Solved: An aluminum saucepan with a diameter of 23 cm and

Lowest Temperature on Earth The ofcial record for the lowest temperature ever recorded on Earth was set at Vostok, Antarctica, on July 21, 1983. The temperature on that day fell to , well below the temperature of dry ice. What is this temperature in degrees Fahrenheit?

More than likely, there is a glowing incandescent lightbulb in your room at this moment. The lament of that bulb, with a temperature of about 4500 F, is almost half as hot as the surface of the Sun. What is this temperature in degrees Celsius?

Normal body temperature for humans is 98.6 F. What is the corresponding temperature in (a) degrees Celsius and (b) kelvins?

What is the temperature 1.0 K on the Fahrenheit scale?

The temperature at the surface of the Sun is about 6000 K. Convert this temperature to the (a)Celsius and (b)Fahrenheit scales.

One day you notice that the outside temperature increased by 27 F between your early morning jog and your lunch at noon. What is the corresponding change in temperature in the (a) Celsius and (b) Kelvin scales?

The gas in a constant-volume gas thermometer has a pressure of 93.5 kPa at 105 C. (a) What is the pressure of the gas at 50.0 C? (b)At what temperature does the gas have a pressure of 115 kPa?

A constant-volume gas thermometer has a pressure of 80.3 kPa at and a pressure of 86.4 kPa at 10.0 C. (a)At what temperature does the pressure of this system extrapolate to zero? (b)What are the pressures of the gas at the freezing and boiling points of water? (c) In general terms, how would your answers to parts (a) and (b) change if a different constantvolume gas thermometer is used? Explain.

Greatest Change in Temperature Aworld record for the greatest change in temperature was set in Spearsh, SD, on January 22, 1943. At 7:30 A.M.the temperature was ; two minutes later the temperature was 45 F. Find the average rate of temperature change during those two minutes in kelvins per second.

We know that corresponds to . What temperature has the same value in both the Fahrenheit and Kelvin scales?

When the bulb of a constant-volume gas thermometer is placed in a beaker of boiling water at 100 C, the pressure of the gas is 227 mmHg. When the bulb is moved to an ice-salt mixture, the pressure of the gas drops to 162 mmHg. Assuming ideal behavior, as in Figure 163, what is the Celsius temperature of the ice-salt mixture?

Bimetallic strip Ais made of copper and steel; bimetallic strip B is made of aluminum and steel. (a) Referring to Table 161, which strip bends more for a given change in temperature? (b) Which of the metals listed in Table 161 would give the greatest amount of bend when combined with steel in a bimetallic strip?

Referring to Table 161, which would be more accurate for all-season outdoor use: a tape measure made of steel or one made of aluminum?

Predict/Explain Abrass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. If the ball and the plate are always kept at the same temperature, (a) should the temperature of the system be increased or decreased in order for the ball to t through the hole?(b)Choose the bestexplanationfrom among the following: I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperature should be decreased. II. Changing the temperature wont change the fact that the ball is larger than the hole. III. Heating the brass plate makes its hole larger, and that will allow the ball to pass through.

Figure 1613 shows ve metal plates, all at the same temperature and all made from the same material. They are all placed in an oven and heated by the same amount. Rank the plates in order of increasing expansion in (a) the vertical and (b) the horizontal direction. Indicate ties where appropriate.

Referring to Problem 15, rank the metal plates in order of increasing expansion in area. Indicate ties where appropriate.

Longest Suspension Bridge The worlds longest suspension bridge is the Akashi Kaikyo Bridge in Japan. The bridge is 3910 m long and is constructed of steel. How much longer is the bridge on a warm summer day (30.0 C) than on a cold winter day

A hole in an aluminum plate has a diameter of 1.178 cm at 23.00 C. (a) What is the diameter of the hole at 199.0 C? (b)At what temperature is the diameter of the hole equal to 1.176 cm?

