College Physics 2013

Eugenia Etkina, Michael Gentle, Alan Van Heuvelen

Chapter 12

First Law of Thermodynamics

Educators


Problem 1

Estimate the thermal energy of the air in your bedroom.
List all of the assumptions you make.

Yaqub K.
Numerade Educator

Problem 2

A helium-filled balloon has a volume of 0.010 $\mathrm{m}^{3} .$ The temperature in the room and in the balloon is $20^{\circ} \mathrm{C}$ . What are the average
speed and the average kinetic energy of a particle of helium inside
the balloon? What is the thermal energy of the helium?

Yaqub K.
Numerade Educator

Problem 3

Imagine that the helium balloon from the previous problem
was placed in an evacuated container of volume 0.020 $\mathrm{m}^{3}$ and that the balloon popped when it touched a sharp edge on the inside of the container. (a) How much work is done on the
helium gas? (b) What happens to the temperature of the helium, its density, the gas pressure, the average kinetic energy of each particle, and the thermal energy of the helium gas? Provide quantitative answers.

Yaqub K.
Numerade Educator

Problem 4

You accidentally release a helium-filled balloon that rises in the atmosphere. As it rises, the temperature of the helium inside decreases from $20^{\circ} \mathrm{C}$ to $10^{\circ} \mathrm{C}$ . What happens to the average speed of helium atoms in the balloon and the thermal energy of the helium inside the balloon? Describe the assumptions you made.

Yaqub K.
Numerade Educator

Problem 5

Air in a cylinder with a piston and initially at $20^{\circ} \mathrm{C}$ expands
at constant atmospheric pressure. (a) What is the work that
the piston does on the gas if the air expands from 0.030 $\mathrm{m}^{3}$ to
0.043 $\mathrm{m}^{3} ?(\mathrm{b})$ How many moles of gas are in the container?
(c) Suppose that the work leads to a corresponding change in
thermal energy (there is no heating). What is the final temperature of the gas?

Yaqub K.
Numerade Educator

Problem 6

In an empty rubber raft the pressure is approximately constant. You push on a large air pump that pushes 1.0 $\mathrm{L}\left(1.0 \times 10^{-3} \mathrm{m}^{3}\right)$ of air into the raft. You exert a $20-\mathrm{N}$ force while pushing the pump handle 0.02 $\mathrm{m} .$ (a) Determine
the work done on the gas. (b) If all of the work is converted to thermal energy of the 1.0 $\mathrm{L}$ of gas, what is the temperature increase of the gas?

Yaqub K.
Numerade Educator

Problem 7

A drop in temperature of the human body core from $37^{\circ} \mathrm{C}$ to about $31^{\circ} \mathrm{C}$ can be fatal. Estimate the thermal energy that must be removed from
a human body to cause this temperature change.

Yaqub K.
Numerade Educator

Problem 8

A 50 -kg person consumes about 2000 kcal of food in one day. If 10$\%$ of this food energy is converted to thermal energy that does not leave the body, what is the person's temperature change? What assumptions did you make?

Yaotang L.
Numerade Educator

Problem 9

Determine the amount of thermal energy provided by heat-
ing to raise the temperature of $(a) 0.50 \mathrm{kg}$ of water by $10^{\circ} \mathrm{C},$
(b) 0.50 $\mathrm{kg}$ of ethanol by $10^{\circ} \mathrm{C},$ and ( $\mathrm{c} ) 0.50 \mathrm{kg}$ of iron by $10^{\circ} \mathrm{C} .$

Yaqub K.
Numerade Educator

Problem 10

Estimate the time interval required for a 600 -kg cast iron
car engine to warm from $30^{\circ} \mathrm{C}$ to $1500^{\circ} \mathrm{C}$ (approximately the
melting temperature of iron) if burning fuel in the engine as it
idles produces thermal energy at a rate of 8000 $\mathrm{J} / \mathrm{s}$ and none
of the energy escapes the car engine.

Yaqub K.
Numerade Educator

Problem 11

A lead bullet of mass $m$ traveling at $v_{i}$ penetrates a wooden block and stops. (a) Represent the process with a bar chart. What system did you choose? (b) Assuming that 50$\%$ of the initial kinetic energy of the bullet is converted into thermal energy in the bullet, write an expression that would allow you to determine the block's temperature increase. (c) List all of the physics ideas that you used to solve this problem.

