College Physics

Hugh D. Young

Chapter 14

Temperature and Heat - all with Video Answers

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Chapter Questions

Problem 1

$\bullet$ (a) While vacationing in Europe, you feel sick and are told that you have a temperature of $40.2^{\circ} \mathrm{C}$ . Should you be concerned? What is your temperature in $^{\circ} \mathrm{F} ?$ (b) The morning weather report in Sydney predicts a high temperature of $12^{\circ} \mathrm{C}$ .
Will you need to bring a jacket? What is this temperature in $^{\circ} \mathrm{F} ?(\mathrm{c})$ A friend has suggested that you go swimming in a pool having water of temperature 350 $\mathrm{K}$ . Is this safe to do? What would this temperature be on the Fahrenheit and Celsius scales?

Dading Chen

Dading Chen

Numerade Educator

Problem 2

Temperatures in biomedicine. (a) Normal body temperature. The average normal body temperature measured in the mouth is 310 $\mathrm{K}$ . What would Celsius and Fahrenheit thermometers read for this temperature? (b) Elevated body temperature. During very vigorous exercise, the body's temperature can go as high as $40^{\circ} \mathrm{C}$ . What would Kelvin and Fahrenheit thermometers read for this temperature? (c) Temperature difference in the body. The surface temperature of the body is normally about 7 $\mathrm{C}^{\circ}$ lower than the internal temperature. Express this temperature difference in kelvins and in Fahrenheit degrees. (d) Blood storage. Blood stored at $4.0^{\circ} \mathrm{C}$ lasts safely for about 3 weeks, whereas blood stored at $-160^{\circ} \mathrm{C}$ lasts for 5 years. Express both temperatures on the Fahrenheit and Kelvin scales. (e) Heat stroke. If the body's temperature is above $105^{\circ} \mathrm{F}$ for a prolonged period, heat stroke can result. Express this temperature on the Celsius and Kelvin scales.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 3

$\bullet$ (a) On January $22,1943,$ the temperature in Spearfish, South Dakota, rose from $-4.0^{\circ} \mathrm{F}$ to $45.0^{\circ} \mathrm{F}$ in just 2 minutes. What was the temperature change in Celsius degrees and in kelvins? (b) The temperature in Browning, Montana, was $44.0^{\circ} \mathrm{Fon}$ January $23,1916,$ and the next day it plummeted to $-56.0^{\circ} \mathrm{F} .$ What
was the temperature change in Celsius degrees and in kelvins?

Dading Chen

Numerade Educator

Problem 4

$\cdot$ Inside the earth and the sun. (a) Geophysicists have esti- mated that the temperature at the center of the earth's core is $5000^{\circ} \mathrm{C}$ (or more), while the temperature of the sun's core is about 15 million $\mathrm{K}$ . Express both of these temperatures in Fahrenheit degrees.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 5

(a) At what temperature do the Fahrenheit and Celsius scales coincide? (b) Is there any temperature at which the Kelvin and Celsius scales coincide?

Dading Chen

Numerade Educator

Problem 6

Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) the midday temperature at the surface of the moon $(400 \mathrm{K}) ;$ (b) the temperature at the tops of the
clouds in the atmosphere of Saturn $(95 \mathrm{K}) ;(\mathrm{c})$ the temperature at the center of the sun $\left(1.55 \times 10^{7} \mathrm{K}\right)$ .

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 7

$\cdot$ The Eiffel Tower in Paris is 984 ft tall and is made mostly of steel. If this is its height in winter when its temperature is $-8.00^{\circ} \mathrm{C},$ how much additional vertical distance must you cover if you decide to climb it during a summer heat wave when its temperature is $40.0^{\circ} \mathrm{C}$ ? (b) Express the coefficient of linear expansion of steel in terms of Fahrenheit degrees.

Dading Chen

Numerade Educator

Problem 8

A steel bridge is built in the summer when its temperature is $35.0^{\circ} \mathrm{C}$ . At the time of construction, its length is 80.00 $\mathrm{m}$ . What is the length of the bridge on a cold winter day when its temperature is $-12.0^{\circ} \mathrm{C} ?$

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 9

$\cdot$ A metal rod is 40.125 $\mathrm{cm}$ long at $20.0^{\circ} \mathrm{C}$ and 40.148 $\mathrm{cm}$ long at $45.0^{\circ} \mathrm{C} .$ Calculate the average coefficient of linear expansion of the rod's material for this temperature range.

Dading Chen

Numerade Educator

Problem 10

$\bullet$ (a) Steel train rails are laid in 12.0 -m-long segments placed end to end. The rails are laid on a winter day when their temperature is $-2.00^{\circ} \mathrm{C}$ . How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is $33.0^{\circ} \mathrm{C} ?$ (b) If the rails are mistakenly laid in contact with each other, what is the stress in them on a summer day when their temperature is $33.0^{\circ} \mathrm{C}$ ?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 11

An underground tank with a capacity of 1700 $\mathrm{L}\left(1.70 \mathrm{m}^{3}\right)$ is completely filled with ethanol that has an initial temperature of $19.0^{\circ} \mathrm{C} .$ After the ethanol has cooled off to the temperature of the tank and ground, which is $10.0^{\circ} \mathrm{C}$ , how much air space will there be above the ethanol in the tank? (See Table $14.2,$ and assume that the volume of the tank doesn't change appreciably.)

Dading Chen

Numerade Educator

Problem 12

$\cdot$ A copper cylinder is initially at $20.0^{\circ} \mathrm{C}$ . At what temperature will its volume be 0.150$\%$ larger than it is at $20.0^{\circ} \mathrm{C}$ ?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 13

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 $\mathrm{m}$ on a winter day at a temperature of $-15^{\circ} \mathrm{C}$ . How much
more interior space does the dome have in the summer, when the temperature is $35^{\circ} \mathrm{C}$ ?

