College Physics With an Integrated Approach to Forces and Kinematics

Alan Giambattista, Betty McCarthy Richardson , Robert C. Richardson

Chapter 14

Heat - all with Video Answers

Educators

Chapter Questions

Problem 1

A mass of $1.4 \mathrm{~kg}$ of water at $22^{\circ} \mathrm{C}$ is poured from a height of $2.5 \mathrm{~m}$ into a vessel containing $5.0 \mathrm{~kg}$ of water at $22^{\circ} \mathrm{C}$. (a) How much does the internal energy of the $6.4 \mathrm{~kg}$ of water increase? (b) Is it likely that the water temperature increases? Explain.

Surjit Tewari

Surjit Tewari

Numerade Educator

Problem 2

The water passing over Victoria Falls, located along the Zambezi River on the border of Zimbabwe and Zambia, drops about $105 \mathrm{~m}$. How much internal energy is produced per kilogram as a result of the fall?

Surjit Tewari

Numerade Educator

Problem 3

How much internal energy is generated when a 20.0-g lead bullet, traveling at $7.00 \times 10^{2} \mathrm{~m} / \mathrm{s}$, comes to a stop as it strikes a metal plate?

Surjit Tewari

Numerade Educator

Problem 4

Nolan threw a baseball, of mass $147.5 \mathrm{~g}$, at a speed of $162 \mathrm{~km} / \mathrm{h}$ to a catcher. How much internal energy was generated when the ball struck the catcher's mitt?

Surjit Tewari

Numerade Educator

Problem 5

A child of mass $15 \mathrm{~kg}$ climbs to the top of a slide that is $1.7 \mathrm{~m}$ above a horizontal run that extends for $0.50 \mathrm{~m}$ at the base of the slide. After sliding down, the child comes to rest just before reaching the very end of the horizontal portion of the slide. (a) How much internal energy was generated during this process?
(b) Where did the generated energy go? (To the slide, to the child, to the air, or to all three?)

Surjit Tewari

Numerade Educator

Problem 6

A 64 -kg sky diver jumped out of an airplane at an altitude of $0.90 \mathrm{~km}$. She opened her parachute after a while and eventually landed on the ground with a speed of $5.8 \mathrm{~m} / \mathrm{s}$. How much energy was dissipated by air resistance during the jump?

Surjit Tewari

Numerade Educator

Problem 7

During basketball practice Shane made a jump shot, releasing a $0.60-\mathrm{kg}$ basketball from his hands at a height of $2.0 \mathrm{~m}$ above the floor with a speed of $7.6 \mathrm{~m} / \mathrm{s}$. The ball swooshes through the net at a height of $3.0 \mathrm{~m}$ above the floor and with a speed of $4.5 \mathrm{~m} / \mathrm{s}$.
How much energy was dissipated by air drag from the time the ball left Shane's hands until it went through the net?

Surjit Tewari

Numerade Educator

Problem 8

An experiment is conducted with a basic Joule apparatus, where a mass is allowed to descend by $1.25 \mathrm{~m}$ and rotate paddles within an insulated container of water. There are several different sizes of descending masses to choose among. If the investigator wishes to deliver $1.00 \mathrm{~kJ}$ to the water within the insulated container after $30.0$ descents, what descending mass value should be used?

Surjit Tewari

Numerade Educator

Problem 9

Convert $1.00 \mathrm{~kJ}$ to kilowatt-hours $(\mathrm{kWh})$.

Surjit Tewari

Numerade Educator

Problem 10

What is the heat capacity of $20.0 \mathrm{~kg}$ of silver?

Surjit Tewari

Numerade Educator

Problem 11

What is the heat capacity of a gold ring that has a mass of $5.00 \mathrm{~g}$ ?

Surjit Tewari

Numerade Educator

Problem 12

If $125.6 \mathrm{~kJ}$ of heat are supplied to $5.00 \times 10^{2} \mathrm{~g}$ of water at $22^{\circ} \mathrm{C}$, what is the final temperature of the water?

Surjit Tewari

Numerade Educator

Problem 13

It is a damp, chilly day in a New England seacoast town suffering from a power failure. To warm up the cold, clammy sheets, Jen decides to fill hot water bottles to tuck between the sheets at the foot of the beds. If she wishes to heat $2.0 \mathrm{~L}$ of water on the wood stove from $20.0^{\circ} \mathrm{C}$ to $80.0^{\circ} \mathrm{C}$, how much heat must flow into the water?

Surjit Tewari

Numerade Educator

Problem 14

An $83-\mathrm{kg}$ man eats a banana of energy content $1.00 \times 10^{2}$ kcal. If all of the energy from the banana is converted into kinetic energy of the man, how fast is he moving, assuming he starts from rest?

Surjit Tewari

Numerade Educator

Problem 15

A high jumper of mass $60.0 \mathrm{~kg}$ consumes a meal of $3.00 \times 10^{3}$ kcal prior to a jump. If $3.3 \%$ of the energy from the food could be converted to gravitational potential energy in a single jump, how high could the athlete jump?

Surjit Tewari

Numerade Educator

Problem 16

What is the heat capacity of a $30.0$ -kg block of ice?

Surjit Tewari

Numerade Educator

Problem 17

What is the heat capacity of $1.00 \mathrm{~m}^{3}$ of (a) aluminum?
(b) iron? See Table $9.1$ for density values.