Yaqub K.
Numerade Educator

Problem 12

A 50 -kg woman repeatedly lifts a 20 -kg barbell 0.80 $\mathrm{m}$ from her chest to an extended posi-
tion above her head. (a) If her body retains 10 $\mathrm{J}$ of thermal
energy for each joule of work done while lifting, how many
times must she lift the barbell to warm her body $0.50^{\circ} \mathrm{C}$ ?
(b) State any assumptions you used.(c) List all of the physics
ideas that you used to solve this problem.

Yaqub K.
Numerade Educator

Problem 13

You add 25 $\mathrm{g}$ of milk at $10^{\circ} \mathrm{C}$ to 200 $\mathrm{g}$ of coffee (essentially
water) at $70^{\circ} \mathrm{C}$ . The coffee is in a Styrofoam cup. If the speciffic heat of milk is 3800 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$ , by how much will the coffee temperature decrease when the milk is added? Indicate any assumptions you made.

Yaqub K.
Numerade Educator

Problem 14

You add $20^{\circ} \mathrm{C}$ water to 0.20 $\mathrm{kg}$ of $40^{\circ} \mathrm{C}$ soup. After a little mixing, the water and soup mixture is at $34^{\circ} \mathrm{C}$ . The specific
heat of the soup is 3800 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$ . Determine everything you can using this information.

Yaqub K.
Numerade Educator

Problem 15

A 30 -kg child has a temperature of $39.0^{\circ} \mathrm{C}\left(102.2^{\circ} \mathrm{F}\right) .$ How much thermal energy must be removed from the child's body by some heating process to lower his
temperature to the normal $37.0^{\circ} \mathrm{C}\left(98.6^{\circ} \mathrm{F}\right)$ body temperature?

Yaqub K.
Numerade Educator

Problem 16

Scientists have proposed that 65 million years ago in what is now the Yucatan peninsula of Mexico, a $1.2 \times 10^{16}-\mathrm{kg}$ meteorite moving at speed 11 $\mathrm{km} / \mathrm{s}$ collided with Earth, and the resulting harsh conditions led to the extinction of many species, including the
dinosaurs. (a) Calculate the kinetic energy of the meteorite before the collision. (b) If 20$\%$ of this energy was converted to thermal energy in the meteorite, which had a specific heat of
$900 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C},$ by how much did its temperature increase?

Yaqub K.
Numerade Educator

Problem 17

You pour 250 $\mathrm{g}$ of tea into a Styrofoam cup, initially at
$80^{\circ} \mathrm{C},$ and stir in a little sugar using a $100-\mathrm{g}$ aluminum $20^{\circ} \mathrm{C}$ spoon and leave the spoon in the cup. What is the highest
possible temperature of the spoon when you finally take it out
of the cup? What is the temperature of the tea at that time?
What assumptions did you make to answer the questions?

Yaqub K.
Numerade Educator

Problem 18

A 500 -g aluminum container holds 300 $\mathrm{g}$ of water. The
water and aluminum are initially at $40^{\circ} \mathrm{C}$ . A $200-\mathrm{g}$ iron block
at $0^{\circ} \mathrm{C}$ is added to the water. What can you determine using
this information? State any assumptions you used. List all
physics ideas that you used to solve this problem.

Yaqub K.
Numerade Educator

Problem 19

A 150 -g insulated aluminum container holds 250 $\mathrm{g}$ of water
initially at $20^{\circ} \mathrm{C} . \mathrm{A} 200-\mathrm{g}$ metal block at $60^{\circ} \mathrm{C}$ is added to the water, resulting in a final temperature of $22.8^{\circ} \mathrm{C} .$ What type of metal is the block? What assumptions did you make to answer the question?

Yaqub K.
Numerade Educator

Problem 20

Gas in a container with a movable piston initially at volume $V_{1},$ pressure $P_{1},$ and a very high temperature $T_{1}$ expands at constant pressure until its temperature and volume
became $T_{2}$ and $V_{2} .$ (a) Describe the process using the concepts of work, heating, and internal energy. (b) Draw a bar chart representing the process. (c) Calculate the work that the environment did on the gas. (d) Explain the process from a microscopic point of view. (e) Represent the process using
P-versus-V, P-versus-T, and V-versus-T graphs.(f) Repeat steps (a)-(e) for a situation in which the gas started with the same initial state but expanded at constant temperature instead of constant pressure.