It is desired to slip an aluminum ring over a steel bar (Figure 1614). At 10.00 C the inside diameter of the ring is 4.000 cm and the diameter of the rod is 4.040 cm. (a)In order for the ring to slip over the bar, should the ring be heated or cooled? Explain. (b)Find the temperature of the ring at which it ts over the bar. The bar remains at 10.0 C.

At 12.25 C a brass sleeve has an inside diameter of 2.19625 cm and a steel shaft has a diameter of 2.19893 cm. It is desired to shrink-t the sleeve over the steel shaft. (a) To what temperature must the sleeve be heated in order for it to slip over the shaft? (b)Alternatively, to what temperature must the shaft be cooled before it is able to slip through the sleeve?

Early in the morning, when the temperature is 5.0 C, gasoline is pumped into a cars 51-Lsteel gas tank until it is lled to the top. Later in the day the temperature rises to 25 C. Since the volume of gasoline increases more for a given temperature increase than the volume of the steel tank, gasoline will spill out of the tank. How much gasoline spills out in this case?

Some cookware has a stainless steel interior and a copper bottom for better heat distribution. Suppose an 8.0-in. pot of this construction is heated to 610 C on the stove. If the initial temperature of the pot is 22 C, what is the difference in diameter change for the copper and the steel?

You construct two wire-frame cubes, one using copper wire, the other using aluminum wire. At 23 C the cubes enclose equal volumes of . (a) If the temperature of the cubes is increased, which cube encloses the greater volume? (b)Find the difference in volume between the cubes when their temperature is 97 C.

A copper ball with a radius of 1.5 cm is heated until its diameter has increased by 0.19 mm. Assuming an initial temperature of 22 C, nd the nal temperature of the ball.

An aluminum saucepan with a diameter of 23 cm and a height of 6.0 cm is lled to the brim with water. The initial temperature of the pan and water is 19 C. The pan is now placed on a stove burner and heated to 88 C. (a) Will water overow from the pan, or will the water level in the pan decrease? Explain. (b) Calculate the volume of water that overows or the drop in water level in the pan, whichever is appropriate.

Sleeping Metabolic Rate When people sleep, their metabolic rate is about . How many Calories does a 75-kg person metabolize while getting a good nights sleep of 8.0 hr?

An exercise machine indicates that you have worked off 2.5 Calories in a minute-and-a-half of running in place. What was your power output during this time? Give your answer in both watts and horsepower.

During a workout, a person repeatedly lifts a 12-lb barbell through a distance of 1.3 ft. How many reps of this lift are required to burn off 150 C?

Consider the apparatus that Joule used in his experiments on the mechanical equivalent of heat, shown in Figure 168. Suppose both blocks have a mass of 0.95 kg and that they fall through a distance of 0.48 m. (a)Find the expected rise in temperature of the water, given that 6200 J are needed for every 1.0 Cincrease. Give your answer in Celsius degrees. (b)Would the temperature rise in Fahrenheit degrees be greater than or less than the result in part (a)? Explain. (c) Find the rise in temperature in Fahrenheit degrees.

It was shown in Example 168 that a typical person radiates about 62 W of power at room temperature. Given this result, how long does it take for a person to radiate away the energy acquired by consuming a 230-Calorie doughnut?

Predict/Explain Two objects are made of the same material but have different temperatures. Object 1 has a mass m, and object 2 has a mass 2m. If the objects are brought into thermal contact, (a) is the temperature change of object 1 greater than, less than, or equal to the temperature change of object 2? (b) Choose the best explanation from among the following: I. The larger object gives up more heat, and therefore its temperature change is greatest. II. The heat given up by one object is taken up by the other object. Since the objects have the same heat capacity, the temperature changes are the same. III. One object loses heat of magnitude Q, the other gains heat of magnitude Q. With the same magnitude of heat involved, the smaller object has the greater temperature change.