Dading Chen

Numerade Educator

Problem 14

The outer diameter of a glass jar and the inner diameter of its iron lid are both 725 $\mathrm{mm}$ at room temperature $\left(20.0^{\circ} \mathrm{C}\right) .$ What will be the size of the mismatch between the lid and the jar if the lid is briefly held under hot water until its temperature rises to $50.0^{\circ} \mathrm{C},$ without changing the temperature of the glass?

Keshav Singh

Numerade Educator

Problem 15

A glass flask whose volume is 1000.00 $\mathrm{cm}^{3}$ at $0.0^{\circ} \mathrm{C}$ is completely filled with mercury at this temperature. When flask and mercury are warmed to $55.0^{\circ} \mathrm{C}, 8.95 \mathrm{cm}^{3}$ of mercury over- flow. Compute the coefficient of volume expansion of the glass. (Consult Table $14.2 . )$

Dading Chen

Numerade Educator

Problem 16

Ensuring a tight fit. Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by "dry ice" (solid $\mathrm{CO}_{2}$ ) before being driven. If the diameter of a hole is $4.500 \mathrm{mm},$ what should be the diameter of a rivet at $23.0^{\circ} \mathrm{C},$ if its diameter is to equal that of the hole when the rivet is cooled to $-78.0^{\circ} \mathrm{C},$ the temperature of dry ice? Assume that the expansion coefficient remains constant at the value given in Table 14.1 .

Keshav Singh

Numerade Educator

Problem 17

$\bullet$ The markings on an aluminum ruler and a brass ruler begin at the left end; when the rulers are at $0.00^{\circ} \mathrm{C}$ , they are perfectly aligned. How far apart will the 20.0 $\mathrm{cm}$ marks be on the two rulers at $100.0^{\circ} \mathrm{C}$ if the left-hand ends are kept precisely aligned?

Dading Chen

Numerade Educator

Problem 18

$\bullet$ (a) How much heat is required to raise the temperature of 0.250 kg of water from $20.0^{\circ} \mathrm{C}$ to $30.0^{\circ} \mathrm{C}$ (b) If this amount of heat is added to an equal mass of mercury that is initially at $20.0^{\circ} \mathrm{C},$ what is its final temperature?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 19

$\bullet$ One of the moving parts of an engine contains 1.60 $\mathrm{kg}$ of aluminum and 0.300 $\mathrm{kg}$ of iron and is designed to operate at $210^{\circ} \mathrm{C} .$ How much heat is required to raise its temperature from $20.0^{\circ}$ to $210^{\circ} \mathrm{C} ?$

Dading Chen

Numerade Educator

Problem 20

$\cdot$ In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200.0 $\mathrm{W}$ electric immersion heater in 0.320 $\mathrm{kg}$ of water. (a) How much heat must be added to the water to raise its temperature from $20.0^{\circ} \mathrm{C}$ to $80.0^{\circ} \mathrm{C} ?$ (b) How much time is required if all of the heater's power goes into heating the water?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 21

$\cdot$ Heat loss during breathing. In very cold weather, a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a) On a cold winter day when the temperature is $-20^{\circ} \mathrm{C},$ what is the amount of heat needed to warm to internal body temperature $\left(37^{\circ} \mathrm{C}\right)$ the 0.50 $\mathrm{L}$ of air exchanged with each breath? Assume that the specific heat capacity of 1.3 $\mathrm{g}$ is 1020 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$ and that 1.0 $\mathrm{L}$ of air has a mass of 1.3 $\mathrm{g}$ . (b) How much heat is lost per hour if the respiration rate is 20 breaths per minute?

Dading Chen

Numerade Educator

Problem 22

$\cdot$ A nail driven into a board increases in temperature. If 60$\%$ of the kinetic energy delivered by a 1.80 kg hammer with a speed of 7.80 $\mathrm{m} / \mathrm{s}$ is transformed into heat that flows into the nail and does not flow out, what is the increase in temperature of an 8.00 g aluminum nail after it is struck 10 times?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 23

$\cdot$ You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is 28.4 $\mathrm{N}$ . You carefully add $1.25 \times 10^{4} \mathrm{J}$ of heat energy to the sample and find that its temperature rises 18.0 $\mathrm{C}^{\circ} .$ What is the sample's specific heat?

Dading Chen

Numerade Educator

Problem 24

$\bullet$ A $25,000$ -kg subway train initially traveling at 15.5 $\mathrm{m} / \mathrm{s}$ slows to a stop in a station and then stays there long enough for its brakes to cool. The station's dimensions are 65.0 $\mathrm{m}$ long by 20.0 $\mathrm{m}$ wide by 12.0 $\mathrm{m}$ high. Assuming all the work done by the brakes in stopping the train is transferred as heat uniformly to all the air in the station, by how much does the air temperature in the station rise? Take the density of the air to be 1.20 $\mathrm{kg} / \mathrm{m}^{3}$ and its specific heat to be 1020 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 25

$\bullet$ You add 8950 J of heat to 3.00 mol of iron. (a) What is the temperature increase of the iron? (b) If this same amount of heat is added to 3.00 $\mathrm{kg}$ of iron, what is the iron's temperature increase? (c) Explain the difference in your results for parts (a) and (b).

Dading Chen

Numerade Educator

Problem 26

$\cdot$ From a height of $35.0 \mathrm{m},$ a 1.25 $\mathrm{kg}$ bird dives (from rest) into a small fish tank containing 50.0 $\mathrm{kg}$ of water. What is the maximum rise in temperature of the water if the bird gives it all of its mechanical energy?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 27

\bullet A 15.0 g bullet traveling horizontally at 865 $\mathrm{m} / \mathrm{s}$ passes through a tank containing 13.5 $\mathrm{kg}$ of water and emerges with a speed of 534 $\mathrm{m} / \mathrm{s}$ . What is the maximum temperature increase that the water could have as a result of this event?