Surjit Tewari

Numerade Educator

Problem 18

What is the heat capacity of a system consisting of (a) a $0.450$ -kg brass cup filled with $0.050$ kg of water? (b) $7.5 \mathrm{~kg}$ of water in a $0.75$ -kg aluminum bucket?

Penny Riley

Numerade Educator

Problem 19

A $0.400-\mathrm{kg}$ aluminum teakettle contains $2.00 \mathrm{~kg}$ of water at $15.0{ }^{\circ} \mathrm{C}$. How much heat is required to raise the temperature of the water (and kettle) to $100.0^{\circ} \mathrm{C}$ ?

Surjit Tewari

Numerade Educator

Problem 20

How much heat is required to raise the body temperature of a $50.0-\mathrm{kg}$ woman from $37.0^{\circ} \mathrm{C}$ to $38.4^{\circ} \mathrm{C}$ ?

Surjit Tewari

Numerade Educator

Problem 21

It takes $880 \mathrm{~J}$ to raise the temperature of $350 \mathrm{~g}$ of lead from 0 to $20.0^{\circ} \mathrm{C}$. What is the specific heat of lead?

Surjit Tewari

Numerade Educator

Problem 22

A mass of $1.00 \mathrm{~kg}$ of water at temperature $T$ is poured from a height of $0.100 \mathrm{~km}$ into a vessel containing water of the same temperature $T$, and a temperature change of $0.100{ }^{\circ} \mathrm{C}$ is measured. What mass of water was in the vessel? Ignore heat flow into the vessel, the thermometer, etc.

Surjit Tewari

Numerade Educator

Problem 23

A thermometer containing $0.10 \mathrm{~g}$ of mercury is cooled from $15.0^{\circ} \mathrm{C}$ to $8.5^{\circ} \mathrm{C}$. How much energy left the mercury in this process?

Surjit Tewari

Numerade Educator

Problem 24

A heating coil inside an electric kettle delivers $2.1 \mathrm{~kW}$ of electric power to the water in the kettle. How long will it take to raise the temperature of $0.50 \mathrm{~kg}$ of water from $20.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C} ?($ Wig tutorial: heating)

Surjit Tewari

Numerade Educator

Problem 25

A cylinder contains $250 \mathrm{~L}$ of hydrogen gas $\left(\mathrm{H}_{2}\right)$ at $0.0^{\circ} \mathrm{C}$ and a pressure of $10.0 \mathrm{~atm}$. How much energy is required to raise the temperature of this gas to $25.0^{\circ} \mathrm{C}$ ?

Vipender Yadav

Numerade Educator

Problem 26

A container of nitrogen gas $\left(\mathrm{N}_{2}\right)$ at $23^{\circ} \mathrm{C}$ contains $425 \mathrm{~L}$ at a pressure of $3.5 \mathrm{~atm}$. If $26.6 \mathrm{~kJ}$ of heat are added to the container, what will be the new temperature of the gas?

Vipender Yadav

Numerade Educator

Problem 27

Imagine that 501 people are present in a movie theater of volume $8.00 \times 10^{3} \mathrm{~m}^{3}$ that is sealed shut so no air can escape. Each person gives off heat at an average rate of $110 \mathrm{~W}$. By how much will the temperature of the air have increased during a $2.0$ -h movie? The initial pressure is $1.01 \times 10^{5} \mathrm{~Pa}$ and the initial temperature is $20.0^{\circ} \mathrm{C}$. Assume that all the heat output of the people goes into heating the air (a diatomic gas).

Surjit Tewari

Numerade Educator

Problem 28

A chamber with a fixed volume of $1.0 \mathrm{~m}^{3}$ contains a monatomic gas at $3.00 \times 10^{2} \mathrm{~K}$. The chamber is heated to a temperature of $4.00 \times 10^{2} \mathrm{~K}$. This operation requires $10.0 \mathrm{~J}$ of heat. (Assume all the energy is transferred to the gas.) How many gas molecules are in the chamber?

Vipender Yadav

Numerade Educator

Problem 29

As heat flows into a substance, its temperature changes according to the graph in the diagram. For what sections of the graph is the substance undergoing a phase change? For the sections you identified, what kind of phase change is occurring? ( Wh tutorial: temperature graph)

Vipender Yadav

Numerade Educator

Problem 30

Given these data, compute the heat of vaporization of water. The specific heat capacity of water is $4.186 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K})$

Matthew Baker

Numerade Educator

Problem 31

Given these data, compute the heat of fusion of water. The specific heat capacity of water is $4.186 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K})$.

Matthew Baker

Numerade Educator

Problem 32

In a physics lab, a student accidentally drops a $25.0-\mathrm{g}$ brass washer into an open dewar of liquid nitrogen at $77.2 \mathrm{~K}$. How much liquid nitrogen boils away as the washer cools from $293 \mathrm{~K}$ to $77.2 \mathrm{~K}$ ? The latent heat of vaporization for nitrogen is $199.1 \mathrm{~kJ} / \mathrm{kg}$.

Surjit Tewari

Numerade Educator

Problem 33

What mass of water at $25.0^{\circ} \mathrm{C}$ added to a Styrofoam cup containing two $50.0$ -g ice cubes from a freezer at $-15.0^{\circ} \mathrm{C}$ will result in a final temperature of $5.0^{\circ} \mathrm{C}$ for the drink?

