The loss of heat by radiation depends on the temperature

Hot water baseboard heating units are frequently used in homes, and a cooling coil is a major component of a refrigerator. The locations of these heating and cooling devices are different because each is designed to maximize the production of convection currents. Where should the heating unit and the cooling coil be located? (a) Heating unit near the floor of the room and cooling coil near the top of the refrigerator (b) Heating unit near the ceiling of the room and cooling coil near the bottom of the refrigerator

The transfer of heat by convection is smallest in (a) solids, (b) liquids, (c) gases.

When excessive heat is produced within the body, it must be transferred to the skin and dispersed if the temperature at the body interior is to be maintained at the normal value of 37.0 C. One possible mechanism for transfer is conduction through body fat. Suppose that heat travels through 0.030 m of fat in reaching the skin, which has a total surface area of 1.7 m2 and a temperature of 34.0 C. Find the amount of heat that reaches the skin in half an hour (1800 s).

In Figure 13.7 the temperatures at the ends of the bar are 85.0 C at the warmer end and 27.0 C at the cooler end. The bar has a length of 0.680 m. What is the temperature at a point that is 0.220 m from the cooler end of the bar?

One wall of a house consists of 0.019-m-thick plywood backed by 0.076-m-thick insulation, as Figure 13.10 shows. The temperature at the inside surface is 25.0 C, while the temperature at the outside surface is 4.0 C, both being constant. The thermal conductivities of the insulation and the plywood are, respectively, 0.030 and 0.080 J/(smC), and the area of the wall is 35 m2 . Find the heat conducted through the wall in one hour (a) with the insulation and (b) without the insulation.

In a refrigerator, heat is removed by a cold refrigerant fluid that circulates within a tubular space embedded inside a metal plate, as Figure 13.12 illustrates. A good refrigerator cools food as quickly as possible. Which arrangement works best: (a) an aluminum plate coated with ice, (b) an aluminum plate without ice, (c) a stainless steel plate coated with ice, or (d) a stainless steel plate without ice?

A poker used in a fireplace is held at one end, while the other end is in the fire. In terms of being cooler to the touch, should a poker be made from (a) a high-thermal-conductivity material, (b) a low-thermal-conductivity material, or (c) can either type be used?

Several days after a snowstorm, the outdoor temperature remains below freezing. The roof on one house is uniformly covered with snow. On a neighboring house, however, the snow on the roof has completely melted. Which house is better insulated?

Concrete walls often contain steel reinforcement bars. Does the steel (a) enhance, (b) degrade, or (c) have no effect on the insulating value of the concrete wall? (Consult Table 13.1.)

To keep your hands as warm as possible during skiing, should you wear mittens or gloves? (Mittens, except for the thumb, do not have individual finger compartments.) Assume that the mittens and gloves are the same size and are made of the same material. You should wear: (a) gloves, because the individual finger compartments mean that the gloves have a smaller thermal conductivity; (b) gloves, because the individual finger compartments mean that the gloves have a larger thermal conductivity; (c) mittens, because they have less surface area exposed to the cold air.

A water pipe is buried slightly beneath the ground. The ground is covered with a thick layer of snow, which contains a lot of small dead-air spaces within it. The air temperature suddenly drops to well below freezing. The accumulation of snow (a) has no effect on whether the water in the pipe freezes, (b) causes the water in the pipe to freeze more quickly than if the snow were not there, (c) helps prevent the water in the pipe from freezing.

Some animals have hair strands that are hollow, air-filled tubes. Others have hair strands that are solid. Which kind, if either, would be more likely to give an animal an advantage for surviving in very cold climates?

Two bars are placed between plates whose temperatures are Thot and Tcold (see the drawing). The thermal conductivity of bar 1 is six times that of bar 2 (k1  6k 2), but bar 1 has only one-third the cross-sectional area . Ignore any heat loss through the sides of the bars. What can you conclude about the amounts of heat Q1 and Q2, respectively, that bar 1 and bar 2 conduct in a given amount of time?

A piece of Styrofoam and a piece of wood are joined together to form a layered slab. The two pieces have the same thickness and cross-sectional area, but the Styrofoam has the smaller thermal conductivity. The temperature of the exposed Styrofoam surface is greater than the temperature of the exposed wood surface, both temperatures being constant. Is the temperature of the Styrofoamwood interface (a) closer to the higher temperature of the exposed Styrofoam surface, (b) closer to the lower temperature of the exposed wood surface, or (c) halfway between the two temperatures?