Dading Chen

Numerade Educator

Problem 28

Maintaining body temperature. While running, a 70 $\mathrm{kg}$ student generates thermal energy at a rate of 1200 $\mathrm{W}$ . To maintain a constant body temperature of $37^{\circ} \mathrm{C},$ this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the heat could not flow out of the student's body, for what amount of time could a student run before irreversible body damage occurred? (Protein structures in the body are damaged irreversibly if the body temperature rises to $44^{\circ} \mathrm{C}$ or above. The specific heat capacity of a typical human body is $3480 \mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}),$ slightly less than that of water. The difference is due to the presence of protein, fat, and minerals, which have lower specific heat capacities.)

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 29

A technician measures the specific heat capacity of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat, which is then transferred to the liquid for 120 s at a constant rate of 65.0 W. The mass of the liquid is $0.780 \mathrm{kg},$ and its temperature increases from $18.55^{\circ} \mathrm{C}$ to $22.54^{\circ} \mathrm{C}$ . (a) Find the average specific heat capacity of the liquid in this temperature range. Assume that negligible heat is transferred to the container that holds the liquid and that no heat is lost to the surroundings. (b) Suppose that in this experiment heat transfer from the liquid to the container or its surroundings cannot be ignored. Is the result calculated in part (a) an overestimate or an underestimate of the average specific heat capacity? Explain.

Dading Chen

Numerade Educator

Problem 30

$\bullet$ Much of the energy of falling water in a waterfall is converted into heat. If all the mechanical energy is converted into heat that stays in the water, how much of a rise in temperature occurs in a 100 m waterfall?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 31

Consult Table 14.4 . (a) How much heat is required to melt 0.150 $\mathrm{kg}$ of lead at $327.3^{\circ} \mathrm{C}$ ? (b) How much heat would be needed to evaporate this lead at $1750^{\circ} \mathrm{C}$ (c) If the total heat added from parts (a) and (b) were put into ice at $0.00^{\circ} \mathrm{C},$ how many grams of the ice would it melt?

Dading Chen

Numerade Educator

Problem 32

A blacksmith cools a $1.20-\mathrm{kg}$ chunk of iron, initially at a temperature of $650.0^{\circ} \mathrm{C},$ by trickling $15.0^{\circ} \mathrm{C}$ water over it. All the water boils away, and the iron ends up at a temperature of $120.0^{\circ} \mathrm{C}$ . How much water did the blacksmith trickle over the iron?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 33

$\cdot$ Treatment for a stroke. One suggested treatment for a person who has suffered a stroke is to immerse the patient in an ice-water bath at $0^{\circ} \mathrm{C}$ to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached $32.0^{\circ} \mathrm{C}$ . To treat a 70.0 $\mathrm{kg}$ patient, what is the minimum
amount of ice (at $0^{\circ} \mathrm{C} )$ that you need in the bath so that its temperature remains at $0^{\circ} \mathrm{C} ?$ The specific heat capacity of the human body is $3480 \mathrm{J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right),$ and recall that normal body temperature is $37.0^{\circ} \mathrm{C}$ .

Dading Chen

Numerade Educator

Problem 34

A container holds 0.550 $\mathrm{kg}$ of ice at $-15.0^{\circ} \mathrm{C}$ . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 800.0 $\mathrm{J} / \mathrm{min}$ for 500.0 min. (a) After how many minutes does the ice start to melt? (b) After how many minutes, from the time when the heating is first started, does the temperature begin to rise above $0.00^{\circ} \mathrm{C}$ (c) Plot a curve showing the temperature as a function of the time elapsed.

Jonah Wagner

Numerade Educator

Problem 35

An asteroid with a diameter of 10 $\mathrm{km}$ and a mass of $2.60 \times 10^{15} \mathrm{kg}$ impacts the earth at a speed of 32.0 $\mathrm{km} / \mathrm{s}$ landing in the Pacific Ocean. If 1.00$\%$ of the asteroid's kinetic energy goes to boiling the ocean water (assume an initial water temperature of $10.0^{\circ} \mathrm{C} ),$ what mass of water will be boiled away by the collision? (For comparison, the mass of water contained in Lake Superior is about $2 \times 10^{15} \mathrm{kg.} )$

Dading Chen

Numerade Educator

Problem 36

$\cdot$ Evaporative cooling. The evaporation of sweat is an important mechanism for temperature control in some warmblooded animals. (a) What mass of water must evaporate from the skin of a 70.0 $\mathrm{kg}$ man to cool his body 1.00 $\mathrm{C}^{\circ}$ . The heat of vaporization of water at body temperature $\left(37^{\circ} \mathrm{C}\right)$ is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg} .$ The specific heat capacity of a typical human body is 3480 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}) .$ (b) What volume of water must the man drink to replenish the evaporated water? Compare this result with the volume of a soft-drink can, which is 355 $\mathrm{cm}^{3} .$

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 37

. An ice-cube tray contains 0.350 $\mathrm{kg}$ of water at $18.0^{\circ} \mathrm{C}$ . How much heat must be removed from the water to cool it to $0.00^{\circ} \mathrm{C}$ and freeze it? Express your answer in joules and in calories.

Dading Chen

Numerade Educator

Problem 38

$\bullet$ How much heat is required to convert 12.0 g of ice at $-10.0^{\circ} \mathrm{C}$ to steam at $100.0^{\circ} \mathrm{C}$ ? Express your answer in joules and in calories.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 39

. Steam burns vs. water burns. What is the amount of heat entering your skin when it receives the heat released (a) by 25.0 g of steam initially at $100.0^{\circ} \mathrm{C}$ that cools to $34.0^{\circ} \mathrm{C} ?$ (b) by 25.0 g of water initially at $100.0^{\circ} \mathrm{C}$ that cools to $34.0^{\circ} \mathrm{C} ?$ (c) What do these results tell you about the relative severity of steam and hot-water burns?