Surjit Tewari

Numerade Educator

Problem 34

How much heat is required to change $1.0 \mathrm{~kg}$ of ice. originally at $-20.0{ }^{\circ} \mathrm{C}$, into steam at $110.0^{\circ} \mathrm{C}$ ? Assume $1.0$ atm of pressure.

Surjit Tewari

Numerade Educator

Problem 35

Ice at $0.0^{\circ} \mathrm{C}$ is mixed with $5.00 \times 10^{2} \mathrm{~mL}$ of water at $25.0^{\circ} \mathrm{C}$. How much ice must melt to lower the water
temperature to $0.0{ }^{\circ} \mathrm{C}$ ?

Surjit Tewari

Numerade Educator

Problem 36

Tina is going to make iced tea by first brewing hot tea, then adding ice until the tea cools. How much ice, at a temperature of $-10.0^{\circ} \mathrm{C}$, should be added to a $2.00 \times 10^{-4} \mathrm{~m}^{3}$ glass of tea at $95.0^{\circ} \mathrm{C}$ to $\mathrm{cool}$ the tea
to $10.0{ }^{\circ} \mathrm{C}$ ? Ignore the temperature change of the glass. (We tutorial: iced tea)

Surjit Tewari

Numerade Educator

Problem 37

Repeat Problem 36 without neglecting the temperature change of the glass. The glass has a mass of $350 \mathrm{~g}$ and the specific heat of the glass is $0.837 \mathrm{~kJ} /(\mathrm{kg} \cdot \mathrm{K}) .$ By what percentage does the answer change from the answer for Problem $36 ?$

Surjit Tewari

Numerade Educator

Problem 38

The graph shows the change in temperature as heat is supplied to a certain mass of ice initially at $-80.0^{\circ} \mathrm{C}$. What is the mass of the ice?

Surjit Tewari

Numerade Educator

Problem 39

How many grams of aluminum at $80.0{ }^{\circ} \mathrm{C}$ would have to be dropped into a hole in a block of ice at $0.0{ }^{\circ} \mathrm{C}$ to melt $10.0 \mathrm{~g}$ of ice?

Surjit Tewari

Numerade Educator

Problem 40

Is it possible to heat the aluminum of Problem 39 to a high enough temperature so that it melts an equal mass of ice? If so, what temperature must the aluminum have?

Surjit Tewari

Numerade Educator

Problem 41

If a leaf is to maintain a temperature of $40^{\circ} \mathrm{C}$ (reasonable for a leaf), it must lose $250 \mathrm{~W} / \mathrm{m}^{2}$ by transpiration (evaporative heat loss). Note that the leaf also loses heat by radiation, but we will neglect this. How much water is lost after 1 h through transpiration only? The area of the leaf is $0.005 \mathrm{~m}^{2}$

Surjit Tewari

Numerade Educator

Problem 42

A birch tree loses $618 \mathrm{mg}$ of water per minute through transpiration (evaporation of water through stomatal pores). What is the rate of heat lost through transpiration?

Surjit Tewari

Numerade Educator

Problem 43

You are given $250 \mathrm{~g}$ of coffee (same specific heat as water) at $80.0^{\circ} \mathrm{C}$ (too hot to drink). In order to cool this to $60.0^{\circ} \mathrm{C}$, how much ice (at $0.0^{\circ} \mathrm{C}$ ) must be added? Ignore heat content of the cup and heat exchanges with the surroundings.

Surjit Tewari

Numerade Educator

Problem 44

A phase diagram is shown. Starting at point $A$, follow the dashed line to point $E$ and consider what happens to the substance represented by this diagram as its pressure and temperature are changed.
(a) Explain what happens for each line segment, $A B, B C, C D$, and $D E$. (b) What is the significance of point $a$ and of point $b$ ?

Narayan Hari

Numerade Educator

Problem 45

Compute the heat of fusion of a substance from these data: $31.15 \mathrm{~kJ}$ will change $0.500 \mathrm{~kg}$ of the solid at $21^{\circ} \mathrm{C}$ to liquid at $327^{\circ} \mathrm{C}$, the melting point. The specific heat of the solid is $0.129 \mathrm{~kJ} /(\mathrm{kg} \cdot \mathrm{K})$

Surjit Tewari

Numerade Educator

Problem 46

A dog loses a lot of heat through panting. The air rushing over the upper respiratory tract causes evaporation and thus heat loss. A dog typically pants at a rate of 670 pants per minute. As a rough calculation, assume that one pant causes $0.010 \mathrm{~g}$ of water to be evaporated from the respiratory tract. What is the rate of heat loss for the dog through panting?

Surjit Tewari

Numerade Educator

Problem 47

(a) What thickness of cork would have the same $\mathrm{R}$ -factor as a $1.0-\mathrm{cm}$ thick stagnant air pocket? (b) What thickness of tin would be required for the same R-factor?

Surjit Tewari

Numerade Educator

Problem 48

A metal rod with a diameter of $2.30 \mathrm{~cm}$ and length of $1.10 \mathrm{~m}$ has one end immersed in ice at $32.0^{\circ} \mathrm{F}$ and the other end in boiling water at $212^{\circ} \mathrm{F}$. If the ice melts at a rate of $1.32 \mathrm{~g}$ every $175 \mathrm{~s}$, what is the thermal conductivity of this metal? Identify the metal. Assume there is no heat lost to the surrounding air.

Narayan Hari

Numerade Educator

Problem 49

Given a slab of material with area $1.0 \mathrm{~m}^{2}$ and thickness $2.0 \times 10^{-2} \mathrm{~m},(\mathrm{a})$ what is the thermal resistance if the material is asbestos? (b) What is the thermal resistance if the material is iron? (c) What is the thermal resistance if the material is copper?

