105-g aluminum calorimeter cup containing 185 g of water and a 17-g glass thermometer at 10.5°C. The final temperature is 35.0°C. What is the specific heat of the substance? (Assume no water boils away.)

Problem 20Q A 22°C day is warm, while a swimming pool at 22°C feels cool. Why?

Problem 21P (II) A 0.095-kg aluminium sphere is dropped from the roof of a 55-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?

Problem 21Q Explain why air temperature readings are always taken with the thermometer in the shade.

Problem 22P (II) Estimate the Calorie content of 65 g of candy from the following measurements. A 15-g sample of the candy is placed in a small aluminum container of mass 0.325 kg filled with oxygen. This container is placed in 1.75 kg of water in an aluminum calorimeter cup of mass 0.624 kg at an initial temperature of 15.0°C. The oxygen–candy mixture in the small container (a “bomb calorimeter”) is ignited, and the final temperature of the whole system is 53.5°C.

Problem 22Q A premature baby in an incubator can be dangerously cooled even when the air temperature in the incubator is warm. Explain.

Problem 23P (II) Determine the energy content of 100 g of Karen’s fudge cookies from the following measurements. A 10-g sample of a cookie is allowed to dry before putting it in a bomb calorimeter (page 396). The aluminum bomb has a mass of 0.615 kg and is placed in 2.00 kg of water contained in an aluminum calorimeter cup of mass 0.524 kg. The initial temperature of the system is 15.0°C, and its temperature after ignition is 36.0°C.

Problem 23Q Does an ordinary electric fan cool the air? Why or why not? If not, why use it?

(I) If \(3.40 \times 10^5 \ \mathrm J\) of energy is supplied to a container of liquid oxygen at \(-183^\circ \ \mathrm C\), how much oxygen can evaporate?

Problem 24Q 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 25P (II) How much heat is needed to melt 23.50 kg of silver that is initially at 25°C?

Problem 25Q 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.

Problem 26P (II) During exercise, a person may give off 185 kcal of heat in 25 min by evaporation of water (at 20°C) from the skin. How much water has been lost?

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

Problem 27P (II) What mass of steam at 100°C must be added to 1.00 kg of ice at 0°C to yield liquid water at 30°C?

Problem 27Q An “emergency blanket” is a thin shiny (metal-coated) plastic foil. Explain how it can help to keep an immobile person warm.

Problem 28P (II) A 28-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 200 kJ/kg? Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point.

Problem 28Q Explain why cities situated by the ocean tend to have less extreme temperatures than inland cities at the same latitude.

Problem 29P (II) High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from your body if you: (a) eat 1.0 kg of -15° C snow which your body warms to body temperature of 37°C; (b) melt 1.0 kg of -15° C snow using a stove and drink the resulting 1.0 kg of water at 2°C, which your body has to warm to 37°C.

A paper cup placed among hot coals will burn if empty (note burn spots at top of cup in Fig. 14–14), but won’t burn if filled with water. Explain. Forget the marshmallows.

Problem 30P (II) An iron boiler of mass 180 kg contains 730 kg of water at 18°C. A heater supplies energy at the rate of 58,000 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 30Q On a cold windy day, a window will feel colder than on an equally cold day with no wind. This is true even if no air leaks in near the window. Why?

Problem 31P (II) 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 32P (II) At a crime scene, the forensic investigator notes that the 6.2-g lead bullet that was stopped in a doorframe apparently melted completely on impact. Assuming the bullet was shot at room temperature (20°C), what does the investigator calculate as the minimum muzzle velocity of the gun?

Problem 33P (II) A 64-kg ice-skater moving at 7.5 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 34P (II) A cube of ice is taken from the freezer at -8.5°C and placed in an 85-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0°C. The final situation is all water at 17.0°C. What was the mass of the ice cube?

Problem 35P (II) A 55-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 36P (I) 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

(I) One end of a 56-cm-long copper rod with a diameter of 2.0 cm is kept at \(460^\circ \mathrm C\), and the other is immersed in water at \(22^\circ \mathrm C\). Calculate the heat conduction rate along the rod.

Problem 38P (II) (a) How much power is radiated by a tungsten sphere (emissivity E = 0.35 ) of radius 19 cm at a temperature of 25°C? (b) If the sphere is enclosed in a room whose walls are kept at -5°C what is the net flow rate of energy out of the sphere?

(II) How long does it take the Sun to melt a block of ice at \(0^{\circ}C\) with a flat horizontal area \(1.0\ m^2\) and thickness 1.0 cm? Assume that the Sun’s rays make an angle of \(35^{\circ}\) with the vertical and that the emissivity of ice is 0.050.