Predict/Explain Acertain amount of heat is transferred to 2 kg of aluminum, and the same amount of heat is transferred to 1 kg of ice. Referring to Table 162, (a) is the increase in temperature of the aluminum greater than, less than, or equal to the increase in temperature of the ice? (b) Choose the best explanation from among the following: I. Twice the specic heat of aluminum is less than the specic heat of ice, and hence the aluminum has the greater temperature change. II. The aluminum has the smaller temperature change since its mass is less than that of the ice. III. The same heat will cause the same change in temperature.

Suppose 79.3 J of heat are added to a 111-g piece of aluminum at 22.5 C. What is the nal temperature of the aluminum?

How much heat is required to raise the temperature of a 55-g glass ball by 15 C?

Estimate the heat required to heat a 0.15-kg apple from 12 C to 36 C. (Assume the apple is mostly water.)

A5.0-g lead bullet is red into a fence post. The initial speed of the bullet is 250 m/s, and when it comes to rest, half its kinetic energy goes into heating the bullet. How much does the bullets temperature increase?

Silver pellets with a mass of 1.0 g and a temperature of 85 C are added to 220 g of water at 14 C. (a) How many pellets must be added to increase the equilibrium temperature of the system to 25 C? Assume no heat is exchanged with the surroundings. (b) If copper pellets are used instead, does the required number of pellets increase, decrease, or stay the same? Explain.(c)Find the number of copper pellets that are required.

A 235-g lead ball at a temperature of 84.2 C is placed in a light calorimeter containing 177 g of water at 21.5 C. Find the equilibrium temperature of the system.

If 2200 J of heat are added to a 190-g object, its temperature increases by 12 C. (a) What is the heat capacity of this object? (b) What is the objects specic heat?

An 97.6-g lead ball is dropped from rest from a height of 4.57 m. The collision between the ball and the ground is totally inelastic. Assuming all the balls kinetic energy goes into heating the ball, nd its change in temperature.

To determine the specic heat of an object, a student heats it to 100 C in boiling water. She then places the 38.0-g object in a 155-g aluminum calorimeter containing 103 g of water. The aluminum and water are initially at a temperature of 20.0 C, and are thermally insulated from their surroundings. If the nal temperature is 22.0 C, what is the specic heat of the object? Referring to Table 162, identify the material in the object.

At the local county fair, you watch as a blacksmith drops a 0.50-kg iron horseshoe into a bucket containing 25 kg of water. (a) If the initial temperature of the horseshoe is 450 C, and the initial temperature of the water is 23 C, what is the equilibrium temperature of the system? Assume no heat is exchanged with the surroundings. (b) Suppose the 0.50-kg iron horseshoe had been a 1.0-kg lead horseshoe instead. Would the equilibrium temperature in this case be greater than, less than, or the same as in part (a)? Explain.

The ceramic coffee cup in Figure 1615, with and , is initially at room temperature (24.0 C). If 225 g of 80.3 C coffee and 12.2 g of 5.00 C cream are added to the cup, what is the equilibrium temperature of the system? Assume that no heat is exchanged with the surroundings, and that the specic heat of coffee and cream are the same as the specic heat of water.

Predict/Explain In a popular lecture demonstration, a sheet of paper is wrapped around a rod that is made from wood on one half and metal on the other half. If held over a ame, the paper on one half of the rod is burned while the paper on the other half is unaffected. (a) Is the burned paper on the wooden half of the rod, or on the metal half of the rod? (b) Choose the best explanation from among the following: I. The metal will be hotter to the touch than the wood; therefore the metal side will be burnt. II. The metal conducts heat better than the wood, and hence the paper on the metal half is unaffected. III. The metal has the smaller specic heat; hence it heats up more and burns the paper on its half of the rod.

Figure 1616 shows a composite slab of three different materials with equal thickness but different thermal conductivities. The opposite sides of the composite slab are held at the xed temperatures and . Given that , rank the materials in order of the temperature difference across them, starting with the smallest. Indicate ties where appropriate.

Heat is transferred from an area where the temperature is 20 C to an area where the temperature is 0 C through a composite slab consisting of four different materials, each with the same thickness. The temperatures at the interface between each of the materials are given in Figure 1617. Rank the four materials in order of increasing thermal conductivity. Indicate ties where appropriate.