Yaqub K.
Numerade Educator

Problem 21

Gas in a closed container undergoes a cyclic process from state 1 to state 2 and then back to state 1 (Figure P12.21). Describe the processes 1-2 and 2-1 qualitatively using the concepts of work, heating, and internal energy. (a) What happened to the thermal energy of the gas as it went from 1 to 2 and then from 2 to 1? What is the net change in the internal energy after the gas returned to state 1? (b) On the P@versus@V graph, show the magnitude of the work that was done on the gas by the environment during process 1-2 and during process 2-1. (c) Was the total work done on the gas positive, negative, or zero during the entire process 1-2-1? (d) Discuss the heating of the gas during process 1-2 and then 2-1. Was the total heating of the gas positive, negative, or zero during thewhole process 1-2-1?

Yaqub K.
Numerade Educator

Problem 22

Jeopardy problem A gas process is described mathematically as follows: $100 \mathrm{J}+(-P)\left(0.001 \mathrm{m}^{3}\right)=0 .$ Pose a problem for which this description could be the answer. Describe the process macroscopically and microscopically.

Yaqub K.
Numerade Educator

Problem 23

Jeopardy problem A gas process is described mathematically as follows: $Q+120 \mathrm{J}=50 \mathrm{J}$ . Pose a problem for which this description could be the answer. Describe the process
macroscopically and microscopically.

Yaqub K.
Numerade Educator

Problem 24

Use the first law of thermodynamics to devise a mathematical
description of a process in which gas is being heated (positive
heating) but its temperature does not change. Represent the
process with a bar chart.

Yaqub K.
Numerade Educator

Problem 25

Use the first law of thermodynamics to devise a mathematical description of a process in which gas is being cooled (negative heating) but its temperature increases. Represent the process with a bar chart.

Yaqub K.
Numerade Educator

Problem 26

Derive an expression for the amount of energy that must be
provided through heating for one mole of gas of molar mass
$M$ to have a temperature increase of 1 $\mathrm{K}$ . Consider different
processes and decide whether the amount of heating is inde-
pendent of the process.

Yaqub K.
Numerade Educator

Problem 27

You are making a table for specific heats of gases. Compared to the specific heats of solid and liquid substances, what additional information do you need to provide when you are listing the values of specific heat for each gas (oxygen, hydrogen, etc.)? Explain your answer.

Yaqub K.
Numerade Educator

Problem 28

One of the experiments that Joule used to test the idea of energy conservation was measurement of the temperature of a gas during the process of gas expansion into a vessel from which all air was evacuated. (a) Why did he choose this experiment? (b) What outcome would he predict based
on the first law of thermodynamics? (c) Draw a picture of the experiment and provide macroscopic and microscopic reasoning for your answer.

Yaqub K.
Numerade Educator

Problem 29

On March 5 $2006,$ a new college basketball attendance record of $33,633$
was set in Syracuse University's Carrier Dome in the last
regular-season game against Villanova. The volume of air in
the dome is about $1.5 \times 10^{6} \mathrm{m}^{3} .$ Estimate the temperature
change of the air in 2 $\mathrm{h}$ , if all the seats in the dome are filled
and each person transfers his or hetabolic thermal energy to the air in the dome at a rate of 100 $\mathrm{W}(100 \mathrm{J} / \mathrm{s}) .$ Assume that no thermal energy leaves the air through the walls, floor, or ceiling of the dome.

Yaqub K.
Numerade Educator

Problem 30

Determine the energy needed to change a $0.50-\mathrm{kg}$ block of ice
at $0^{\circ} \mathrm{C}$ into water at $20^{\circ} \mathrm{C} .$

Yaqub K.
Numerade Educator

Problem 31

$*$ When $1.4 \times 10^{5} \mathrm{J}$ of energy is removed from 0.60 kg of
water initially at $20^{\circ} \mathrm{C},$ will all the water freeze? If not, how
much remains unfrozen?

Yaqub K.
Numerade Educator

Problem 32

An electric heater warms ice at a rate of $H .(\text { a })$ What do you
need to do to determine the mass of ice that melts in $\Delta t$ min?
(b) What assumptions did you use? How will your answer
change if you use different assumptions?

Yaqub K.
Numerade Educator

Problem 33

$*$ Determine the number of grams of ice at $0^{\circ} \mathrm{C}$ that must
be added to a cup with 250 $\mathrm{g}$ of tea at $40^{\circ} \mathrm{C}$ to cool the tea
to $35^{\circ} \mathrm{C}$

Yaqub K.
Numerade Educator

Problem 34

An ice-making machine removes thermal energy from ice-cold water at a rate of $H .$ Determine the time interval needed to form $m$ kg of ice at ice melting temperature.