Problem 40P (II) Heat conduction to skin. Suppose 150 W of heat flows by conduction from the blood capillaries beneath the skin to the body’s surface area of 1.5m2 If the temperature difference is 0.50 C°, estimate the average distance of capillaries below the skin surface.

Two rooms, each a cube 4.0 m per side, share a 14-cm thick brick wall. Because of a number of 100-W light bulbs in one room, the air is at \(30^\circ \mathrm C\), while in the other room it is at \(10^\circ \mathrm C\). How many of the 100-W bulbs are needed to maintain the temperature difference across the wall?

Problem 42P (II) 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 0.50 mm thick. What is the difference in temperature between the inner and outer surfaces of the glass?

Problem 43P (III) Approximately how long should it take 8.2 kg of ice at 0°C to melt when it is placed in a carefully sealed Styrofoam ice chest of dimensions 25cm X 35cm X 55cm whose walls are 1.5 cm thick? Assume that the conductivity of Styrofoam is double that of air and that the outside temperature is 34°C.

(III) 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 \(205^{0} \mathrm{C}\). The aluminum end is placed in an ice bath held at a constant temperature of \(0.0^{0} \mathrm{C}\). Calculate the temperature at the point where the two rods are joined. Equation transcription: Text transcription: 205^{0}{C} 0.0^{0}{C}

(III) 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 \(195 f t^{2}\) and the temperature difference across it is \(35^{0} F\)? Equation transcription: Text transcription: 195 f t^{2} 35^{0} F

Problem 46GP A soft-drink can contains about 0.35 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 liquid 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 (essentially water)?

(a) Estimate 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, \(1.5 x 10^{11} m\) away (Fig. 14–20). Equation transcription: Text transcription: T=5500{~K} 7.0 times 10^{8}{~m} 1.5 x 10^{11} m

Problem 48GP 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.)

Problem 49GP What will be the final result when equal masses of ice at 0°C and steam at 100°C are mixed together?

Problem 50GP A mountain climber wears a goose-down jacket 3.5 cm thick with total surface area 0.95 m2. The temperature at the surface of the clothing is -18oC and at the skin is 34°C. Determine the rate of heat flow by conduction through the jacket assuming (a) it is dry and the thermal conductivity k is that of goose down, and (b) the jacket is wet, so k is that of water and the jacket has matted to 0.50 cm thickness.

Problem 51GP During light activity, a 70-kg person may generate 200 kcal/h. Assuming that 20% of this goes into useful work and the other 80% is converted to heat, estimate the temperature rise of the body after 45 min if none of this heat is transferred to the environment.

Problem 52GP 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°C and the interior at 37°C, and that the surface area is 1.5 m2. 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.

A bicyclist consumes 9.0 L of water over the span of 3.5 hours during a race. Making the approximation that 80% of the cyclist’s energy goes into evaporating this water (at \(20^{0} \mathrm{C}\)) as sweat, how much energy in kcal did the rider use during the ride? [Hint: See page 399.] Equation transcription: Text transcription: 20^{0}{C}

Problem 54GP If coal gives off 30 MJ/kg when burned, how much coal is needed to heat a house requiring 2.0*105 MJ for the whole winter? Assume that 30% of the heat is lost up the chimney.

Problem 55GP A 15-g lead bullet is tested by firing it into a fixed block of wood with a mass of 35 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 bullet’s entering speed.

Problem 56GP A 310-kg marble boulder rolls off the top of a cliff and falls a vertical height of 120 m before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in the rock.

Problem 57GP A 2.3-kg lead ball is placed in a 2.5-L insulated pail of water initially at 20.0°C. If the final temperature of the water–lead combination is 32.0°C, what was the initial temperature of the lead ball?

Problem 58GP A microwave oven is used to heat 250 g of water. On its maximum setting, the oven can raise the temperature of the liquid water from 20°C to 100°C in 1 min 45 s(1 = 105 s). (a) At what rate does the oven put energy into the liquid water? (b) If the power input from the oven to the water remains constant, determine how many grams of water will boil away if the oven is operated for 2min (rather than just 1 min 45 s).

In a typical squash game (Fig. 14–21), two people hit a soft rubber ball at a wall. Assume that the ball hits the wall at a velocity of 22 m/s and bounces back at a velocity of 12 m/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 \(1200\ J/kg \cdot C^{\circ}\).)