Dading Chen

Numerade Educator

Problem 40

$\bullet$ Bicycling on a warm day. If the air temperature is the same as the temperature of your skin (about $30^{\circ} \mathrm{C}$ ), your body cannot get rid of heat by transferring it to the air. In that case, it gets rid of the heat by evaporating water (sweat). During bicycling, a typical 70 kg person's body produces energy at a rate of about 500 $\mathrm{W}$ due to metabolism, 80$\%$ of which is converted
to heat. (a) How many kilograms of water must the person's body evaporate in an hour to get rid of this heat? The heat of vaporization of water at body temperature is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg}$ (b) The evaporated water must, of course, be replenished, or the person will dehydrate. How many 750 $\mathrm{mL}$ bottles of water must the bicyclist drink per hour to replenish the lost water? (Recall that the mass of a liter of water is 1.0 kg.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 41

Overheating. (a) By how much would the body temperature of the bicyclist in the previous problem increase in an hour if he were unable to get rid of the excess heat? (b) Is this temperature increase large enough to be serious? To find out, how high a fever would it be equivalent to, in $^{\circ} \mathrm{F} ?$ [Recall that the normal internal body temperature is $98.6^{\circ} \mathrm{F}$ and the specific heat capacity of the body is 3480 $\mathrm{J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right) .1$

Dading Chen

Numerade Educator

Problem 42

$\cdot$ You have 750 $\mathrm{g}$ of water at $10.0^{\circ} \mathrm{C}$ in a large insulated beaker. How much boiling water at $100.0^{\circ} \mathrm{C}$ must you add to this beaker so that the final temperature of the mixture will be $75^{\circ} \mathrm{C}$ ?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 43

$\bullet$ A 0.500 kg chunk of an unknown metal that has been in boiling water for several minutes is quickly dropped into an insulating Styrofoam TM beaker containing 1.00 kg of water at room temperature $\left(20.0^{\circ} \mathrm{C}\right) .$ After waiting and gently stirring for 5.00 minutes, you observe that the water's temperature has reached a constant value of $22.0^{\circ} \mathrm{C}$ (a) Assuming that the Styrofoam absorbs a negligibly small amount of heat and that no heat was lost to the surroundings, what is the specific heat capacity of the metal? (b) Which is more useful for storing
energy from heat, this metal or an equal weight of water? Explain. (c) What if the heat absorbed by the Styrofoam"" actually is not negligible. How would the specific heat capacity you calculated in part (a) be in error? Would it be too large, too small, or still correct? Explain your reasoning.

Dading Chen

Numerade Educator

Problem 44

$\bullet$ A copper pot with a mass of 0.500 $\mathrm{kg}$ contains 0.170 $\mathrm{kg}$ of water, and both are at a temperature of $20.0^{\circ} \mathrm{C} . \mathrm{A} 0.250 \mathrm{kg}$ block of iron at $85.0^{\circ} \mathrm{C}$ is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 45

$\bullet$ In a physics lab experiment, a student immersed 200 one-cent coins (each having a mass of 3.00 g) in boiling water. After they reached thermal equilibrium, she quickly fished them out and dropped them into 0.240 $\mathrm{kg}$ of water at $20.0^{\circ} \mathrm{C}$ in an insulated container of negligible mass. What was the final temperature of the coins? [One-cent coins are made of a metal alloy-mostly zinc-with a specific heat capacity of 390 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}) . ]$

Dading Chen

Numerade Educator

Problem 46

$\bullet$ A laboratory technician drops an 85.0 g solid sample of unknown material at a temperature of $100.0^{\circ} \mathrm{C}$ into a calorimeter. The calorimeter can is made of 0.150 $\mathrm{kg}$ of copper and contains 0.200 $\mathrm{kg}$ of water, and both the can and water are initially at $19.0^{\circ} \mathrm{C}$ . The final temperature of the system is measured to be $26.1^{\circ} \mathrm{C}$ . Compute the specific heat capacity of the sample. (Assume no heat loss to the surroundings.)

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 47

A 4.00 $\mathrm{kg}$ silver ingot is taken from a furnace, where its temperature is $750^{\circ} \mathrm{C},$ and placed on a very large block of ice at $0.00^{\circ} \mathrm{C}$ . Assuming that all the heat given up by the silver is used to melt the ice and that not all the ice melts, how much ice is melted?

Dading Chen

Numerade Educator

Problem 48

$\bullet$ An insulated beaker with negligible mass contains 0.250 $\mathrm{kg}$ of water at a temperature of $75.0^{\circ} \mathrm{C}$ . How many kilograms of ice at a temperature of $-20.0^{\circ} \mathrm{C}$ must be dropped in the water so that the final temperature of the system will be $30.0^{\circ} \mathrm{C}$ ?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 49

A Styrofoam" bucket of negligible mass contains 1.75 $\mathrm{kg}$ of water and 0.450 $\mathrm{kg}$ of ice. More ice, from a refrigerator at $-15.0^{\circ} \mathrm{C},$ is added to the mixture in the bucket, and when thermal equilibrium has been reached, the total mass of ice in the bucket is 0.778 $\mathrm{kg} .$ Assuming no heat exchange with the surroundings, what mass of ice was added?