Yaqub K.
Numerade Educator

Problem 35

Preventing freezing in canning cellar A tub containing
50 $\mathrm{kg}$ of water is placed in a farmer's canning cellar, initially
at $10^{\circ} \mathrm{C} .$ On a cold evening the cellar loses thermal energy
through the walls at a rate of 1200 $\mathrm{J} / \mathrm{s}$ . Without the tub of
water, the fruit would freeze in 4 $\mathrm{h}$ (the fruit freezes at $-1^{\circ} \mathrm{C}$ because the sugar in the fruit lowers the freezing temperature). By what time interval does the presence of the water
delay the freezing of the fruit?

Yaqub K.
Numerade Educator

Problem 36

Passive solar energy storage material A Dow Chemical
product called TESC- 81 (primarily a salt, calcium chloride
hexahydrate) is used as an energy-storage material for solar
applications. Energy from the Sun raises the temperature of
the solid material, causing it to melt at $27^{\circ} \mathrm{C}\left(81^{\circ} \mathrm{F}\right)$ . At night the energy is released as the salt cools and returns to the solid
state. (a) Determine the energy required to raise the tempera-
ture of 1.0 $\mathrm{kg}$ of solid TESC- 81 from $20^{\circ} \mathrm{C}$ to the liquid state
at $27^{\circ} \mathrm{C} .$ (b) How warm would 1.0 $\mathrm{kg}$ of water become if it
started at $20^{\circ} \mathrm{C}$ and absorbed the same energy? (c) Discuss the desirability of TESC- $-81$ as a thermal energy-storage material
compared to water. For TESC- $81, c(\text { solid })=1900 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$
and $L_{\mathrm{f}}=1.7 \times 10^{5} \mathrm{J} / \mathrm{kg} .$

Yaqub K.
Numerade Educator

Problem 37

How much energy is required to convert (a) 0.10 $\mathrm{kg}$ of water
at $100^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C}$ and (b) 0.10 $\mathrm{kg}$ of liquid ethanol
at $78^{\circ} \mathrm{C}$ to ethanol vapor at $78^{\circ} \mathrm{C} ?$

Yaqub K.
Numerade Educator

Problem 38

Cooling with alcohol rub During a back rub, 80 $\mathrm{g}$ of ethanol
(rubbing alcohol) is converted from a liquid to a gas. Deter-
mine the thermal energy removed from a person's body by
this conversion. Indicate any assumptions you made.

Yaqub K.
Numerade Educator

Problem 39

Energy in a lightning flash A lightning flash releases about
$10^{10} \mathrm{J}$ of electrical energy. If all this energy is added to 50 $\mathrm{kg}$ of
water (the amount of water in a $165-\mathrm{lb}$ person) at $37^{\circ} \mathrm{C},$ what
are the final state and temperature of the water?

Yaqub K.
Numerade Educator

Problem 40

A kettle containing 0.75 kg of boiling water absorbs thermal
energy from a gas stove at a rate of 600 $\mathrm{J} / \mathrm{s}$ . What time interval
is required for the water to boil away, leaving a charred kettle?

Yaqub K.
Numerade Educator

Problem 41

Cooling nuclear power plant A nuclear power plant generates waste thermal energy at a rate of $1000 \mathrm{MW}=1000 \times 10^{6} \mathrm{W}$ . If this energy is transfered by hot water passing through tubes in the water in an evaporative cooling tower, how much water must evaporate to cool the plant (a) per second and (b) per day?

Yaqub K.
Numerade Educator

Problem 42

Energy changes when it rains Estimate the energy that is released or absorbed as water condenses and falls to Earth. Use the following information. Clouds are formed when moisture in the gaseous state in the air condenses. A rainstorm follows, dropping 2 $\mathrm{cm}$ of rain over an area 2 $\mathrm{km} \times 2 \mathrm{km}$ . Note that the mass of 1 $\mathrm{m}^{3}$ of water is 1000 $\mathrm{kg}$ .