On a sunny day identical twins wear different shirts. Twin 1 wears a dark shirt; twin 2 wears a light-colored shirt. Which twin has the warmer shirt?

Two bowls of soup with identical temperatures are placed on a table. Bowl 1 has a metal spoon in it; bowl 2 does not. After a few minutes, is the temperature of the soup in bowl 1 greater than, less than, or equal to the temperature of the soup in bowl 2?

Aglass window 0.35 cm thick measures 84 cm by 36 cm. How much heat ows through this window per minute if the inside and outside temperatures differ by 15 C?

To compare the relative efciency of air and glass as insulators, repeat the previous problem with a 0.35-cm-thick layer of air instead of glass. By what factor is the rate of heat transfer reduced?

Assuming your skin temperature is 37.2 C and the temperature of your surroundings is 21.8 C, determine the length of time required for you to radiate away the energy gained by eating a 306-Calorie ice cream cone. Let the emissivity of your skin be 0.915 and its area be .

Find the heat that ows in 1.0 s through a lead brick 15 cm long if the temperature difference between the ends of the brick is 9.5 C. The cross-sectional area of the brick is .

Consider a double-paned window consisting of two panes of glass, each with a thickness of 0.500 cm and an area of , separated by a layer of air with a thickness of 1.75 cm. The temperature on one side of the window is 0.00 C; the temperature on the other side is 20.0 C. In addition, note that the thermal conductivity of glass is roughly 36 times greater than that of air. (a) Approximate the heat transfer through this window by ignoring the glass. That is, calculate the heat ow per second through 1.75 cm of air with a temperature difference of 20.0 C. (The exact result for the complete window is 19.1 J/s.) (b) Use the approximate heat ow found in part (a) to nd an approximate temperature difference across each pane of glass. (The exact result is 0.157 C.)

Two metal rods of equal lengthone aluminum, the other stainless steelare connected in parallel with a temperature of 20.0 C at one end and 118 C at the other end. Both rods have a circular cross section with a diameter of 3.50 cm. (a) Determine the length the rods must have if the combined rate of heat ow through them is to be 27.5 J per second. (b) If the length of the rods is doubled, by what factor does the rate of heat ow change?

Two cylindrical metal rodsone copper, the other leadare connected in parallel with a temperature of 21.0 C at one end and 112 C at the other end. Both rods are 0.650 m in length, and the lead rod is 2.76 cm in diameter. If the combined rate of heat ow through the two rods is 33.2 J/s, what is the diameter of the copper rod?

Two metal rodsone lead, the other copperare connected in series, as shown in Figure 1618. These are the same two rods that were connected in parallel in Example 167. Note that each rod is 0.525 m in length and has a square cross section 1.50 cm on a side. The temperature at the lead end of the rods is 2.00 C; the temperature at the copper end is 106 C. (a)The average temperature of the two ends is 54.0 C. Is the temperature in the middle, at the lead-copper interface, greater than, less than, or equal to 54.0 C? Explain. (b) Given that the heat ow through each of these rods in 1.00 s is 1.41 J, nd the temperature at the lead-copper interface.

Consider two cylindrical metal rods with equal cross sectionone lead, the other aluminumconnected in series. The temperature at the lead end of the rods is 20.0 C; the temperature at the aluminum end is 80.0 C. (a) Given that the temperature at the lead-aluminum interface is 50.0 C, and that the lead rod is 14 cm long, what condition can you use to nd the length of the aluminum rod? (b) Find the length of the aluminum rod.

Acopper rod 81 cm long is used to poke a re. The hot end of the rod is maintained at 105 C and the cool end has a constant temperature of 21 C. What is the temperature of the rod 25 cm from the cool end?

Two identical objects are placed in a room at 21 C. Object 1 has a temperature of 98 C, and object 2 has a temperature of 23 C. What is the ratio of the net power emitted by object 1 to that radiated by object 2?