Surjit Tewari

Numerade Educator

Problem 50

A copper rod of length $0.50 \mathrm{~m}$ and cross-sectional area $6.0 \times 10^{-2} \mathrm{~cm}^{2}$ is connected to an iron rod with the same cross section and length $0.25 \mathrm{~m}$. One end of the copper is immersed in boiling water and the other end is at the junction with the iron. If the far end of the iron rod is in an ice bath at $0^{\circ} \mathrm{C}$, find the rate of heat transfer passing from the boiling water to the ice bath. Assume there is no heat loss to the surrounding air. (Tutorial: composite rod)

Keshav Singh

Numerade Educator

Problem 51

For a temperature difference $\Delta T=20.0^{\circ} \mathrm{C}$, one slab of material conducts $10.0 \mathrm{~W} / \mathrm{m}^{2}$; another of the same shape conducts $20.0 \mathrm{~W} / \mathrm{m}^{2} .$ What is the rate of heat flow per $\mathrm{m}^{2}$ of surface area when the slabs are placed side by side with $\Delta T_{\text {tot }}=20.0^{\circ} \mathrm{C}$ ?

Surjit Tewari

Numerade Educator

Problem 52

A wall consists of a layer of wood and a layer of cork insulation of the same thickness. The temperature inside is $20.0^{\circ} \mathrm{C}$ and the temperature outside is $0.0^{\circ} \mathrm{C}$. (a) What is the temperature at the interface between the wood and cork if the cork is on the inside and the wood on the outside? (b) What is the temperature at the interface if the wood is inside and the cork is outside? (c) Does it matter whether the cork is placed on the inside or the outside of the wooden wall? Explain.

Surjit Tewari

Numerade Educator

Problem 53

The thermal conductivity of the fur (including the skin) of a male Husky dog is $0.026 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$. The dog's heat output is measured to be $51 \mathrm{~W}$, its internal temperature is $38^{\circ} \mathrm{C}$, its surface area is $1.31 \mathrm{~m}^{2}$, and the thickness of the fur is $5.0 \mathrm{~cm}$. How cold can the outside temperature be before the dog must increase its heat output?

Surjit Tewari

Numerade Educator

Problem 54

The thermal resistance of a seal's fur and blubber combined is $0.33 \mathrm{~K} / \mathrm{W}$. If the seal's internal temperature is $37^{\circ} \mathrm{C}$ and the temperature of the sea is about $0^{\circ} \mathrm{C}$, what must be the heat output of the seal in order for it to maintain its internal temperature?

Surjit Tewari

Numerade Educator

Problem 55

A hiker is wearing wool clothing of $0.50-\mathrm{cm}$ thickness to keep warm. Her skin temperature is $35^{\circ} \mathrm{C}$ and the outside temperature is $4.0^{\circ} \mathrm{C}$. Her body surface area is $1.2 \mathrm{~m}^{2} .$ (a) If the thermal conductivity of wool is $0.040 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$, what is the rate of heat conduction through her clothing? (b) If the hiker is caught in a rainstorm, the thermal conductivity of the soaked wool increases to $0.60 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$ (that of water). Now what is the rate of heat conduction?

Surjit Tewari

Numerade Educator

Problem 56

A window whose glass has $\kappa=1.0 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$ is covered completely with a sheet of foam of the same thickness as the glass, but with $\kappa=0.025 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}) .$ How is the rate at which heat is conducted through the window changed by the addition of the foam?

Manish Jain

Numerade Educator

Problem 57

A copper bar of thermal conductivity $401 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$ has one end at $104^{\circ} \mathrm{C}$ and the other end at $24^{\circ} \mathrm{C}$. The length of the bar is $0.10 \mathrm{~m}$ and the cross-sectional area is $1.0 \times 10^{-6} \mathrm{~m}^{2}$. (a) What is the rate of heat conduction, $\mathscr{P}$ along the bar? (b) What is the temperature gradient in the bar? (c) If two such bars were placed in series (end to end) between the same temperature baths, what would $\mathscr{P}$ be? (d) If two such bars were placed in parallel (side by side) with the ends in the same temperature baths, what would $\mathscr{P}$ be? (e) In the series case, what is the temperature at the junction where the bars meet?

Manish Jain

Numerade Educator

Problem 58

One cross-country skier is wearing a down jacket that is $2.0 \mathrm{~cm}$ thick. The thermal conductivity of goose down is $0.025 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$. Her companion on the ski outing is wearing a wool jacket that is $0.50 \mathrm{~cm}$ thick. The thermal conductivity of wool is $0.040 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$. (a) If both jackets have the same surface area and the skiers both have the
same body temperature, which one will stay warmer longer? (b) How much longer can the person with the warmer jacket stay outside for the same amount of heat loss?

Manish Jain

Numerade Educator

Problem 59

If a blackbody is radiating at $T=1650 \mathrm{~K}$, at what wavelength is the maximum intensity?

Surjit Tewari

Numerade Educator

Problem 60

Wien studied the spectral distribution of many radiating bodies to finally discover a simple relation between wavelength and intensity. Use the limited data shown in Fig. $14.17$ to find the constant predicted by Wien for the product of wavelength of maximum emission and temperature.