Dading Chen

Numerade Educator

Problem 50

$\cdot$ A slab of a thermal insulator with a cross-sectional area of 100 $\mathrm{cm}^{2}$ is 3.00 cm thick. Its thermal conductivity is 0.075 $\mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ If the temperature difference between opposite faces is $80 \mathrm{C}^{\circ},$ how much heat flows the slab in 1 day?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 51

You are asked to design a cylindrical steel rod 50.0 $\mathrm{cm}$ long, with a circular cross section, that will conduct 150.0 $\mathrm{J} / \mathrm{s}$ from a furnace at $400.0^{\circ} \mathrm{C}$ to a container of boiling water under 1 atmosphere of pressure. What must the rod's diameter be?

Dading Chen

Numerade Educator

Problem 52

Conduction through the skin. The blood plays an important role in removing heat from the body by bringing this heat directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. We shall assume that the blood is brought to the bottom layer of skin at a temperature of $37^{\circ} \mathrm{C}$ and that the outer surface of the skin is at $30.0^{\circ} \mathrm{C}$ . Skin varies in thickness from 0.50 $\mathrm{mm}$ to a few millimeters on the palms and soles, so we shall assume an average thickness of $0.75 \mathrm{mm} . \mathrm{A} 165 \mathrm{lb}, 6 \mathrm{ft}$ person has a surface area of about 2.0 $\mathrm{m}^{2}$ and loses heat at a net rate of 75 $\mathrm{W}$ while resting. On the basis of our assumptions, what is the thermal conductivity of this person's skin?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 53

A pot with a steel bottom 8.50 $\mathrm{mm}$ thick rests on a hot stove. The area of the bottom of the pot is 0.150 $\mathrm{m}^{2} .$ The water inside the pot is at $100.0^{\circ} \mathrm{C},$ and 0.390 $\mathrm{kg}$ are evaporated every 3.00 min. Find the temperature of the lower surface of the pot,
which is in contact with the stove.

Dading Chen

Numerade Educator

Problem 54

\bullet A carpenter builds an exterior house wall with a layer of wood 3.0 $\mathrm{cm}$ thick on the outside and a layer of Styrofoam"" insulation 2.2 $\mathrm{cm}$ thick on the inside wall surface. The wood has a thermal conductivity of $0.080 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}),$ and the Sty-
rofoam TM has a thermal conductivity of 0.010 $\mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$ . The interior surface temperature is $19.0^{\circ} \mathrm{C},$ and the exterior surface temperature is $-10.0^{\circ} \mathrm{C}$ . (a) What is the temperature at the plane where the wood meets the Styrofoamm? (b) What is the rate of heat flow per square meter through this wall?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 55

$\bullet$ A picture window has dimensions of 1.40 $\mathrm{m} \times 2.50 \mathrm{m}$ and is made of glass 5.20 $\mathrm{mm}$ thick. On a winter day, the outside temperature is $-20.0^{\circ} \mathrm{C}$ , while the inside temperature is a comfortable $19.56^{\circ} \mathrm{C}$ (a) At what rate is heat being lost through the window by conduction? (b) At what rate would heat be lost through the window if you covered it with a $0.750-\mathrm{mm}$ -thick layer of paper (thermal conductivity 0.0500 $\mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) )$ ?

Dading Chen

Numerade Educator

Problem 56

$\bullet$ One end of an insulated metal rod is maintained at $100^{\circ} \mathrm{C}$ , while the other end is maintained at $0^{\circ} \mathrm{C}$ by an ice-water mixture. The rod is 60.0 $\mathrm{cm}$ long and has a cross-sectional area of 1.25 $\mathrm{cm}^{2} .$ The heat conducted by the rod melts 8.50 $\mathrm{g}$ of ice in 10.0 min. Find the thermal conductivity $k$ of the metal.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 57

$\bullet$ Mammal insulation. Animals in cold climates often depend on two layers of insulation: a layer of body fat [of thermal conductivity 0.20 $\mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) ]$ surrounded by a layer of air trapped inside fur or down. We can model a black bear (Ursus americanus) as a sphere 1.5 $\mathrm{m}$ in diameter having a layer of fat 4.0 $\mathrm{cm}$ thick. (Actually, the thickness varies with the season, but we are interested in hibernation, when the fat layer is thickest.) In studies of bear hibernation, it was found that the outer surface layer of the fur is at $2.7^{\circ} \mathrm{C}$ during hibernation, while the inner surface of the fat layer is at $31.0^{\circ} \mathrm{C}$ . (a) What is the temperature at the fat-inner fur boundary, and (b) how thick should the air layer (contained within the fur) be so that the bear loses heat at a rate of 50.0 $\mathrm{W} ?$

Dading Chen

Numerade Educator

Problem 58

A box-shaped wood stove has dimensions of 0.75 $\mathrm{m} \times$ $1.2 \mathrm{m} \times 0.40 \mathrm{m},$ an emissivity of $0.85,$ and a surface temperature of $205^{\circ} \mathrm{C}$ . Calculate its rate of radiation into the surrounding space.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 59

Radiation by the body. The amount of heat radiated by the body depends on its surface temperature and area. Typically, this temperature is about $30^{\circ} \mathrm{C}$ (although it can vary). The surface area depends on the person's height and weight. Anempirical formula for the surface area of a person's body is $A\left($ in $\mathrm{m}^{2}\right)=(0.202) M^{0.425} h^{0.725}$
where $M$ is the person's mass (in kilograms) and $h$ is his or her height (in meters).(a) What would be the surface area of a 165 lb $(75 \mathrm{kg}), 6 \mathrm{ft}(1.83 \mathrm{m})$ person? (This is a good chance to use the $y^{x}$ key of your calculator.) (b) How much heat would the person radiate away per second at a skin temperature of $30^{\circ} \mathrm{C} ?$ (At the low temperatures of room-temperature objects, nearly all the heat radiated is infrared radiation, for which the emissivity is essentially $1,$ regardless of the amount of skin pigment.) (c) How much net heat would radiation remove from the person's body if the air temperature is $20^{\circ} \mathrm{C} ?$
(d) Take measurements on your own body to test the validity of the area formula. Treat yourself as a sphere and several cylinders.