The temperature within the Earth’s crust increases about \(1.0^{0} \mathrm{C}\) for each 30 m of depth. The thermal conductivity of the crust is \(0.80 J / s^{0} C . m\). (a) Determine the heat transferred from the interior to the surface for the entire Earth in 1.0 h. (b) Compare this heat to the \(1000 \mathrm{~W} / \mathrm{m}^{2}\) that reaches the Earth’s surface in 1.0 h from the Sun. Equation transcription: Text transcription: 0.80 J / s^{0} C . m 1000{~W} /{m}^{2} 1.0^{0}{C}

Problem 61GP An iron meteorite melts when it enters the Earth’s atmosphere. If its initial temperature was -105oC outside of Earth’s atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earth’s atmosphere.

Problem 62GP The temperature of the glass surface of a 75-W lightbulb is 75°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.

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 \(36.6^{0} \mathrm{C}\) to \(35.6^{0} \mathrm{C}\) if metabolism were nearly to stop. Assume a mass of 65 kg. (See Table 14–1.) Equation transcription: Text transcription: 36.6^{0}{C} 35.6^{0}{C}

A 12-g lead bullet traveling at 220 m/s passes through a thin wall and emerges at a speed 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 \(20^{\circ}C\), will any of the bullet melt, and if so, how much?

Problem 65GP A leaf of area 40 cm2 and mass 4.5*10-4 kg 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 energy absorbed per second by the leaf from the Sun, and then (b) estimate the rate of rise of the leaf’s temperature. (c) Will the temperature rise continue for hours? Why or why not? (d) Calculate the temperature the leaf would reach if it lost all its heat by radiation to the surroundings at 24°C. (e) In what other ways can the heat be dissipated by the leaf?

Using the result of part (a) in Problem 65, 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 \(35^{\circ}C\).

Problem 67GP After a hot shower and dishwashing, there seems to be no hot water left in the 65-gal (245-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 45°C? (b) How long would it take if the heater output is 9500 W?

Problem 68GP A house thermostat is normally set to 22°C, but at night it is turned down to 16°C for 9.0 h. Estimate how much more heat would be needed (state as a percentage of daily usage) if the thermostat were not turned down at night. Assume that the outside temperature averages 0°C for the 9.0 h at night and 8°C for the remainder of the day, and that the heat loss from the house is proportional to the temperature difference inside and out. To obtain an estimate from the data, you must make other simplifying assumptions; state what these are.

To what temperature will 8200 J of heat raise 3.0 kg of water that is initially at 10.0C?

How much heat (in joules) is required to raise the temperature of 34.0 kg of water from 15C to 95C?

When a diver jumps into the ocean, water leaks into the gap region between the divers skin and her wetsuit, forming a water layer about 0.5 mm thick. Assuming the total surface area of the wetsuit covering the diver is about and that ocean water enters the suit at 10C and is warmed by the diver to skin temperature of 35C, estimate how much energy (in units of candy ) is required by this heating process.

An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatthours? (c) If your power company charges about 10 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 F. Show that 1 Btu = 0.252 kcal = 1056 J

How many joules and kilocalories are generated when the brakes are used to bring a 1300-kg car to rest from a speed of 95 km/h?

A water heater can generate How much water can it heat from 12C to 42C per hour?

A small immersion heater is rated at 375 W. Estimate how long it will take to heat a cup of soup (assume this is 250 mL of water) from 15C to 75C.

An automobile cooling system holds 18 L of water. How much heat does it absorb if its temperature rises from 15C to 95C?

What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 4.1 kg of the metal from 18.0C to 37.2C?

(a) How much energy is required to bring a 1.0-L pot of water at 20C to 100C? (b) For how long could this amount of energy run a 60-W lightbulb?

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 141.]

How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water initially at 11C? Assume that the part of the pot which is heated with the water is made of 280 g of aluminum, and that no water boils away.

What will be the equilibrium temperature when a 265-g block of copper at 245C is placed in a 145-g aluminum calorimeter cup containing 825 g of water at 12.0C?

(II) A 31.5-g glass thermometer reads \(23.6^\circ \mathrm C\) before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads \(41.8^\circ \mathrm C\). What was the original temperature of the water? Ignore the mass of fluid inside the glass thermometer.

A 0.40-kg iron horseshoe, just forged and very hot (Fig. 1416), is dropped into 1.25 L of water in a 0.30-kg iron pot initially at 20.0C. If the final equilibrium temperature is 25.0C, estimate the initial temperature of the hot horseshoe.

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

The heat capacity, C, of an object is defined as the amount of heat needed to raise its temperature by 1 C. Thus, to raise the temperature by requires heat Q given by (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 kg of water? (c) Of 45 kg of water?