Ablock has the dimensions L, 2L, and 3L. When one of the faces is maintained at the temperature and the other face is held at the temperature , the rate of heat conduction through the block is P. Answer the following questions in terms of P. (a) What is the rate of heat conduction in this block if one of the faces is held at the temperature and the other face is held at the temperature ? (b) What is the rate of heat conduction in this block if one of the faces is held at the temperature and the other face is held at the temperature

Asteel tape measure is marked in such a way that it gives accurate length measurements at a normal room temperature of 20 C. If this tape measure is used outdoors on a cold day when the temperature is 0C, are its measurements too long, too short, or accurate?

Predict/Explain Apendulum is made from an aluminum rod with a mass attached to its free end. If the pendulum is cooled, (a) does the pendulums period increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The period of a pendulum depends only on its length and the acceleration of gravity. It is independent of mass and temperature. II. Cooling makes everything move more slowly, and hence the period of the pendulum increases. III. Cooling shortens the aluminum rod, which decreases the period of the pendulum.

Acopper ring stands on edge with a metal rod placed inside it, as shown in Figure 1619. As this system is heated, will the rod ever touch the top of the ring? Answer yes or no for the case of a rod that is made of (a) copper, (b) aluminum, and (c) steel.

Referring to the copper ring in the previous problem, imagine that initially the ring is hotter than room temperature, and that an aluminum rod that is colder than room temperature ts snugly inside the ring. When this system reaches thermal equilibrium at room temperature, is the rod (A, rmly wedged in the ring; or B, can it be removed easily)?

Predict/Explain The specic heat of alcohol is about half that of water. Suppose you have 0.5 kg of alcohol at the temperature 20 C in one container, and 0.5 kg of water at the temperature 30 C in a second container. When these uids are poured into the same container and allowed to come to thermal equilibrium, (a) is the nal temperature greater than, less than, or equal to 25 C? (b) Choose the best explanation from among the following: I. The low specic heat of alcohol pulls in more heat, giving a nal temperature that is less than 25. II. More heat is required to change the temperature of water than to change the temperature of alcohol. Therefore, the nal temperature will be greater than 25. III. Equal masses are mixed together; therefore, the nal temperature will be 25, the average of the two initial temperatures.

Hot tea is poured from the same pot into two identical mugs. Mug 1 is lled to the brim; mug 2 is lled only halfway. Is the rate of cooling of mug 1 (A, greater than; B, less than; or C, equal to) the rate of cooling of mug 2?

Making Steel Sheets In the continuous-caster process, steel sheets 25.4 cm thick, 2.03 m wide, and 10.0 m long are produced at a temperature of 872 C. What are the dimensions of a steel sheet once it has cooled to 20.0 C?

The Coldest Place in the Universe The Boomerang nebula holds the distinction of having the lowest recorded temperature in the universe, a frigid . What is this temperature in kelvins?

When technicians work on a computer, they often ground themselves to prevent generating a spark. If an electrostatic discharge does occur, it can cause temperatures as high as 1500 C in a localized area of a circuit. Temperatures this high can melt aluminum, copper, and silicon. What is this temperature in (a) degrees Fahrenheit and (b) kelvins?

Two objects at the same initial temperature absorb equal amounts of heat. If the nal temperature of the objects is different, it may be because they differ in which of the following properties: mass; coefcient of expansion; thermal conductivity; specic heat?

The Hottest Living Things From the surreal realm of deep-sea hydrothermal vents 200 miles offshore from Puget Sound, comes a newly discovered hyperthermophilicor extreme heat-lovingmicrobe that holds the record for the hottest existence known to science. This microbe is tentatively known as Strain 121 for the temperature at which it thrives: 121 C. (At sea level, water at this temperature would boil vigorously, but the extreme pressures at the ocean oor prevent boiling from occurring.) What is this temperature in degrees Fahrenheit?

The heat Q will warm 1 g of material Aby 1 C, the heat 2Q will warm 3 g of material B by 3 C, the heat 3Q will warm 3 g of material C by 1 C, and the heat 4Q will warm 4 g of material D by 2 C. Rank these materials in order of increasing specic heat. Indicate ties where appropriate.