Yaqub K.
Numerade Educator

Problem 43

Insulating a house You insulate your house using insulation rated as $\mathrm{R}-12$ , which will conduct 1$/ 12 \mathrm{Btu} / \mathrm{h}$ of thermal energy through each square foot of surface if there is a $1^{\circ} \mathrm{F}$ temperature difference across the material (R-12 insulation is said to have a thermal resistance $R$ of 12 $\mathrm{h} \cdot \mathrm{ft}^{2} \cdot^{\circ} \mathrm{F} / \mathrm{B} \mathrm{tu} ) .$ The conduction rate through a material of area $A$ , across which there is a temperature difference $T_{2}-T_{1},$ is
$$H_{\text { Conduction }}=(1 / R) A\left(T_{2}-T_{1}\right)$$
Use this information to determine the conductive energy flow rate across (a) an 8.0 $\mathrm{ft} \times 16.0 \mathrm{ft}$ R-15 wall; (b) a $3.0 \mathrm{ft} \times 7.0 \mathrm{ft} \mathrm{R}-4$ door; and $(\mathrm{c})$ a $3.0 \mathrm{ft} \times 4.0 \mathrm{ft} \mathrm{R}-1.5$ window. Assume that the inside temperature is $68^{\circ} \mathrm{F}$ and the outside temperature is $20^{\circ} \mathrm{F} .$ (d) Convert each answer from $\mathrm{Btu} / \mathrm{h}$ to $\mathrm{J} / \mathrm{s}=\mathrm{W} .$

Yaqub K.
Numerade Educator

Problem 44

$* *$ Igloo thermal energy conduction A typical snow igloo (thermal conductivity about 1$/ 10$ of ice $)$ is shaped like a hemisphere of radius 1.5 $\mathrm{m}$ with $0.36-\mathrm{m}$ thick walls. What is the conductive heating rate through the walls if the inside temperature is $10^{\circ} \mathrm{C}$ and the outside temperature is $-10^{\circ} \mathrm{C} ?$ $[\text { Hint: Use the conductive heating equation from the previous }$ problem, but replace 1$/ R$ by the thermal conductivity $K . ]$

Yaqub K.
Numerade Educator

Problem 45

After a vigorous workout, you stand in shorts in a $20^{\circ} \mathrm{C}$ room
in front of a fan that blows air past you. What are the signs
$(+\text { or }-)$ of the convective and radiative heating rates? Will
you perspire to keep cool? Explain your answer.

Yaqub K.
Numerade Educator

Problem 46

To cool hot soup, you blow across the top of a bowl of soup. Assuming that the soup is the system, what are the signs $(+\text { or }-)$ of the different heating mechanisms and the effect of this energy transfer on the soup?

Yaqub K.
Numerade Educator

Problem 47

While blowing across the bowl of soup in the previous problem, you wonder how efficiently the soup can cool by itself through evaporation. You notice that the bowl of hot soup loses 0.40 $\mathrm{g}$ of water by evaporation in 1 $\mathrm{min}$ . What is the average evaporative heating rate of the soup during that minute? Assume that soup is primarily water.

Yaqub K.
Numerade Educator

Problem 48

EST $\# *$ Solar collector You wish to install a solar panel that will run at least five lightbulbs, a TV, and a microwave. How large should the panel be if the average sunlight incident on a photoelectric solar collector on a roof for the 8 -h time interval is 700 $\mathrm{W} / \mathrm{m}^{2}$ and the radiant energy is converted to electricity with an efficiency of 20$\% ?$

Yaqub K.
Numerade Educator

Problem 49

BIO Marathon You are training for a marathon. While training, you lose energy by evaporation at a rate of 380 $\mathrm{W}$ . How much water mass do you lose while running for 3.5 $\mathrm{h}$ ?

Yaqub K.
Numerade Educator

Problem 50

Cooling beer keg A keg of beer is covered with a wet towel. Imagine that the keg gains energy from its surroundings at a rate of 20 $\mathrm{W}$ . (a) At what rate in grams per second must water evaporate from a towel placed over the keg to cool the keg at the same rate that energy is being absorbed? (b) How much water in grams is evaporated in 2.0 $\mathrm{h}$ ?

Check back soon!

Problem 51

A canteen is covered with wet canvas. If 15 g of water evaporates from the canvas and if 50$\%$ of the thermal energy used to evaporate the water is supplied by the 400 $\mathrm{g}$ of water in the
canteen, what is the temperature change of the water in the canteen?

Yaqub K.
Numerade Educator

Problem 52

Evaporative cooling Each year a layer of water of average depth 0.8 $\mathrm{m}$ evaporates from each square meter of Earth's surface. Estimate the average energy transfer rate in watts needed to continue this process.