Surjit Tewari

Numerade Educator

Problem 61

An incandescent lightbulb has a tungsten filament that is heated to a temperature of $3.00 \times 10^{3} \mathrm{~K}$ when an electric current passes through it. If the surface area of the filament is approximately $1.00 \times 10^{-4} \mathrm{~m}^{2}$ and it has an emissivity of $0.32$, what is the power radiated by the bulb?

Surjit Tewari

Numerade Educator

Problem 62

A tungsten filament in a lamp is heated to a temperature of $2.6 \times 10^{3} \mathrm{~K}$ by an electric current. The tungsten has an emissivity of $0.32 .$ What is the surface area of the filament if the lamp delivers $40.0 \mathrm{~W}$ of power?

Surjit Tewari

Numerade Educator

Problem 63

A person of surface area $1.80 \mathrm{~m}^{2}$ is lying out in the sunlight to get a tan. If the intensity of the incident sunlight is $7.00 \times 10^{2} \mathrm{~W} / \mathrm{m}^{2}$, at what rate must heat be lost by the person in order to maintain a constant body temperature? (Assume the effective area of skin exposed to the Sun is $42 \%$ of the total surface area, $57 \%$ of the incident radiation is absorbed, and that internal metabolic processes contribute another $90 \mathrm{~W}$ for an inactive person.)

Surjit Tewari

Numerade Educator

Problem 64

A student wants to lose some weight. He knows that rigorous aerobic activity uses about $700 \mathrm{kcal} / \mathrm{h}(2900 \mathrm{~kJ} / \mathrm{h})$
and that it takes about 2000 kcal per day $(8400 \mathrm{~kJ})$ just to support necessary biological functions, including keeping the body warm. He decides to burn calories faster simply by sitting naked in a $16^{\circ} \mathrm{C}$ room and letting his body radiate calories away. His body has a surface area of about $1.7 \mathrm{~m}^{2}$ and his skin temperature is $35^{\circ} \mathrm{C}$. Assuming an emissivity of $1.0$, at what rate (in kcal/h) will this student "burn" calories?

Surjit Tewari

Numerade Educator

Problem 65

An incandescent light bulb radiates at a rate of $60.0 \mathrm{~W}$ when the temperature of its filament is $2820 \mathrm{~K}$. During a brownout (temporary drop in line voltage), the power radiated drops to $58.0 \mathrm{~W}$. What is the temperature of the filament? Neglect changes in the filament's length and cross-sectional area due to the temperature change. ( Vis tutorial: light bulb)

Surjit Tewari

Numerade Educator

Problem 66

If the maximum intensity of radiation for a blackbody is found at $2.65 \mu \mathrm{m}$, what is the temperature of the radiating body?

Surjit Tewari

Numerade Educator

Problem 66

If the maximum intensity of radiation for a blackbody is found at $2.65 \mu \mathrm{m}$, what is the temperature of the radiating body?

Surjit Tewari

Numerade Educator

Problem 67

A black wood stove has a surface area of $1.20 \mathrm{~m}^{2}$ and a surface temperature of $175^{\circ} \mathrm{C}$. What is the net rate at which heat is radiated into the room? The room temperature is $20^{\circ} \mathrm{C}$.

Surjit Tewari

Numerade Educator

Problem 68

A lizard of mass $3.0 \mathrm{~g}$ is warming itself in the bright sunlight. It casts a shadow of $1.6 \mathrm{~cm}^{2}$ on a piece of paper held perpendicularly to the Sun's rays. The intensity of sunlight at the Earth is $1.4 \times 10^{3} \mathrm{~W} / \mathrm{m}^{2}$, but only half of this energy penetrates the atmosphere and is absorbed by the lizard. (a) If the lizard has a specific heat of $4.2 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$, what is the rate of increase of the lizard's temperature? (b) Assuming that there is no heat loss by the lizard (to simplify), how long must the lizard lie in the Sun in order to raise its temperature by $5.0^{\circ} \mathrm{C}$ ?

Surjit Tewari

Numerade Educator

Problem 69

At a tea party, a coffeepot and a teapot are placed on the serving table. The coffeepot is a shiny silver-plated pot with emissivity of $0.12$; the teapot is ceramic and has an emissivity of $0.65 .$ Both pots hold $1.00 \mathrm{~L}$ of liquid at $98^{\circ} \mathrm{C}$ when the party begins. If the room temperature is at $25^{\circ} \mathrm{C}$, what is the rate of radiative heat loss from the two pots? [Hint: To find the surface area, approximate the pots with cubes of similar volume.]

Narayan Hari

Numerade Educator

Problem 70

If the total power per unit area from the Sun incident on a horizontal leaf is $9.00 \times 10^{2} \mathrm{~W} / \mathrm{m}^{2}$, and we assume that $70.0 \%$ of this energy goes into heating the leaf, what would be the rate of temperature rise of the leaf? The specific heat of the leaf is $3.70 \mathrm{~kJ} /\left(\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$, the leaf's area is $5.00 \times 10^{-3} \mathrm{~m}^{2}$, and its mass is $0.500 \mathrm{~g}$.

Surjit Tewari

Numerade Educator

Problem 71

Consider the leaf of Problem 70 . Assume that the top surface of the leaf absorbs $70.0 \%$ of $9.00 \times 10^{2} \mathrm{~W} / \mathrm{m}^{2}$ of radiant energy, while the bottom surface absorbs all of the radiant energy incident on it due to its surroundings at $25.0{ }^{\circ} \mathrm{C}$. (a) If the only method of heat loss for the leaf were thermal radiation, what would be the temperature of the leaf? (Assume that the leaf radiates like a blackbody.)
(b) If the leaf is to remain at a temperature of $25.0^{\circ} \mathrm{C}$, how much power per unit area must be lost by other methods such as transpiration (evaporative heat loss)?