In many biological systems it is of more interest to know how much heat is required to raise the temperature of a given volume of material rather than a given mass of material. Calculate the heat needed to raise the temperature of one cubic meter of (a) air and (b) water by one degree Celsius. Compare with the corresponding specic heats (for a given mass) listed in Table 162.

Brain Power As you read this problem, your brain is consuming about 22 W of power. (a) How many steps with a height of 21 cm must you climb to expend a mechanical energy equivalent to one hour of brain operation? (b)Atypical human brain, which is 77% water, has a mass of 1.4 kg. Assuming that the 22 W of brain power is converted to heat, what temperature rise would you estimate for the brain in one hour of operation? Ignore the signicant heat transfer that occurs between a human head and its surroundings, as well as the 23% of the brain that is not water.

The Cricket ThermometerThe rate of chirping of the snowy tree cricket (Oecanthus fultoni Walker) varies with temperature in a predictable way. A linear relationship provides a good match to the chirp rate, but an even more accurate relationship is the following: In this expression, N is the number of chirps in 13.0 s and T is the temperature in kelvins. If a cricket is observed to chirp 185 times in 60.0 s, what is the temperature in degrees Fahrenheit?

If heat is transferred to 150 g of water at a constant rate for 2.5 min, its temperature increases by 13 C. When heat is transferred at the same rate for the same amount of time to a 150-g object of unknown material, its temperature increases by 61 C. (a)From what material is the object made? (b)What is the heating rate?

Apendulum consists of a large weight suspended by a steel wire that is 0.9500 m long. (a)If the temperature increases, does the period of the pendulum increase, decrease, or stay the same? Explain. (b) Calculate the change in length of the pendulum if the temperature increase is 150.0 C. (c) Calculate the period of the pendulum before and after the temperature increase. (Assume that the coefcient of linear expansion for the wire is , and that at the location of the pendulum.)

Once the aluminum ring in Problem 19 is slipped over the bar, the ring and bar are allowed to equilibrate at a temperature of 22 C. The ring is now stuck on the bar. (a) If the temperatures of both the ring and the bar are changed together, should the system be heated or cooled to remove the ring? (b) Find the temperature at which the ring can be removed.

Asteel plate has a circular hole with a diameter of 1.000 cm. In order to drop a Pyrex glass marble 1.003 cm in diameter through the hole in the plate, how much must the temperature of the system be raised? (Assume the plate and the marble are always at the same temperature.)

A226-kg rock sits in full sunlight on the edge of a cliff 5.25 m high. The temperature of the rock is 30.2 C. If the rock falls from the cliff into a pool containing of water at 15.5 C, what is the nal temperature of the rockwater system? Assume that the specic heat of the rock is .

Water going over Iguau Falls on the border of Argentina and Brazil drops through a height of about 72 m. Suppose that all the gravitational potential energy of the water goes into raising its temperature. Find the increase in water temperature at the bottom of the falls as compared with the top.

A 0.22-kg steel pot on a stove contains 2.1 L of water at 22 C. When the burner is turned on, the water begins to boil after 8.5 minutes. (a)At what rate is heat being transferred from the burner to the pot of water? (b)At this rate of heating, would it take more time or less time for the water to start to boil if the pot were made of gold rather than steel?

Suppose you could convert the 525 Calories in the cheeseburger you ate for lunch into mechanical energy with 100% efciency. (a)How high could you throw a 0.145-kg baseball with the energy contained in the cheeseburger? (b) How fast would the ball be moving at the moment of release?

You turn a crank on a device similar to that shown in Figure 168 and produce a power of 0.18 hp. If the paddles are immersed in 0.65 kg of water, for what length of time must you turn the crank to increase the temperature of the water by 5.0 C?