The supergiant star Betelgeuse has a surface temperature of about 2900 K (about one-half that of our sun) and emits a radiant power (in joules per second, or watts) of approximately 4  1030 W (about 10 000 times as great as that of our sun). Assuming that Betelgeuse is a perfect emitter (emissivity e  1) and spherical, find its radius.

An unused wood-burning stove has a constant temperature of 18 C (291 K), which is also the temperature of the room in which the stove stands. The stove has an emissivity of 0.900 and a surface area of 3.50 m2 . What is the net radiant power generated by the stove?

The wood-burning stove in Example 7 (emissivity  0.900 and surface area  3.50 m2 ) is being used to heat a room. The fire keeps the stove surface at a constant 198 C (471 K) and the room at a constant 29 C (302 K). Determine the net radiant power generated by the stove.

One day during the winter the sun has been shining all day. Toward sunset a light snow begins to fall. It collects without melting on a cement playground, but melts instantly on contact with a black asphalt road adjacent to the playground. Why the difference? (a) Being black, asphalt has a higher emissivity than cement, so the asphalt absorbs more radiant energy from the sun during the day and, consequently, warms above the freezing point. (b) Being black, asphalt has a lower emissivity than cement, so it absorbs more radiant energy from the sun during the day and, consequently, warms above the freezing point

If you were stranded in the mountains in cold weather, it would help to minimize energy losses from your body if you curled up into the tightest ball possible. Which factor in the relation Q eT 4 At (Equation 13.2) are you using to the best advantage by curling into a ball? (

Two identical cubes have the same temperature. One of them, however, is cut in two and the pieces are separated (see the drawing). The radiant energy emitted by the cube cut into two pieces is Qtwo pieces and that emitted by the uncut cube is Qcube. What is true about the radiant energy emitted in a given time?

Two objects have the same size and shape. Object A has an emissivity of 0.3, and object B has an emissivity of 0.6. Each radiates the same power. How is the Kelvin temperature TA of A related to the Kelvin temperature TB of B? (a) TA TB (b) TA 2TB (c) TA TB (d) (e) TA v 4 TA v2 TB 2 TB 1 2

Two pots are identical, except that in one case the flat bottom is aluminum and in the other it is copper. Each pot contains the same amount of boiling water and sits on a heating element that has a temperature of 155 C. In the aluminum-bottom pot, the water boils away completely in 360 s. How long does it take the water in the copper-bottom pot to boil away completely?

Is the heat needed to boil away the water in the aluminumbottom pot less than, greater than, or the same as the heat needed in the copper-bottom pot?

One of the factors in Equation 13.1 that influences the amount of heat conducted through the bottom of each pot is the temperature difference T between the upper and lower surfaces of the pots bottom. Is this temperature difference for the aluminum-bottom pot less than, greater than, or the same as that for the copper-bottom pot?

Is the time required to boil away the water completely in the copper-bottom pot less than, greater than, or the same as that required for the aluminum-bottom pot?

One half of a kilogram of liquid water at 273 K (0 C) is placed outside on a day when the temperature is 261 K (12 C). Assume that heat is lost from the water only by means of radiation and that the emissivity of the radiating surface is 0.60. How long does it take for the water to freeze into ice at 0 C when the surface area from which the radiation occurs is (a) 0.035 m2 (as it could be in a cup) and (b) 1.5 m2 (as it could be if the water were spilled out to form a thin sheet)?

In case (a) is the heat that must be removed to freeze the water less than, greater than, or the same as in case (b)?

The loss of heat by radiation depends on the temperature of the radiating object. Does the temperature of the water change as the water freezes?

The water both loses and gains heat by radiation. How, then, can heat transfer by radiation lead to freezing of the water?

Will it take longer for the water to freeze in case (a) when the area is smaller or in case (b) when the area is larger?