Narayan Hari

Numerade Educator

Problem 72

A hotel room is in thermal equilibrium with the rooms on either side and with the hallway on a third side. The room loses heat primarily through a $1.30$ -cm-thick glass window that has a height of $76.2 \mathrm{~cm}$ and a width of $156 \mathrm{~cm}$. If the temperature inside the room is $75^{\circ} \mathrm{F}$ and the temperature outside is $32^{\circ} \mathrm{F}$, what is the approximate rate (in $\mathrm{kJ} / \mathrm{s}$ ) at which heat must be added to the room to maintain a constant temperature of $75^{\circ} \mathrm{F}$ ? Ignore the stagnant air layers on either side of the glass.

Surjit Tewari

Numerade Educator

Problem 73

While camping, some students decide to make hot chocolate by heating water with a solar heater that focuses sunlight onto a small area. Sunlight falls on their solar heater, of area $1.5 \mathrm{~m}^{2}$, with an intensity of $750 \mathrm{~W} / \mathrm{m}^{2}$. How long will it take $1.0 \mathrm{~L}$ of water at $15.0^{\circ} \mathrm{C}$ to rise to a boiling temperature of $100.0^{\circ} \mathrm{C}$ ?

Surjit Tewari

Numerade Educator

Problem 74

Five ice cubes, each with a mass of $22.0 \mathrm{~g}$ and at a temperature of $-50.0^{\circ} \mathrm{C}$, are placed in an insulating container. How much heat will it take to change the ice cubes completely into steam?

Surjit Tewari

Numerade Educator

Problem 75

A $10.0-\mathrm{g}$ iron bullet with a speed of $4.00 \times 10^{2} \mathrm{~m} / \mathrm{s}$ and a temperature of $20.0^{\circ} \mathrm{C}$ is stopped in a $0.500-\mathrm{kg}$ block of wood, also at $20.0{ }^{\circ} \mathrm{C}$. (a) At first all of the bullet's
kinetic energy goes into the internal energy of the bullet. Calculate the temperature increase of the bullet.
(b) After a short time the bullet and the block come to the same temperature $T$. Calculate $T$, assuming no heat is lost to the environment.

Narayan Hari

Numerade Educator

Problem 76

If the temperature surrounding the sunbather in Problem 63 is greater than the normal body temperature of $37^{\circ} \mathrm{C}$ and the air is still, so that radiation, conduction, and convection play no part in cooling the body, how much water (in liters per hour) from perspiration must be given off to maintain the body temperature? The heat of vaporization of water is $2430 \mathrm{~J} / \mathrm{g}$ at normal skin temperature.

Narayan Hari

Numerade Educator

Problem 77

If $4.0 \mathrm{~g}$ of steam at $100.0^{\circ} \mathrm{C}$ condenses to water on a burn victim's skin and cools to $45.0^{\circ} \mathrm{C}$, (a) how much heat is given up by the steam? (b) If the skin was originally at $37.0^{\circ} \mathrm{C}$, how much tissue mass was involved in cooling the steam to water? See Table $14.1$ for the specific heat of human tissue.

Surjit Tewari

Numerade Educator

Problem 78

If $4.0 \mathrm{~g}$ of boiling water at $100.0^{\circ} \mathrm{C}$ was splashed onto a burn victim's skin, and if it cooled to $45.0^{\circ} \mathrm{C}$ on the $37.0^{\circ} \mathrm{C}$ skin, (a) how much heat is given up by the water? (b) How much tissue mass, originally at $37.0^{\circ} \mathrm{C}$, was involved in cooling the water? See Table $14.1$. Compare the result with that found in Problem 77 .

Surjit Tewari

Numerade Educator

Problem 79

The amount of heat generated during the contraction of muscle in an amphibian's leg is given by
$$
Q=0.544 \mathrm{~mJ}+(1.46 \mathrm{~mJ} / \mathrm{cm}) \Delta x
$$
where $\Delta x$ is the length shortened. If a muscle of length $3.0 \mathrm{~cm}$ and mass $0.10 \mathrm{~g}$ is shortened by $1.5 \mathrm{~cm}$ during a contraction, what is the temperature rise? Assume that the specific heat of muscle is $4.186 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$.

Surjit Tewari

Numerade Educator

Problem 80

Many species cool themselves by sweating, because as the sweat evaporates, heat is given up to the surroundings. A human exercising strenuously has an evaporative heat loss rate of about $650 \mathrm{~W}$. If a person exercises strenuously for $30.0$ min, how much water must he drink to replenish his fluid loss? The heat of vaporization of water is $2430 \mathrm{~J} / \mathrm{g}$ at normal skin temperature.

Surjit Tewari

Numerade Educator

Problem 81

A wall consists of a layer of wood outside and a layer of insulation inside. The temperatures inside and outside the wall are $+22^{\circ} \mathrm{C}$ and $-18^{\circ} \mathrm{C} ;$ the temperature at the wood/insulation boundary is $-8.0{ }^{\circ} \mathrm{C}$. By what factor would the heat loss through the wall increase if the insulation were not present?