Yaqub K.
Numerade Educator

Problem 53

The rate of water evaporation from a fish bowl is 0.050 $\mathrm{g} / \mathrm{s}$ and the natural thermal energy transfer rate to the bowl by conduction, convection, and radiation is $+36 \mathrm{W}$ . What power electric heater must you buy to keep the temperature in the fish bowl constant?

Yaqub K.
Numerade Educator

Problem 54

Tree leaf A tree leaf of mass of 0.80 $\mathrm{g}$ and specific heat of 3700 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$ absorbs energy from the sunlight at a rate of 2.8 $\mathrm{J} / \mathrm{s} .$ If this energy is not removed from the leaf, how much does the temperature of the leaf change in 1 $\mathrm{min}$ ? [Note: Do not be surprised if your answer is large. A leaf clearly needs other heat transfer mechanisms to control its temperature.]

Yaqub K.
Numerade Educator

Problem 55

Warming a spaceship Your friend says that natural convection would not work on a spaceship orbiting the Earth. Do you agree or disagree with her statement? Explain.

Yaqub K.
Numerade Educator

Problem 56

Passive solar energy storage Solar energy entering the windows of your house is absorbed and stored by a concrete wall of mass $m$ . The wall's temperature increases by $10^{\circ} \mathrm{C}$
during the sunlight hours. What mass of water, in terms of $m,$ would have the same temperature increase if it absorbed an equal amount of energy? What assumptions did you make?

Yaqub K.
Numerade Educator

Problem 57

Which is lighter: dry or wet air? Explain your answer.

Yaqub K.
Numerade Educator

Problem 58

If you drop a burning candle, it stops burning almost instantly. Suggest two explanations for this phenomenon and then propose testing experiments to rule out those explanations.

Yaqub K.
Numerade Educator

Problem 59

Losing liquid while running While running, you need to transfer 320 $\mathrm{J} / \mathrm{s}$ of thermal energy from your body to the moisture on your skin in order to remain at the same temperature. What mass of perspiration must you evaporate each second? Indicate any assumptions you made.

Yaqub K.
Numerade Educator

Problem 60

Running a marathon When you run a marathon, the opposing force that air exerts on you does $-150 \mathrm{J}$ of work each second. You convert 1000 $\mathrm{J}$ of internal chemical energy
to thermal energy each second. (a) How much thermal energy must be removed from your body per second to keep your temperature constant? (b) If 50$\%$ of this energy loss is caused by evaporation, how much water do you lose per second? (c) How much water do you lose in 3 $\mathrm{h}$ ?

Yaqub K.
Numerade Educator

Problem 61

Global climate change Assume that because of increasing $\mathrm{CO}_{2}$ concentration in the atmosphere, the net radiation energy transfer rate for Earth and its atmosphere is $+0.002 \times 1350 \mathrm{W} / \mathrm{m}^{2}$ , corresponding to a 0.2$\%$ decrease in radiation leaving Earth. (a) Determine the extra thermal energy added to Earth and its atmosphere in 10 years. [Note: The radiation falls on an area approximately equal to $\pi r_{\text { Earth }}^{2}$ where $r_{\text { Earth }}=6.4 \times 10^{6} \mathrm{m} . ](\mathrm{b})$ If 30$\%$ of this energy is used to melt the polar ice caps, how many kilograms of ice will melt in 10 years? (c) How many cubic meters of ice will melt? (d) By how much will the level of the oceans rise in 10 years?

Yaqub K.
Numerade Educator

Problem 62

Standard house 1 On an average winter day $\left(3^{\circ} \mathrm{C} \text { or } 38^{\circ} \mathrm{F}\right)$ in a typical house, energy already in the house is lost at the following rates: (i) 2.1 $\mathrm{kW}$ is lost through partially insulated walls and the roof by conduction; (ii) 0.3 $\mathrm{kW}$ is lost through the floor by conduction; and (iii) 1.9 $\mathrm{kW}$ is lost by conduction through the windows. Additional heating is also needed at the following rates: (iv) 2.3 $\mathrm{kW}$ to heat the air infiltrating the house through cracks, flues, and other openings and (v) 1.1 $\mathrm{kW}$ to humidify the incoming air (because warm air must contain more water vapor than cold air for people to be comfortable). What is the total rate at which energy is lost from this house?