Dading Chen

Numerade Educator

Problem 60

How large is the sun? By measuring the spectrum of wave- lengths of light from our sun, we know that its surface temperature is 5800 $\mathrm{K}$ . By measuring the rate at which we receive its energy on earth, we know that it is radiating a total of $3.92 \times 10^{26} \mathrm{J} / \mathrm{s}$ and behaves nearly like an ideal blackbody. Use this information to calculate the diameter of our sun.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 61

$\bullet$ Basal metabolic rate. The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 75 $\mathrm{kg}(165 \mathrm{lb})$ person of height 1.83 $\mathrm{m}$ (6 ft) would have a body surface area of approximately 2.0 $\mathrm{m}^{2}$ . (a) What is the net amount of heat this person could radiate per second into a room at $18^{\circ} \mathrm{C}$ (about $65^{\circ} \mathrm{F}$ ) if his skin's surface temperature is $30^{\circ} \mathrm{C}$ ? (At such temperatures, nearly all the heat is infrared radiation, for which the body's emissivity is 1.0 , regardless of the amount of pigment.) (b) Normally, 80$\%$ of the energy produced by metabolism goes into heat, while the rest goes into things like pumping blood and repairing cells.
Also normally, a person at rest can get rid of this excess heat just through radiation. Use your answer to part (a) to find this person's basal metabolic rate.

Dading Chen

Numerade Educator

Problem 62

$\cdot$ The emissivity of tungsten is $0.35 .$ A tungsten sphere with a radius of 1.50 $\mathrm{cm}$ is suspended within a large evacuated enclo- sure whose walls are at 290 $\mathrm{K}$ . What power input is required to maintain the sphere at a temperature of 3000 $\mathrm{K}$ if heat conduction along the supports is negligible?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 63

$\cdot$ Size of a lightbulb filament. The operating temperature of a tungsten filament in an incandescent lightbulb is $2450 \mathrm{K},$ and its emissivity is $0.35 .$ Find the surface area of the filament of a 150 $\mathrm{W}$ bulb if all the electrical energy consumed by the bulb is radiated by the filament as light. (In reality, only a small fraction of the radiation appears as visible light.)

Dading Chen

Numerade Educator

Problem 64

A spherical pot of hot coffee contains 0.75 L of liquid (essentially water) at an initial temperature of $95^{\circ} \mathrm{C}$ . The pot has an emissivity of $0.60,$ and the surroundings are at a temperature of $20.0^{\circ} \mathrm{C}$ . Calculate the coffee's rate of heat loss by radiation.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 65

An 8.50 kg block of ice at $0^{\circ} \mathrm{C}$ is sliding on a rough horizontal icehouse floor (also at $0^{\circ} \mathrm{C} )$ at 15.0 $\mathrm{m} / \mathrm{s} .$ Assume that half of any heat generated goes into the floor and the rest goes into the ice. (a) How much ice melts after the speed of the ice has been reduced to 10.0 $\mathrm{m} / \mathrm{s} ?$ (b) What is the maximum amount of ice that will melt?

Dading Chen

Numerade Educator

Problem 66

$\bullet$ Use Fig. 14.9 to find the approximate coefficient of volume expansion of water at $2.0^{\circ} \mathrm{C}$ and at $8.0^{\circ} \mathrm{C} .$

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 67

Global warming. As the earth warms, sea level will rise due to melting of the polar ice and thermal expansion of the oceans. Estimates of the expected temperature increase vary, but 3.5 $\mathrm{C}^{\circ}$ by the end of the century has been plausibly suggested. If we assume that the temperature of the oceans also increases by this amount, how much will sea level rise by the year 2100 due only to the thermal expansion of the water? Assume, reasonably, that the ocean basins do not expand appreciably. The average depth of the ocean is $4000 \mathrm{m},$ and the coefficient of volume expansion of water at $20^{\circ} \mathrm{C}$ is $0.207 \times 10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1}$

Dading Chen

Numerade Educator

Problem 68

$\bullet$ A Foucault pendulum consists of a brass sphere with a diameter of 35.0 $\mathrm{cm}$ suspended from a steel cable 10.5 $\mathrm{m}$ long (both measurements made at $20.0^{\circ} \mathrm{C} ) .$ Due to a design oversight, the swinging sphere clears the floor by a distance of only 2.00 $\mathrm{mm}$ when the temperature is $20.0^{\circ} \mathrm{C}$ . At what temperature will the sphere begin to brush the floor?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 69

$\bullet$ On-demand water heaters. Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. Some utility companies are encouraging the use of on- demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. No water tank is involved, so no heat is wasted. A typical household shower flow rate is 2.5 gal $/ \min (9.46 \mathrm{L} / \mathrm{min}$ ) with the tap water being heated from $50^{\circ} \mathrm{F}\left(10^{\circ} \mathrm{C}\right)$ to $120^{\circ} \mathrm{F}\left(49^{\circ} \mathrm{C}\right)$ by the on-demand heater. What rate of heat input (either electrical or from gas) is required to operate such a unit, assuming that all the heat goes into the water?