The heat conducted through a bar depends on which of the following? A. The coefficient of linear expansion B. The thermal conductivity C. The specific heat capacity D. The length of the bar E. The cross-sectional area of the bar (a) A, B, and D (b) A, C, and D (c) B, C, D, and E (d) B, D, and E (e) C, D, and E

Two bars are conducting heat from a region of higher temperature to a region of lower temperature. The bars have identical lengths and crosssectional areas, but are made from different materials. In the drawing they are placed in parallel between the two temperature regions in arrangement A, whereas they are placed end to end in arrangement B. In which arrangement is the heat that is conducted the greatest? (a) The heat conducted is the same in both arrangements. (b) Arrangement A (c) Arrangement B (d) It is not possible to determine which arrangement conducts more heat

The drawing shows a composite slab consisting of three materials through which heat is conducted from left to right. The materials have identical thicknesses and cross-sectional areas. Rank the materials according to their thermal conductivities, largest first. (a) k 1, k 2, k 3 (b) k 1, k 3, k 2 (c) k 2, k 1, k 3 (d) k 2, k 3, k 1 (e) k 3, k 2, k 1 6. The long single bar on the left in the drawing has a thermal conductivity of 240 J/(smC). The ends of the bar are at temperatures of 400 and 200 C, and the temperature of its midpoint is halfway between these two temperatures, or 300 C. The two bars on the right are half as long as the bar on the left, and the thermal conductivities of these bars are different (see the drawing). All of the bars have the same cross-sectional area. What can be said about the temperature at the point where the two bars on the right are joined together? (a) The temperature at the point where the two bars are joined together is 300 C. (b) The temperature at the point where the two bars are joined together is greater than 300 C. (c) The temperature at the point where the two bars are joined together is less than 300 C.

Three cubes are made from the same material. As the drawing indicates, they have different sizes and temperatures. Rank the cubes according to the radiant energy they emit per second, largest first. (a) A, B, C (b) A, C, B (c) B, A, C (d) B, C, A (e) C, B, A

An astronaut in the space shuttle has two objects that are identical in all respects, except that one is painted black and the other is painted silver. Initially, they are at the same temperature. When taken from inside the space shuttle and placed in outer space, which object, if either, cools down at a faster rate? (a) The object painted black (b) The object painted silver (c) Both objects cool down at the same rate. (d) It is not possible to determine which object cools down at the faster rate. 11. The emissivity e of object B is that of object A, although both objects are identical in size and shape. If the objects radiate the same energy per second, what is the ratio TB/TA of their Kelvin temperatures? (a) (b) (c) (d) 2 (e) 4

The amount of heat per second conducted from the blood capillaries beneath the skin to the surface is 240 J/s. The energy is transferred a distance of 2.0  103 m through a body whose surface area is 1.6 m2 . Assuming that the thermal conductivity is that of body fat, determine the temperature difference between the capillaries and the surface of the skin.

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.8 C. The temperature at the inside surface of the wall is 20.0 C. The wall is 0.10 m thick and has an area of 9.0 m2 . Assume that one kilowatt hour of electrical energy costs $0.10. How many hours are required for one dollars worth of energy to be conducted through the wall?

A persons body is covered with 1.6 m2 of wool clothing. The thickness of the wool is 2.0  103 m. The temperature at the outside surface of the wool is 11 C, and the skin temperature is 36 C. How much heat per second does the person lose due to conduction?

Two objects are maintained at constant temperatures, one hot and one cold. Two identical bars can be attached end to end, as in part a of the drawing, or one on top of the other, as in part b. When either of these arrangements is placed between the hot and the cold objects for the same amount of time, heat Q flows from left to right. Find the ratio Qa /Qb.

One end of an iron poker is placed in a fire where the temperature is 502 C, and the other end is kept at a temperature of 26 C. The poker is 1.2 m long and has a radius of 5.0  103 m. Ignoring the heat lost along the length of the poker, find the amount of heat conducted from one end of the poker to the other in 5.0 s.

The block in the drawing has dimensions L0  2L0  3L0, where L0 0.30 m. The block has a thermal conductivity of 250 J/(smC). In drawings A, B, and C, heat is conducted through the block in three different directions; in each case the temperature of the warmer surface is 35 C and that of the cooler surface is 19 C. Determine the heat that flows in 5.0 s for each case

In the conduction equation Q (kA T)t/L, the combination of terms kA/L is called the conductance. The human body has the ability to vary the conductance of the tissue beneath the skin by means of vasoconstriction and vasodilation, in which the flow of blood to the veins and capillaries is decreased and increased, respectively. The conductance can be adjusted over a range such that the tissue beneath the skin is equivalent to a thickness of 0.080 mm of Styrofoam or 3.5 mm of air. By what factor (high/low) can the body adjust the conductance?