Yaqub K.
Numerade Educator

Problem 63

$*$ Standard house 2 On the same day in the same house described in the previous problem, some thermal energy is supplied by heating in the following amounts: (i) sunlight through windows, $0.5 \mathrm{kW} ;$ (ii) thermal energy given off by the inhabitants, $0.2 \mathrm{kW} ;$ and (iii) thermal energy from appliances, 1.2 kW. How many kilowatts must be supplied to this standard house by the heating system to keep its temperature constant?

Yaqub K.
Numerade Educator

Problem 64

$*$ Standard house 3 Suppose that the following design changes are made to the house described in the previous two problems: (i) additional insulation of walls, roof, and floors, cutting thermal losses by $60 \% ;(\text { ii ) tightly fitting }$ double-glazed windows with selective coatings to reduce the
passage of infrared light, cutting conduction losses by 70$\%$ and (iii) elimination of cracks, closing of flues, and so on, cutting infiltration losses by 70$\% .$ What is the total rate at which energy is lost from this house?

Yaqub K.
Numerade Educator

Problem 65

Standard house 4 After further improvements (shifting windows from the north to the south sides and replacing outmoded appliances), thermal energy is supplied to the house described above at the following rates: (i) sunlight through windows, $1.0 \mathrm{kW} ;$ (ii) people's warmth, $0.2 \mathrm{kW} ;$ and (iii) appliance warmth, 0.8 $\mathrm{kW}$ . How many kilowatts must be supplied by the heating system of this house to keep it at constant temperature?

Yaqub K.
Numerade Educator

Problem 66

Metabolism warms bedroom Because of its metabolic processes, your body continually emits thermal energy. Suppose that the air in your bedroom absorbs all of this thermal energy during the time you sleep at night. Estimate the temperature change you expect in this air. Indicate any assumptions you make.

Yaqub K.
Numerade Educator

Problem 67

You have an $850-\mathrm{W}$ electric kettle. Estimate the least amount of time you have to boil water before 10 guests arrive for a tea break. State clearly all numbers that you use in your estimate.

Yaqub K.
Numerade Educator

Problem 68

House ventilation For purposes of ventilation, the inside air in a home should be replaced with outside air once every 2 hours. This air infiltration occurs naturally by leakage through tiny cracks around doors and windows, even in well- caulked and weather-stripped homes. ( a) Estimate the mass
of air lost every 2 $\mathrm{h}$ and each second. (b) Estimate the energy per second needed to warm outside air leaking into the house during a winter night. State your assumptions.

Yaqub K.
Numerade Educator

Problem 69

Frostbite When exposed to very cold temperatures, the human body maintains core body temperature by reducing blood circulation to the skin and extremities, and skin and extremity temperatures drop. This can eventually lead to frost bite. Explain why this helps conserve thermal energy.

Yaqub K.
Numerade Educator

Problem 70

Heating an event center with metabolic energy Estimate the temperature change in some enclosure on your campus during an athletic event. Assume that there is no thermal energy transfer into or out of the building during the event. Indicate any other assumptions you make.

Yaqub K.
Numerade Educator

Problem 71

Lightning warms body A lightning flash releases about $10^{10} \mathrm{J}$ of electrical energy. Quantitatively estimate the effect on your body if you absorbed 10$\%$ of the energy. State
clearly any assumptions you made.

Yaqub K.
Numerade Educator

Problem 72

If no condensation occurred, how high would $40^{\circ} \mathrm{C}$ humid air have to rise before its temperature decreased to $10^{\circ} \mathrm{C} ?$

(a) 1000 m (b) 2000 m (c) 3000 m
(d) 6000 m (e) 10,000 m

Yaqub K.
Numerade Educator

Problem 73

When rising humid air starts to condense, why does its temperature change less rapidly with increasing elevation?

(a) Its density increases, making it more difficult to change temperature.
(b) Thermal energy released during condensation causes less thermal energy change.
(c) The gas expands less, causing less negative work.
(d) The temperature of the surrounding air is changing less.

Yaqub K.
Numerade Educator

Problem 74

After crossing a mountain top on a warm sunny day, what should cool dry air do?
(a) $\operatorname{sink}$ , because it is denser than warmer air below
(b) Warm, because the surrounding gas does positive work in causing it to contract
(c) Not change, as the surrounding air transfers little thermal energy by heating $(Q \approx 0)$
(d) and b are correct.

Yaqub K.
Numerade Educator

Problem 75

Why does humid air rise in dry air?
(a) Water is attracted to the clouds above.
(b) A water molecule has lower mass than other air molecules.
(c) 1 $\mathrm{m}^{3}$ of humid air has fewer molecules than 1 $\mathrm{m}^{3}$ of dry air at the same $T$ and $P .$
(d) $\mathrm{b}$ and $\mathrm{c}$ are correct.
(e) None of the above is correct.