Dading Chen

Numerade Educator

Problem 70

$\bullet$ Burning fat by exercise. Each pound of fat contains 3500 food calories. When the body metabolizes food, 80$\%$ of this energy goes to heat. Suppose you decide to run without stopping, an activity that produces 1290 $\mathrm{W}$ of metabolic power for a typical person. (a) For how many hours must you run to burn up 1 lb of fat? Is this a realistic exercise plan? (b) If you followed your planned exercise program, how much heat would your body produce when you burn up a pound of fat (c) If you needed to get rid of all of this excess heat by evaporating water (i.e., sweating), how many liters would you need to evaporate? The heat of vaporization of water at body temperature is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg}$

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 71

Shivering. You have no doubt noticed that you usually shiver when you get out of the shower. Shivering is the body's way of generating heat to restore its internal temperature to the normal $37^{\circ} \mathrm{C},$ and it produces approximately 290 $\mathrm{W}$ of heat power per square meter of body area. $\mathrm{A} 68 \mathrm{kg}(150 \mathrm{lb}), 1.78 \mathrm{m}$ (5 foot, 10 inch) person has approximately 1.8 $\mathrm{m}^{2}$ of surface area. How long would this person have to shiver to raise his or her body temperature by $1.0 \mathrm{C}^{\circ},$ assuming that none of this heat is lost by the body? The specific heat capacity of the body is about 3500 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$ .

Dading Chen

Numerade Educator

Problem 72

A steel ring with a $2.5000-$ in. inside diameter at $20.0^{\circ} \mathrm{C}$ is to be warmed and slipped over a brass shaft with a 2.5020 -in. outside diameter at $20.0^{\circ} \mathrm{C}$ (a) To what temperature should the ring be warmed? (b) If the ring and the shaft together are cooled by some means such as liquid air, at what temperature will the ring just slip off the shaft?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 73

$\bullet$ Pasta time! You are making pesto for your pasta and have a cylindrical measuring cup 10.0 $\mathrm{cm}$ high made of ordinary glass $\left(\beta=2.7 \times 10^{-5}\left(\mathrm{C}^{\circ}\right)^{-1}\right)$ and that is filled with olive oil $\left(\beta=6.8 \times 10^{-4}\left(\mathrm{C}^{\circ}\right)^{-1}\right)$ to a height of 1.00 $\mathrm{mm}$ below the top of the cup. Initially, the cup and oil are at a kitchen temperature of $22.0^{\circ} \mathrm{C}$ You get a phone call and forget about the olive oil, which you inadvertently leave on the hot stove. The cup and oil heat up slowly and have a common temperature. At what temperature will the olive oil start to spill out of the cup?

Dading Chen

Numerade Educator

Problem 74

A copper calorimeter can with mass 0.100 $\mathrm{kg}$ contains 0.160 $\mathrm{kg}$ of water and 0.018 $\mathrm{kg}$ of ice in thermal equilibrium at atmospheric pressure. If 0.750 $\mathrm{kg}$ of lead at a temperature of $255^{\circ} \mathrm{C}$ is dropped into the can, what is the final temperature of the system if no heat is lost to the surroundings?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 75

$\bullet$ A piece of ice at $0^{\circ} \mathrm{C}$ falls from rest into a lake whose tem- perature is $0^{\circ} \mathrm{C},$ and 1.00$\%$ of the ice melts. Compute the minimum height from which the ice has fallen.

Dading Chen

Numerade Educator

Problem 76

. Hot air in a physics lecture. (a) A typical student listening attentively to a physics lecture has a heat output of 100 W. How much heat energy does a class of 90 physics students release into a lecture hall over the course of a 50 min lecture? (b) Assume that all the heat energy in part (a) is transferred to the 3200 $\mathrm{m}^{3}$ of air in the room. The air has a specific heat capacity of 1020 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$ and a density of 1.20 $\mathrm{kg} / \mathrm{m}^{3} .$ If none of the heat escapes and the air-conditioning system is off, how much will the temperature of the air in the room rise during the 50 min lecture? (c) If the class is taking an exam, the heat output per student rises to 280 $\mathrm{W}$ . What is the temperature rise during 50 min in this case?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 77

". "The Ship of the Desert." Camels require very little water because they are able to tolerate relatively large changes in their body temperature. While humans keep their body temperatures constant to within one or two Celsius degrees, a dehydrated camel permits its body temperature to drop to $34.0^{\circ} \mathrm{C}$ overnight and rise to $40.0^{\circ} \mathrm{C}$ during the day. To see how effective this mechanism is for saving water, calculate how many liters of water a 400 -kg camel would have to drink if it attempted to keep its body temperature at a constant $34.0^{\circ} \mathrm{C}$ by evaporation of sweat during the day $(12$ hours) instead of letting it rise to $40.0^{\circ} \mathrm{C}$ . (Note: The specific heat of a camel or other mammal is about the same as that of a typical human, 3480 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}) .$ The heat of vaporization of water at $34^{\circ} \mathrm{C}$ is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg} . )$

Dading Chen

Numerade Educator

Problem 78

$\bullet$ A worker pours 1.250 $\mathrm{kg}$ of molten lead at a temperature of $327.3^{\circ} \mathrm{C}$ into 0.5000 $\mathrm{kg}$ of water at a temperature of $75.00^{\circ} \mathrm{C}$ in an insulated bucket of negligible mass. Assuming no heat loss to the surroundings, calculate the mass of lead and water remaining in the bucket when the materials have reached thermal equilibrium.

Narayan Hari

Numerade Educator

Problem 79

Time for a lake to freeze over. When the air temperature is below $0^{\circ} \mathrm{C},$ the water at the surface of a lake freezes to form a sheet of ice. If the upper surface of an ice sheet 25.0 $\mathrm{cm}$ thick is at $-10.0^{\circ} \mathrm{C}$ and the bottom surface is at $0.00^{\circ} \mathrm{C},$ calculate the time it will take to add 2.0 $\mathrm{mm}$ to the thickness of this sheet.