Narayan Hari

Numerade Educator

Problem 82

Two 62 -g ice cubes are dropped into $186 \mathrm{~g}$ of water in a glass. If the water is initially at a temperature of $24^{\circ} \mathrm{C}$ and the ice is at $-15^{\circ} \mathrm{C}$, what is the final temperature of the drink?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 83

A $0.500-\mathrm{kg}$ slab of granite is heated so that its temperature increases by $7.40^{\circ} \mathrm{C}$. The amount of heat supplied to the granite is $2.93 \mathrm{~kJ}$. Based on this information, what is the specific heat of granite?

Surjit Tewari

Numerade Educator

Problem 84

A spring of force constant $k=8.4 \times 10^{3} \mathrm{~N} / \mathrm{m}$ is compressed by $0.10 \mathrm{~m} .$ It is placed into a vessel containing $1.0 \mathrm{~kg}$ of water and then released. Assuming all the energy from the spring goes into heating the water, find the change in temperature of the water.

Surjit Tewari

Numerade Educator

Problem 85

One end of a cylindrical iron rod of length $1.00 \mathrm{~m}$ and of radius $1.30 \mathrm{~cm}$ is placed in the blacksmith's fire and reaches a temperature of $327^{\circ} \mathrm{C}$. If the other end of the rod is being held in your hand $\left(37^{\circ} \mathrm{C}\right)$, what is the rate of heat flow along the rod? The thermal conductivity of iron varies with temperature, but an average value between the two temperatures is $67.5 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$ tutorial: conduction)

Surjit Tewari

Numerade Educator

Problem 86

A blacksmith heats a $0.38-\mathrm{kg}$ piece of iron to $498^{\circ} \mathrm{C}$ in his forge. After shaping it into a decorative design, he places it into a bucket of water to cool. If the available water is at $20.0{ }^{\circ} \mathrm{C}$, what minimum amount of water must be in the bucket to cool the iron to $23.0^{\circ} \mathrm{C} ?$ The water in the bucket should remain in the liquid phase.

Surjit Tewari

Numerade Educator

Problem 87

The student from Problem 64 realizes that standing naked in a cold room will not give him the desired weight loss results since it is much less efficient than simply exercising. So he decides to burn calories through conduction. He fills the bathtub with $16^{\circ} \mathrm{C}$ water and gets in. The water right next to his skin warms up to the same temperature as his skin, $35^{\circ} \mathrm{C}$, but the water only $3.0 \mathrm{~mm}$ away remains at $16^{\circ} \mathrm{C}$. At what rate (in $\mathrm{kcal} / \mathrm{h}$ ) would he "burn" calories?The thermal conductivity of water at this temperature is $0.58 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}) .$ [Warning: Do not try this. Sitting in water this cold can lead to hypothermia and even death.]

Surjit Tewari

Numerade Educator

Problem 88

A stainless steel saucepan, with a base that is made of 0.350-cm-thick steel $[\kappa=46.0 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})]$ fused to a $0.150-\mathrm{cm}$ thickness of copper $[\kappa=401 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})]$, sits
on a ceramic heating element at $104.00^{\circ} \mathrm{C}$. The diameter of the pan is $18.0 \mathrm{~cm}$ and it contains boiling water at $100.00^{\circ} \mathrm{C}$. (a) If the copper-clad bottom is touching the heat source, what is the temperature at the copper-steel interface? (b) At what rate will the water evaporate from the pan?

Manish Jain

Numerade Educator

Problem 89

A $75-\mathrm{kg}$ block of ice at $0.0^{\circ} \mathrm{C}$ breaks off from a glacier, slides along the frictionless ice to the ground from a height of $2.43 \mathrm{~m}$, and then slides along a horizontal surface consisting of gravel and dirt. Find how much of the mass of the ice is melted by the friction with the rough surface, assuming $75 \%$ of the internal energy generated is used to heat the ice.

Surjit Tewari

Numerade Educator

Problem 90

Small animals eat much more food per $\mathrm{kg}$ of body mass than do larger animals. The basal metabolic rate (BMR) is the minimal energy intake necessary to sustain life in a state of complete inactivity. The table lists the BMR, mass, and surface area for five animals. (a) Calculate the BMR/kg of body mass for each animal. Is it true that smaller animals must consume much more food per $\mathrm{kg}$ of body mass? (b) Calculate the $\mathrm{BMR} / \mathrm{m}^{2}$ of surface area. (c) Can you explain why the $\mathrm{BMR} / \mathrm{m}^{2}$ is approximately the same for animals of different sizes? Consider what happens to the food energy metabolized by an animal in a resting state.

Manish Jain

Numerade Educator

Problem 91

Imagine a person standing naked in a room at $23.0^{\circ} \mathrm{C}$. The walls are well insulated, so they also are at $23.0^{\circ} \mathrm{C}$. The person's surface area is $2.20 \mathrm{~m}^{2}$ and his basal metabolic rate is 2167 kcal/day. His emissivity is 0.97. (a) If the person's skin temperature were $37.0^{\circ} \mathrm{C}$ (the same as the internal body temperature), at what net rate would heat be lost through radiation? (Ignore losses by conduction and convection.) (b) Clearly the heat loss in (a) is not sustainable-but skin temperature is less than internal body temperature. Calculate the skin temperature such that the net heat loss due to radiation is equal to the basal metabolic rate. (c) Does wearing clothing slow the loss of heat by radiation, or does it only decrease losses by conduction and convection? Explain.