The 1.20-kg head of a hammer has a speed of just before it strikes a nail (Fig. 1417) and is brought to rest. Estimate the temperature rise of a 14-g iron nail generated by eight such hammer blows done in quick succession. Assume the nail absorbs all the energy

A 215-g sample of a substance is heated to 330C and then plunged into a 105-g aluminum calorimeter cup containing 185 g of water and a 17-g glass thermometer at 10.5C. The final temperature is 35.0C. What is the specific heat of the substance? (Assume no water boils away.)

A 0.095-kg aluminium sphere is dropped from the roof of a 55-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?

Estimate the Calorie content of 65 g of candy from the following measurements. A 15-g sample of the candy is placed in a small aluminum container of mass 0.325 kg filled with oxygen. This container is placed in 1.75 kg of water in an aluminum calorimeter cup of mass 0.624 kg at an initial temperature of 15.0C. The oxygencandy mixture in the small container (a bomb calorimeter) is ignited, and the final temperature of the whole system is 53.5C.

Determine the energy content of 100 g of Karens fudge cookies from the following measurements. A 10-g sample of a cookie is allowed to dry before putting it in a bomb calorimeter (page 396). The aluminum bomb has a mass of 0.615 kg and is placed in 2.00 kg of water contained in an aluminum calorimeter cup of mass 0.524 kg. The initial temperature of the system is 15.0C, and its temperature after ignition is 36.0C.

If of energy is supplied to a container of liquid oxygen at how much oxygen can evaporate?

How much heat is needed to melt 23.50 kg of silver that is initially at 25C?

During exercise, a person may give off 185 kcal of heat in 25 min by evaporation of water (at 20C) from the skin. How much water has been lost? [Hint: See page 399.]

(II) What mass of steam at \(100^\circ \mathrm C\) must be added to 1.00 kg of ice at \(0^\circ \mathrm C\) to yield liquid water at \(30^\circ \mathrm C\)?

A 28-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 Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point

(II) High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from your body if you: (a) eat 1.0 kg of \(-15^{\circ}C\) snow which your body warms to body temperature of \(37^{\circ}C\) snow which your body warms to body temperature of \(37^{\circ}C\); (b) melt 1.0 kg of \(-15^{\circ}C\) snow using a stove and drink the resulting 1.0 kg of water at \(2^{\circ}C\), which your body has to warm to \(37^{\circ}C\).

An iron boiler of mass 180 kg contains 730 kg of water at 18C. A heater supplies energy at the rate of How long does it take for the water (a) to reach the boiling point, and (b) to all have changed to steam?

Determine the latent heat of fusion of mercury using the following calorimeter data: 1.00 kg of solid Hg at its melting point of is placed in a 0.620-kg aluminum calorimeter with 0.400 kg of water at 12.80C; the resulting equilibrium temperature is 5.06C.

At a crime scene, the forensic investigator notes that the 6.2-g lead bullet that was stopped in a doorframe apparently melted completely on impact. Assuming the bullet was shot at room temperature (20C), what does the investigator calculate as the minimum muzzle velocity of the gun?

A 64-kg ice-skater moving at glides to a stop. Assuming the ice is at 0C and that 50% of the heat generated by friction is absorbed by the ice, how much ice melts?

A cube of ice is taken from the freezer at and placed in an 85-g aluminum calorimeter filled with 310 g of water at room temperature of 20.0C. The final situation is all water at 17.0C. What was the mass of the ice cube?

A 55-g bullet traveling at penetrates a block of ice at 0C and comes to rest within the ice. Assuming that the temperature of the bullet doesnt change appreciably, how much ice is melted as a result of the collision?

Calculate the rate of heat flow by conduction through the windows of Example 148, assuming that there are strong gusty winds and the external temperature is 5C

One end of a 56-cm-long copper rod with a diameter of 2.0 cm is kept at 460C, and the other is immersed in water at 22C. Calculate the heat conduction rate along the rod.

(a) How much power is radiated by a tungsten sphere (emissivity ) of radius 19 cm at a temperature of 25C? (b) If the sphere is enclosed in a room whose walls are kept at what is the net flow rate of energy out of the sphere?

How long does it take the Sun to melt a block of ice at 0C with a flat horizontal area and thickness 1.0 cm? Assume that the Suns rays make an angle of 35 with the vertical and that the emissivity of ice is 0.050

Heat conduction to skin. Suppose 150 W of heat flows by conduction from the blood capillaries beneath the skin to the bodys surface area of If the temperature difference is 0.50 C, estimate the average distance of capillaries below the skin surface.

Two rooms, each a cube 4.0 m per side, share a 14-cmthick brick wall. Because of a number of 100-W lightbulbs in one room, the air is at 30C, while in the other room it is at 10C. How many of the 100-W bulbs are needed to maintain the temperature difference across the wall?