Dading Chen

Numerade Educator

Problem 80

Jogging in the heat of the day. You have probably seen people jogging in extremely hot weather and wondered "Why? As we shall see, there are good reasons not to do this! When jogging strenuously, an average runner of mass 68 $\mathrm{kg}$ and surface area 1.85 $\mathrm{m}^{2}$ produces energy at a rate of up to $1300 \mathrm{W}, 80 \%$ of which is converted to heat. The jogger radiates heat, but actually absorbs more from the hot air than he radiates away. At such high levels of activity, the skin's temperature can be elevated to around $33^{\circ} \mathrm{C}$ instead of the usual $30^{\circ} \mathrm{C} .$ (We shall neglect conduction, which would bring even more heat into his body.) The only way for the body to get rid of this extra heat is by evaporating water (sweating). (a) How much heat per second is produced just by the act of jogging? (b) How much net heat per second does the runner gain just from radiation if the air temperature is $40.0^{\circ} \mathrm{C}$ (104 F)? (Remember that he radiates out, but the environment radiates back in.) (c) What is the total amount of excess heat this runner's body must get rid of per second? (d) How much water must the jogger's body evaporate every minute due to his activity? The heat of vaporization of water at body temperature is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg}$ . (e) How many 750 $\mathrm{mL}$ bottles of water must he drink after (or preferably before!) jogging for a half hour? Recall that a liter of water has a mass of 1.0 $\mathrm{kg}$ .

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 81

Overheating while jogging. (a) If the jogger in the previous problem were not able to get rid of the excess heat, by how much would his body temperature increase above the normal $37^{\circ} \mathrm{C}$ in a half hour of jogging? The specific heat capacity for a human is about 3500 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$ . (b) How high a fever (in $^{\circ} \mathrm{F} )$ would this temperature increase be equivalent to? Is the increase large enough to be of concern? (Recall that normal body temperature is $98.6^{\circ} \mathrm{F} . )$

Dading Chen

Numerade Educator

Problem 82

A A thirsty nurse cools a 2.00 L bottle of a soft drink (mostly water) by pouring it into a large aluminum mug of mass 0.257 $\mathrm{kg}$ and adding 0.120 $\mathrm{kg}$ of ice initially at $-15.0^{\circ} \mathrm{C}$ . If the soft drink and mug are initially at $20.0^{\circ} \mathrm{C},$ what is the final
temperature of the system, assuming no heat losses?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 83

$\bullet$ One experimental method of measuring an insulating material's thermal conductivity is to construct a box of the material and measure the power input to an electric heater inside the box that maintains the interior at a measured temperature above the outside surface. Suppose that in such an
apparatus a power input of 180 $\mathrm{W}$ is required to keep the interior surface of the box 65.0 $\mathrm{C}^{\circ}$ (about 120 $\mathrm{F}^{\circ} )$ above the temperature of the outer surface. The total area of the box is $2.18 \mathrm{m}^{2},$ and the wall thickness is 3.90 $\mathrm{cm} .$ Find the thermal conductivity of the material in SI units.

Dading Chen

Numerade Educator

Problem 84

$\bullet$ The icecaps of Greenland and Antarctica contain about 1.75$\%$ of the total water (by mass) on the earth's surface; the oceans contain about $97.5 \%,$ and the other 0.75$\%$ is mainly groundwater. Suppose the icecaps, currently at an average temperature of about $-30^{\circ} \mathrm{C},$ somehow slid into the ocean and melted. What would be the resulting temperature decrease of the ocean? Assume that the average temperature of ocean water is currently $5.00^{\circ} \mathrm{C}$

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 85

$\bullet$ The effect of urbanization on plant growth. A study published in July 2004 indicated that temperature increases in urban areas in the eastern United States are causing plants to bud up to 7 days early compared with plants in rural areas just a few miles away, thereby disrupting biological cycles. Average temperatures in the urban areas were up to 3.5 $\mathrm{C}^{\circ}$ higher than in the rural areas. By what percent will the radiated heat per square meter increase due to such a temperature difference if the rural temperature was $0^{\circ} \mathrm{C}$ the average?

Dading Chen

Numerade Educator

Problem 86

. Basal metabolic rate. The energy output of an animal engaged in an activity is called the basal metabolic rate (BMR) and is a measure of the conversion of food energy into other forms of energy. A simple calorimeter to measure the BMR consists of an insulated box with a thermometer to measure the temperature of the air. The air has a density of 1.29 $\mathrm{kg} / \mathrm{m}^{3}$ and a specific heat capacity of 1020 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}) .$ A 50.0 $\mathrm{g}$ hamster is placed in a calorimeter that contains 0.0500 $\mathrm{m}^{3}$ of air at room temperature. (a) When the hamster is running in a wheel, the temperature of the air in the calorimeter rises 1.8 $\mathrm{C}^{\circ}$ per hour. How much heat does the running hamster generate in an
hour? (Assume that all this heat goes into the air in the calorimeter. Neglect the heat that goes into the walls of the box and into the thermometer, and assume that no heat is lost to the surroundings.) (b) Assuming that the hamster converts seed into heat with an efficiency of 10$\%$ and that hamster seed has a food energy value of 24 $\mathrm{J} / \mathrm{g}$ , how many grams of seed must the hamster eat per hour to supply the energy found in part (a)?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 87

. A thermos for liquid helium. A physicist uses a cylindrical metal can 0.250 $\mathrm{m}$ high and 0.090 $\mathrm{m}$ in diameter to store liquid helium at $4.22 \mathrm{K} ;$ at that temperature the heat of vaporization of helium is $2.09 \times 10^{4} \mathrm{J} / \mathrm{kg} .$ Completely surrounding the metal can are walls maintained at the temperature of liquid nitrogen, 77.3 $\mathrm{K}$ , with vacuum between the can and the surrounding walls. How much helium is lost per hour? The emissivity of the metal can is 0.200 . The only heat transfer between the metal can and the surrounding walls is by radiation.

Dading Chen

Numerade Educator