A closed box is filled with dry ice at a temperature of 78.5 C, while the outside temperature is 21.0 C. The box is cubical, measuring 0.350 m on a side, and the thickness of the walls is 3.00  102 m. In one day, 3.10  106 J of heat is conducted through the six walls. Find the thermal conductivity of the material from which the box is made.

One end of a brass bar is maintained at 306 C, while the other end is kept at a constant, but lower, temperature. The cross-sectional area of the bar is 2.6  104 m2 . Because of insulation, there is negligible heat loss through the sides of the bar. Heat flows through the bar, however, at the rate of 3.6 J/s. What is the temperature of the bar at a point 0.15 m from the hot end?

A wall in a house contains a single window. The window consists of a single pane of glass whose area is 0.16 m2 and whose thickness is 2.0 mm. Treat the wall as a slab of the insulating material Styrofoam whose area and thickness are 18 m2 and 0.10 m, respectively. Heat is lost via conduction through the wall and the window. The temperature difference between the inside and outside is the same for the wall and the window. Of the total heat lost by the wall and the window, what is the percentage lost by the window?

A composite rod is made from stainless steel and iron and has a length of 0.50 m. The cross section of this composite rod is shown in the drawing and consists of a square within a circle. The square cross section of the steel is 1.0 cm on a side. The temperature at one end of the rod is 78 C, while it is 18 C at the other end. Assuming that no heat exits through the cylindrical outer surface, find the total amount of heat conducted through the rod in two minutes.

Review Conceptual Example 5 before attempting this problem. To illustrate the effect of ice on the aluminum cooling plate, consider the drawing shown here and the data that it contains. Ignore any limitations due to significant figures. (a) Calculate the heat per second per square meter that is conducted through the icealuminum combination. (b) Calculate the heat per second per square meter that would be conducted through the aluminum if the ice were not present. Notice how much larger the answer is in (b) as compared to (a).

A cubical piece of heat-shield tile from the space shuttle measures 0.10 m on a side and has a thermal conductivity of 0.065 J/(smC). The outer surface of the tile is heated to a temperature of 1150 C, while the inner surface is maintained at a temperature of 20.0 C. (a) How much heat flows from the outer to the inner surface of the tile in five minutes? (b) If this amount of heat were transferred to two liters (2.0 kg) of liquid water, by how many Celsius degrees would the temperature of the water rise?

Two pots are identical except that the flat bottom of one is aluminum, whereas that of the other is copper. Water in these pots is boiling away at 100.0 C at the same rate. The temperature of the heating element on which the aluminum bottom is sitting is 155.0 C. Assume that heat enters the water only through the bottoms of the pots and find the temperature of the heating element on which the copper bottom rests.

A pot of water is boiling under one atmosphere of pressure. Assume that heat enters the pot only through its bottom, which is copper and rests on a heating element. In two minutes, the mass of water boiled away is m 0.45 kg. The radius of the pot bottom is R 6.5 cm, and the thickness is L 2.0 mm. What is the temperature TE of the heating element in contact with the pot? Ir

In a house the temperature at the surface of a window is 25 C. The temperature outside at the window surface is 5.0 C. Heat is lost through the window via conduction, and the heat lost per second has a certain value. The temperature outside begins to fall, while the conditions inside the house remain the same. As a result, the heat lost per second increases. What is the temperature at the outside window surface when the heat lost per second doubles?

In an aluminum pot, 0.15 kg of water at 100 C boils away in four minutes. The bottom of the pot is 3.1 103 m thick and has a surface area of 0.015 m2 . To prevent the water from boiling too rapidly, a stainless steel plate has been placed between the pot and the heating element. The plate is 1.4 103 m thick, and its area matches that of the pot. Assuming that heat is conducted into the water only through the bottom of the pot, find the temperature at (a) the aluminumsteel interface and (b) the steel surface in contact with the heating element. *

The drawing shows a solid cylindrical rod made from a center cylinder of lead and an outer concentric jacket of copper. Except for its ends, the rod is insulated (not shown), so that the loss of heat from the curved surface is negligible. When a temperature difference is maintained between its ends, this rod conducts one-half the amount of heat that it would conduct if it were solid copper. Determine the ratio of the radii r1/r2.