Yaqub K.
Numerade Educator

Problem 76

If 1 $\mathrm{m}^{3}$ of dry air rises 5000 $\mathrm{m}$ and has no temperature change,
what would its volume be?
$\begin{array}{ll}{\text { (a) } 0.3 \mathrm{m}^{3}} & {\text { (b) } 0.5 \mathrm{m}^{3}} & {\text { (c) } 1.5 \mathrm{m}^{3}} \\ {\text { (d) } 2.0 \mathrm{m}^{3}} & {\text { (e) Too little information to answer }}\end{array}$

Yaqub K.
Numerade Educator

Problem 77

The magnitude of the thermal energy released from the
water molecules to the air if 1.0 $\mathrm{g}$ of water vapor condensed to
1.0 $\mathrm{g}$ of liquid water is closest to which of the following?
$\begin{array}{ll}{\text { (a) } 300 \mathrm{J}} & {\text { (b) } 500 \mathrm{J}} & {\text { (c) } 1000 \mathrm{J}} \\ {\text { (d) } 2000 \mathrm{J}} & {\text { (e) } 2 \times 10^{6} \mathrm{J}}\end{array}$

Yaqub K.
Numerade Educator

Problem 78

The initial kinetic energy of the meteorite was closest to
$\begin{array}{ll}{\text { (a) } 2 \times 10^{13} \mathrm{J}} & {\text { (b) } 3 \times 10^{15} \mathrm{J}} \\ {\text { (c) } 3 \times 10^{16} \mathrm{J}} & {\text { (d) } 5 \times 10^{16} \mathrm{J}}\end{array}$

Yaqub K.
Numerade Educator

Problem 79

The radius of the meteorite was closest to
$\begin{array}{ll}{\text { (a) } 10 \mathrm{m}} & {\text { (b) } 30 \mathrm{m}} & {\text { (c) } 50 \mathrm{m}} \\ {\text { (d) } 100 \mathrm{m}} & {\text { (e) } 1000 \mathrm{m}}\end{array}$

Yaqub K.
Numerade Educator

Problem 80

The gravitational potential energy change was closest to
$\begin{array}{llll}{\text { (a) } 10^{7} \mathrm{J}} & {\text { (b) } 10^{9} \mathrm{J}} & {\text { (c) } 10^{\text { 11 }} \mathrm{J}}\end{array}$
(d) $10^{13} \mathrm{J} \quad$ (e) $10^{15} \mathrm{J}$

Yaqub K.
Numerade Educator

Problem 81

The energy needed to warm the solid meteorite to its
melting temperature at $1700^{\circ} \mathrm{C}$ is closest to
$\begin{array}{ll}{\text { (a) } 2 \times 10^{13} \mathrm{J}} & {\text { (b) } 5 \times 10^{14} \mathrm{J}} \\ {\text { (c) } 7 \times 10^{14} \mathrm{J}} & {\text { (d) } 3 \times 10^{15} \mathrm{J}}\end{array}$

Yaqub K.
Numerade Educator

Problem 82

The energy needed to melt the solid meteorite at its
$1700^{\circ} \mathrm{C}$ melting temperature is closest to
$\begin{array}{ll}{\text { (a) } 2 \times 10^{13} \mathrm{J}} & {\text { (b) } 5 \times 10^{14} \mathrm{J}} \\ {\text { (c) } 7 \times 10^{14} \mathrm{J}} & {\text { (d) } 3 \times 10^{15} \mathrm{J}}\end{array}$

Yaqub K.
Numerade Educator

Problem 83

The energy needed to vaporize the melted meteorite at its
$2600^{\circ} \mathrm{C}$ boiling temperature is closest to
$\begin{array}{ll}{\text { (a) } 2 \times 10^{13} \mathrm{J}} & {\text { (b) } 5 \times 10^{14} \mathrm{J}} \\ {\text { (c) } 7 \times 10^{14} \mathrm{J}} & {\text { (d) } 3 \times 10^{15} \mathrm{J}}\end{array}$

Yaqub K.
Numerade Educator

Problem 84

Is the initial kinetic energy enough to vaporize the meteorite?
(a) Yes
(b) No
(c) Too little information to answer

Yaqub K.
Numerade Educator