Chapter 14

(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 \({ }^{\circ} \mathrm{F}\) ? (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?

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.

(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 \(44.0^{\circ} \mathrm{F}\) on 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?

Inside the earth and the sun. (a) Geophysicists have estimated 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.

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

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 \((95 \mathrm{~K}) ;\) (c) the temperature at the center of the sun \(\left(1.55 \times 10^{7} \mathrm{~K}\right)\)

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.

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?

(a) How much heat is required to raise the temperature of \(0.250 \mathrm{~kg}\) 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?

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?

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 of air 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?

I A nail driven into a board increases in temperature. If \(60 \%\) of the kinetic energy delivered by a \(1.80 \mathrm{~kg}\) 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 \(8.00 \mathrm{~g}\) aluminum nail after it is struck 10 times?

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?

A \(5.00 \mathrm{~kg}\) lead sphere is dropped from the top of a \(60.0-\mathrm{m}\) -tall building. If all of its kinetic energy is converted into heat when it hits the sidewalk, how much will its temperature rise? (Ignore air resistance.)

| 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?

A \(15.0 \mathrm{~g}\) 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?

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 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 heats.)

A technician measures the specific heat 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 \(120 \mathrm{~s}\) at a constant rate of \(65.0 \mathrm{~W}\). 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 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? Explain.

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 \(100 \mathrm{~m}\) waterfall?

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 of the human body is \(3480 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right),\) and recall that normal body temperature is \(37.0^{\circ} \mathrm{C}.\)

The evaporation of sweat is an important mechanism for temperature control in some warm-blooded 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 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 \(355 \mathrm{~cm}^{3}\).

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.

What is the amount of heat entering your skin when it receives the heat released (a) by \(25.0 \mathrm{~g}\) of steam initially at \(100.0^{\circ} \mathrm{C}\) that cools to \(34.0^{\circ} \mathrm{C} ?\) (b) by \(25.0 \mathrm{~g}\) 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 bums?

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 \(70 \mathrm{~kg}\) 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 \(1.0 \mathrm{~kg} .\) )

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 \(75^{\circ} \mathrm{C} ?\)

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 \(20.0^{\circ} \mathrm{C}\). 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.

A laboratory technician drops an \(85.0 \mathrm{~g}\) 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 of the sample. (Assume no heat loss to the surroundings.)

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 \(30.0^{\circ} \mathrm{C} ?\)

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?

A slab of a thermal insulator with a cross-sectional area of \(100 \mathrm{~cm}^{2}\) is \(3.00 \mathrm{~cm}\) 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 through the slab in 1 day?

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 \(0.75 \mathrm{~mm}\). 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?

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 \(3.00 \mathrm{~min}\). Find the temperature of the lower surface of the pot, which is in contact with the stove.

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 Styrofoam 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 Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

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 \(0.0500 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})) ?\)

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 \(10.0 \mathrm{~min}\). Find the thermal conductivity \(k\) of the metal.

A box-shaped coal-burning stove has exhausted most of its fuel, and its surface temperature has fallen to \(27^{\circ} \mathrm{C}\). After more coal is added, the surface temperature eventually rises to \(327^{\circ} \mathrm{C}\). By what factor does the stove's radiation heat transfer to the surroundings increase after the coal is added?

How large is the sun? By measuring the spectrum of wavelengths 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 carth, 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.

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 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.

The emissivity of tungsten is \(0.35 .\) A tungsten sphere with a radius of \(1.50 \mathrm{~cm}\) is suspended within a large evacuated enclosure 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?

A spherical pot of hot coffee contains \(0.75 \mathrm{~L}\) 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.

An \(8.50 \mathrm{~kg}\) 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?

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 \(0.207 \times 10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1}\)

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 \(2.5 \mathrm{gal} / \mathrm{min}(9.46 \mathrm{~L} / \mathrm{min})\) 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?

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 \(2.42 \times 10^{6} \mathrm{~J} / \mathrm{kg}\)

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. A \(68 \mathrm{~kg}(150 \mathrm{lb}), 1.78 \mathrm{~m}(5 \mathrm{ft}, 10\) in.) 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 of the body is about \(3500 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K}).\)

You are making pesto for your pasta and have a cylindrical measuring cup \(10.0 \mathrm{~cm}\) high made of ordinary glass \(\left(\beta=2.7 \times 10^{-5}\left(\mathrm{C}^{\circ}\right)^{-1}\right)\) 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?

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. (a) What is the temperature of the ice-water mixture? (b) 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? (Assume no heat is lost to the surroundings.)

A \(0.4 \mathrm{~kg}\) piece of ice at \(-10^{\circ} \mathrm{C}\) is dropped from a height \(h .\) Upon impact, \(5 \%\) of its kinetic energy is converted into heat energy. If the impact transforms all of the ice into water that has a final temperature of \(0^{\circ} \mathrm{C},\) find \(h\)

(a) A typical student listening attentively to a physics lecture has a heat output of \(100 \mathrm{~W}\). 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 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 \(50 \mathrm{~min}\) in this case?

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 \(400 \mathrm{~kg}\) 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 \(2.42 \times 10^{6} \mathrm{~J} / \mathrm{kg} .\)