Two cylindrical rods are identical, except that one has a thermal conductivity k1 and the other has a thermal conductivity k 2. As the drawing shows, they are placed between two walls that are maintained at different temperatures TW (warmer) and TC (cooler). When the rods are arranged as in part a of the drawing, a total heat Q flows from the warmer to the cooler wall, but when the rods are arranged as in part b, the total heat flow is Q. Assuming that the conductivity k 2 is twice as great as k1 and that heat flows only along the lengths of the rods, determine the ratio Q/Q.

Light bulb 1 operates with a filament temperature of 2700 K, whereas light bulb 2 has a filament temperature of 2100 K. Both filaments have the same emissivity, and both bulbs radiate the same power. Find the ratio A1/A2 of the filament areas of the bulbs.

The amount of radiant power produced by the sun is approximately 3.9 1026 W. Assuming the sun to be a perfect blackbody sphere with a radius of 6.96 108 m, find its surface temperature (in kelvins). 2

In an old house, the heating system uses radiators, which are hollow metal devices through which hot water or steam circulates. In one room the radiator has a dark color (emissivity  0.75). It has a temperature of 62 C. The new owner of the house paints the radiator a lighter color (emissivity  0.50). Assuming that it emits the same radiant power as it did before being painted, what is the temperature (in degrees Celsius) of the newly painted radiator?

A person is standing outdoors in the shade where the temperature is 28 C. (a) What is the radiant energy absorbed per second by his head when it is covered with hair? The surface area of the hair (assumed to be flat) is 160 cm2 and its emissivity is 0.85. (b) What would be the radiant energy absorbed per second by the same person if he were bald and the emissivity of his head were 0.65? T

The Kelvin temperature of an object is T1, and the object radiates a certain amount of energy per second. The Kelvin temperature of the object is then increased to T2, and the object radiates twice the energy per second that it radiated at the lower temperature. What is the ratio T2/T1?

Multiple-Concept Example 8 reviews the approach that is used in problems such as this. A person eats a dessert that contains 260 Calories. (This Calorie unit, with a capital C, is the one used by nutritionists; 1 Calorie  4186 J. See Section 12.7.) The skin temperature of this individual is 36 C and that of her environment is 21 C. The emissivity of her skin is 0.75 and its surface area is 1.3 m2 . How much time would it take for her to emit a net radiant energy from her body that is equal to the energy contained in this dessert? 2

Consult Multiple-Concept Example 8 to see the concepts that are pertinent here. A persons body is producing energy internally due to metabolic processes. If the body loses more energy than metabolic processes are generating, its temperature will drop. If the drop is severe, it can be life-threatening. Suppose that a person is unclothed and energy is being lost via radiation from a body surface area of 1.40 m2 , which has a temperature of 34 C and an emissivity of 0.700. Also suppose that metabolic processes are producing energy at a rate of 115 J/s. What is the temperature of the coldest room in which this person could stand and not experience a drop in body temperature?

A baking dish is removed from a hot oven and placed on a cooling rack. As the dish cools down to 35 C from 175 C, its net radiant power decreases to 12.0 W. What was the net radiant power of the baking dish when it was first removed from the oven? Assume that the temperature in the kitchen remains at 22 C as the dish cools down. 28

Sirius B is a white star that has a surface temperature (in kelvins) that is four times that of our sun. Sirius B radiates only 0.040 times the power radiated by the sun. Our sun has a radius of 6.96 108 m. Assuming that Sirius B has the same emissivity as the sun, find the radius of Sirius B.

Multiple-Concept Example 8 discusses the ideas on which this problem depends. Suppose the skin temperature of a naked person is 34 C when the person is standing inside a room whose temperature is 25 C. The skin area of the individual is 1.5 m2 . (a) Assuming the emissivity is 0.80, find the net loss of radiant power from the body. (b) Determine the number of food Calories of energy (1 food Calorie  4186 J) that are lost in one hour due to the net loss rate obtained in part (a). Metabolic conversion of food into energy replaces this loss.

A solar collector is placed in direct sunlight where it absorbs energy at the rate of 880 J/s for each square meter of its surface. The emissivity of the solar collector is e  0.75. What equilibrium temperature does the collector reach? Assume that the only energy loss is due to the emission of radiation.

Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical container (r 0.30 m). The container is a perfect blackbody radiator. The container is surrounded by a spherical shield whose temperature is 77 K. A vacuum exists in the space between the container and the shield. The latent heat of vaporization for helium is 2.1 104 J/kg. What mass of liquid helium boils away through a venting valve in one hour?