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 0.50 mm thick. What is the difference in temperature between the inner and outer surfaces of the glass?

Approximately how long should it take 8.2 kg of ice at 0C 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 34C.

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 1418). The copper end is placed in a furnace maintained at a constant temperature of 205C. The aluminum end is placed in an ice bath held at a constant temperature of 0.0C. Calculate the temperature at the point where the two rods are joined

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.1419. What is the total rate of heat loss through such a wall, if its total area is 195 ft2 and the temperature difference across it is 35 F?

A soft-drink can contains about 0.35 kg of liquid at 5C. Drinking this liquid can actually consume some of the fat in the body, since energy is needed to warm the liquid to body temperature (37C). How many food Calories should the drink have so that it is in perfect balance with the heat needed to warm the liquid (essentially water)?

(a) Estimate the total power radiated into space by the Sun, assuming it to be a perfect emitter at The Suns radius is (b) From this, determine the power per unit area arriving at the Earth, away (Fig. 1420)

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

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

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

During light activity, a 70-kg person may generate Assuming that 20% of this goes into useful work and the other 80% is converted to heat, estimate the temperature rise of the body after 45 min if none of this heat is transferred to the environment.

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 34C and the interior at 37C, and that the surface area is 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

A bicyclist consumes 9.0 L of water over the span of 3.5 hours during a race. Making the approximation that 80% of the cyclists energy goes into evaporating this water (at 20C) as sweat, how much energy in kcal did the rider use during the ride? [Hint: See page 399.]

If coal gives off when burned, how much coal is needed to heat a house requiring for the whole winter? Assume that 30% of the heat is lost up the chimney.

A 15-g lead bullet is tested by firing it into a fixed block of wood with a mass of 35 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 bullets entering speed

A 310-kg marble boulder rolls off the top of a cliff and falls a vertical height of 120 m before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in the rock

A 2.3-kg lead ball is placed in a 2.5-L insulated pail of water initially at 20.0C. If the final temperature of the waterlead combination is 32.0C, what was the initial temperature of the lead ball?

A microwave oven is used to heat 250 g of water. On its maximum setting, the oven can raise the temperature of the liquid water from 20C to 100C in (a) At what rate does the oven put energy into the liquid water? (b) If the power input from the oven to the water remains constant, determine how many grams of water will boil away if the oven is operated for 2 min (rather than just 1 min 45 s).

In a typical squash game (Fig. 1421), two people hit a soft rubber ball at a wall. Assume that the ball hits the wall at a velocity of and bounces back at a velocity of 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 )

The temperature within the Earths crust increases about 1.0 C for each 30 m of depth. The thermal conductivity of the crust is (a) Determine the heat transferred from the interior to the surface for the entire Earth in 1.0 h. (b) Compare this heat to the 1000 W m2 that reaches the Earths surface in 1.0 h from the Sun

An iron meteorite melts when it enters the Earths atmosphere. If its initial temperature was outside of Earths atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earths atmosphere

The temperature of the glass surface of a 75-W lightbulb is 75C when the room temperature is 18C. 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.

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 36.6C to 35.6C if metabolism were nearly to stop. Assume a mass of 65 kg. (See Table 141.)

A 12-g lead bullet traveling at passes through a thin wall and emerges at a speed of If the bullet absorbs 50% of the heat generated, (a) what will be the temperature rise of the bullet? (b) If the bullets initial temperature was 20C, will any of the bullet melt, and if so, how much?

A leaf of area and mass directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of (a) Estimate the energy absorbed per second by the leaf from the Sun, and then (b) estimate the rate of rise of the leafs temperature. (c) Will the temperature rise continue for hours? Why or why not? (d) Calculate the temperature the leaf would reach if it lost all its heat by radiation to the surroundings at 24C. (e) In what other ways can the heat be dissipated by the leaf?

Using the result of part (a) in Problem 65, 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 35C.

After a hot shower and dishwashing, there seems to be no hot water left in the 65-gal (245-L) water heater. This suggests that the tank has emptied and refilled with water at roughly 10C. (a) How much energy does it take to reheat the water to 45C? (b) How long would it take if the heater output is 9500 W?

A house thermostat is normally set to 22C, but at night it is turned down to 16C for 9.0 h. Estimate how much more heat would be needed (state as a percentage of daily usage) if the thermostat were not turned down at night. Assume that the outside temperature averages 0C for the 9.0 h at night and 8C for the remainder of the day, and that the heat loss from the house is proportional to the temperature difference inside and out. To obtain an estimate from the data, you must make other simplifying assumptions; state what these are