Manish Jain

Numerade Educator

Problem 92

Bare, dark-colored basalt has a thermal conductivity of $3.1 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$, whereas light-colored sandstone's thermal conductivity is only $2.4 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})$. Even though the same amount of radiation is incident on both and their
surface temperatures are the same, the temperature gradient within the two materials will differ. For the same patch of area, what is the ratio of the depth in basalt as compared with the depth in sandstone that gives the same temperature difference?

Ankur S

Numerade Educator

Problem 93

The power expended by a cheetah is $160 \mathrm{~kW}$ while running at $110 \mathrm{~km} / \mathrm{h}$, but its body temperature cannot exceed $41.0^{\circ} \mathrm{C}$. If $70.0 \%$ of the energy expended is dissipated within its body, how far can it run before it overheats? Assume that the initial temperature of the cheetah is $38.0^{\circ} \mathrm{C}$, its specific heat is $3.5 \mathrm{~kJ} /\left(\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$, and its mass is $50.0 \mathrm{~kg}$.

Sachin Rao

Numerade Educator

Problem 94

A scientist working late at night in her low-temperature physics laboratory decides to have a cup of hot tea, but discovers the lab hot plate is broken. Not to be deterred, she puts about 8 oz of water, at $12^{\circ} \mathrm{C}$, from the tap into a lab dewar (essentially a large thermos bottle) and begins shaking it up and down. With each shake the water is thrown up and falls back down a distance of $33.3 \mathrm{~cm}$. If she can complete 30 shakes per minute, how long will it take to heat the water to $87^{\circ} \mathrm{C}$ ? Would this really work? If not, why not?

Surjit Tewari

Numerade Educator

Problem 95

A $2.0$ -kg block of copper at $100.0^{\circ} \mathrm{C}$ is placed into $1.0 \mathrm{~kg}$ of water in a $2.0$ -kg iron pot. The water and the iron pot are at $25.0^{\circ} \mathrm{C}$ just before the copper block is placed into the pot. What is the final temperature of the water, assuming negligible heat flow to the environment?

Prabhat Tyagi

Numerade Educator

Problem 96

A piece of gold of mass $0.250 \mathrm{~kg}$ and at a temperature of $75.0{ }^{\circ} \mathrm{C}$ is placed into a $1.500-\mathrm{kg}$ copper pot containing $0.500 \mathrm{~L}$ of water. The pot and water are at $22.0^{\circ} \mathrm{C}$ before the gold is added. What is the final temperature of the water?

Manish Jain

Numerade Educator

Problem 97

For a cheetah, $70.0 \%$ of the energy expended during exertion is internal work done on the cheetah's system and is dissipated within his body; for a dog only $5.00 \%$ of the energy expended is dissipated within the dog's body. Assume that both animals expend the same total amount of energy during exertion, both have the same heat capacity, and the cheetah is $2.00$ times as heavy as the dog.
(a) How much higher is the temperature change of the cheetah compared to the temperature change of the dog?
(b) If they both start out at an initial temperature of $35.0^{\circ} \mathrm{C}$, and the cheetah has a temperature of $40.0^{\circ} \mathrm{C}$ after the exertion, what is the final temperature of the dog? Which animal probably has more endurance? Explain.

Melissa Walsh

Numerade Educator

Problem 98

A 20.0-g lead bullet leaves a rifle at a temperature of $87.0^{\circ} \mathrm{C}$ and hits a steel plate. If the bullet melts, what is the minimum speed it must have?

Surjit Tewari

Numerade Educator

Problem 99

The inner vessel of a calorimeter contains $2.50 \times 10^{2} \mathrm{~g}$ of tetrachloromethane, $\mathrm{CCl}_{4}$, at $40.00{ }^{\circ} \mathrm{C}$. The vessel is surrounded by $2.00 \mathrm{~kg}$ of water at $18.00{ }^{\circ} \mathrm{C}$. After a time. the $\mathrm{CCl}_{4}$ and the water reach the equilibrium temperature of $18.54^{\circ} \mathrm{C}$. What is the specific heat of $\mathrm{CCl}_{4}$ ?

Narayan Hari

Numerade Educator

Problem 100

On a very hot summer day, Daphne is off to the park for a picnic. She puts $0.10 \mathrm{~kg}$ of ice at $0^{\circ} \mathrm{C}$ in a thermos and then adds a grape-flavored drink, which she has mixed from a powder using room temperature water $\left(25^{\circ} \mathrm{C}\right)$. How much grape-flavored drink will just melt all the ice?

Surjit Tewari

Numerade Educator

Problem 101

It requires $17.10 \mathrm{~kJ}$ to melt $1.00 \times 10^{2} \mathrm{~g}$ of urethane $\left[\mathrm{CO}_{2}\left(\mathrm{NH}_{2}\right) \mathrm{C}_{2} \mathrm{H}_{5}\right]$ at $48.7^{\circ} \mathrm{C}$. What is the latent heat of
fusion of urethane in $\mathrm{kJ} / \mathrm{mol}$ ?

Narayan Hari

Numerade Educator

Problem 102

A 20.0-g lead bullet leaves a rifle at a temperature of $47.0^{\circ} \mathrm{C}$ and travels at a velocity of $5.00 \times 10^{2} \mathrm{~m} / \mathrm{s}$ until it hits a large block of ice at $0{ }^{\circ} \mathrm{C}$ and comes to rest within it. How much ice will melt?

Surjit Tewari

Numerade Educator