A solid sphere has a temperature of 773 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cubes temperature?

A solid cylinder is radiating power. It has a length that is ten times its radius. It is cut into a number of smaller cylinders, each of which has the same length. Each small cylinder has the same temperature as the original cylinder. The total radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smaller cylinders are there?

A small sphere (emissivity 0.90, radius r1) is located at the center of a spherical asbestos shell (thickness 1.0 cm, outer radius r2 ). The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 800.0 C, while the temperature of the inner surface of the shell is 600.0 C, both temperatures remaining constant. Assuming that r2/r1 10.0 and ignoring any air inside the shell, find the temperature of the outer surface of the shell. 35. s

Due to a temperature difference T, heat is conducted through an aluminum plate that is 0.035 m thick. The plate is then replaced by a stainless steel plate that has the same temperature difference and crosssectional area. How thick should the steel plate be so that the same amount of heat per second is conducted through it?

A copper pipe with an outer radius of 0.013 m runs from an outdoor wall faucet into the interior of a house. The temperature of the faucet is 4.0 C, and the temperature of the pipe, at 3.0 m from the faucet, is 25 C. In fifteen minutes, the pipe conducts a total of 270 J of heat to the outdoor faucet from the house interior. Find the inner radius of the pipe. Ignore any water inside the pipe.

How many days does it take for a perfect blackbody cube (0.0100 m on a side, 30.0 C) to radiate the same amount of energy that a onehundred-watt light bulb uses in one hour?

An object is inside a room that has a constant temperature of 293 K. Via radiation, the object emits three times as much power as it absorbs from the room. What is the temperature (in kelvins) of the object? Assume that the temperature of the object remains constant.

The concrete wall of a building is 0.10 m thick. The temperature inside the building is 20.0 C, while the temperature outside is 0.0 C. Heat is conducted through the wall. When the building is unheated, the inside temperature falls to 0.0 C, and heat conduction ceases. However, the wall does emit radiant energy when its temperature is 0.0 C. The radiant energy emitted per second per square meter at 0.0 C is the same as the heat lost per second per square meter due to conduction when the temperature inside the building is 20.0 C. What is the emissivity of the wall? * 40.

Part (a) of the drawing shows a rectangular bar whose dimensions are L0  2L0  3L0. The bar is at the same constant temperature as the room (not shown) in which it is located. The bar is then cut, lengthwise, into two identical pieces, as shown in part (b) of the drawing. The temperature of each piece is the same as that of the original bar. (a) What is the ratio of the power absorbed by the two bars in part (b) of the drawing to the single bar in part (a)? (b) Suppose that the temperature of the single bar in part (a) is 450.0 K. What would the temperature (in kelvins) of the room and the two bars in part (b) have to be so that the two bars absorb the same power as the single bar in part (a)?

Multiple-Concept Example 3 discusses an approach to problems such as this. The ends of a thin bar are maintained at different temperatures. The temperature of the cooler end is 11 C, while the temperature at a point 0.13 m from the cooler end is 23 C and the temperature of the warmer end is 48 C. Assuming that heat flows only along the length of the bar (the sides are insulated), find the length of the bar. *

A copper rod has a length of 1.5 m and a cross-sectional area of 4.0  104 m2 . One end of the rod is in contact with boiling water and the other with a mixture of ice and water. What is the mass of ice per second that melts? Assume that no heat is lost through the side surface of the rod.

Two cylindrical rods have the same mass. One is made of silver (density 10 500 kg/m3 ), and one is made of iron (density 7860 kg/m3 ). Both rods conduct the same amount of heat per second when the same temperature difference is maintained across their ends. What is the ratio (silver-to-iron) of (a) the lengths and (b) the radii of these rods? *

One end of a 0.25-m copper rod with a cross-sectional area of 1.2  104 m2 is driven into the center of a sphere of ice at 0 C (radius 0.15 m). The portion of the rod that is embedded in the ice is also at 0 C. The rod is horizontal and its other end is fastened to a wall in a room. The rod and the room are kept at a constant temperature of 24 C. The emissivity of the ice is 0.90. What is the ratio of the heat per second gained by the sphere through conduction to the net heat per second gained by the ice due to radiation? Neglect any heat gained through the sides of the rod. (a)