Heat Transport in the Human Body The core temperature of the human body is 37.0 C, and the skin, with a surface area of , has a temperature of 34.0 C. (a) Find the rate of heat transfer out of the body under the following assumptions: (i) The average thickness of tissue between the core and the skin is 1.20 cm; (ii) the thermal conductivity of the tissue is that of water. (b)Without repeating the calculation of part (a), what rate of heat transfer would you expect if the skin temperature were to fall to 31.0 C? Explain.

The Solar Constant The surface of the Sun has a temperature of 5500 C. (a)Treating the Sun as a perfect blackbody, with an emissivity of 1.0, nd the power that it radiates into space. The radius of the Sun is , and the temperature of space can be taken to be 3.0 K. (b)Thesolar constantis the number of watts of sunlight power falling on a square meter of the Earths upper atmosphere. Use your result from part (a) to calculate the solar constant, given that the distance from the Sun to the Earth is .

Bars of two different metals are bolted together, as shown in Figure 1620. Show that the distance D does not change with temperature if the lengths of the two bars have the following ratio: .

Agrandfather clock has a simple brass pendulum of length L. One night, the temperature in the house is 25.0 C and the period of the pendulum is 1.00 s. The clock keeps correct time at this temperature. If the temperature in the house quickly drops to 17.1 C just after 10 P.M., and stays at that value, what is the actual time when the clock indicates that it is 10 A.M. the next morning?

Asheet of aluminum has a circular hole with a diameter of 10.0 cm. A 9.99-cm-long steel rod is placed inside the hole, along a diameter of the circle, as shown in Figure 1621. It is desired to change the temperature of this system until the steel rod just touches both sides of the circle. (a) Should the temperature of the system be increased or decreased? Explain. (b) By how much should the temperature be changed?

A layer of ice has formed on a small pond. The air just above the ice is at , the water-ice interface is at 0 C, and the water at the bottom of the pond is at 4.0 C. If the total depth from the top of the ice to the bottom of the pond is 1.4 m, how thick is the layer of ice? Note: The thermal conductivity of ice is and that of water is .

A Double-Paned Window An energy-efcient doublepaned window consists of two panes of glass, each with thickness and thermal conductivity , separated by a layer of air of thickness and thermal conductivity . Show that the equilibrium rate of heat ow through this window per unit area, A, is In this expression, and are the temperatures on either side of the window.

How hot is the Blackbird when it lands, assuming it is 8.0 inches longer than at takeoff, its coefcient of linear expansion is , and its temperature at takeoff is 23 C? A. 280 C B. 310 C C. 560 C D. 3400 C

Predict If the SR-71 were painted white instead of black, would its in-ight temperature be greater than, less than, or equal to its temperature with black paint?

Explain Choose the best explanation for the previous problem from among the following: A. Heating by air resistance is the same for any color of paint; therefore, the plane will have the same temperature regardless of color. B. Black is a more efcient radiator of heat than white. Therefore, the black paint radiates more heat, and allows the airplane to stay cooler. C. Black objects are generally hotter than white ones, all other things being equal. Therefore, the plane would be cooler with white paint.

How long is the Blackbird when it is 120 C? A. 107 ft 7.8 in. B. 107 ft 8.2 in. C. 108 ft 0.8 in. D. 108 ft 1.4 in.

Referring to Example 165Suppose the mass of the block is to be increased enough to make the nal temperature of the system equal to 22.5 C. What is the required mass? Everything else in Example 165 remains the same.

Referring to Example 165 Suppose the initial temperature of the block is to be increased enough to make the nal temperature of the system equal to 22.5 C. What is the required initial temperature? Everything else remains the same as in Example 165.

Suppose the lead rod is replaced with a second copper rod. (a) Will the heat that ows in 1.00 s increase, decrease, or stay the same? Explain. (b) Find the heat that ows in 1.00 s with two copper rods. Everything else remains the same as in Example 167.

Suppose the temperature of the hot plate is to be changed to give a total heat ow of 25.2 J in 1.00 s. (a) Should the new temperature of the hot plate be greater than or less than 106 C? Explain. (b) Find the required temperature of the hot plate. Everything else is the same as in Example 167.