Essential University Physics Global Edition

Richard Wolfson

Chapter 16

Temperature and Heat - all with Video Answers

Educators

Chapter Questions

Problem 1

Does a thermometer measure its own temperature or the temperature of its surroundings? Explain.

Dading Chen

Dading Chen

Numerade Educator

Problem 2

Compare the relative sizes of the kelvin, the degree Celsius, the degree Fahrenheit, and the degree Rankine.

Dading Chen

Numerade Educator

Problem 3

If you put a thermometer in direct sunlight, what do you measure: the air temperature, the temperature of the Sun, or some other temperature?

Dading Chen

Numerade Educator

Problem 4

When wooden and metal chairs are kept in the garden overnight, the metal ones always seem colder. Why?

Jacob Paiste

Numerade Educator

Problem 5

Deserts are always very hot during the day and get very cold at night. Why?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 6

Should a material used as a heating element have low or high thermal conductivity? Why?

Narayan Hari

Numerade Educator

Problem 7

What is the difference between heat energy and internal energy?

Nathan Silvano

Numerade Educator

Problem 8

Glass and fiberglass are made from the same material, yet have dramatically different thermal conductivities. Why?

Dading Chen

Numerade Educator

Problem 9

To keep your hands warm while skiing, you should wear mittens instead of gloves. Why?

Dading Chen

Numerade Educator

Problem 10

Global warming at Earth's surface is generally producing greater temperature rises over land than over the oceans. Why might this be?

Dading Chen

Numerade Educator

Problem 11

A 2017 Stanford University study suggests there's a $50 \%$ chance EN that the global temperature increase by the year 2100 will lie in the range $3.0^{\circ} \mathrm{C}$ to $4.2^{\circ} \mathrm{C}$. Translate this range into Fahrenheit.

Shoukat Ali

Other Schools

Problem 12

An American meteorologist predicts an overnight low of $14^{\circ} \mathrm{F}$. How would a Mexican meteorologist express that prediction?

Dading Chen

Numerade Educator

Problem 13

Normal room temperature is $75^{\circ} \mathrm{F}$. What's this in Celsius?

Dading Chen

Numerade Educator

Problem 14

The outdoor temperature rises by $27^{\circ} \mathrm{F}$. What's that rise in Celsius?

Dading Chen

Numerade Educator

Problem 15

At what temperature do the Fahrenheit and Celsius scales coincide?

Dading Chen

Numerade Educator

Problem 16

The normal boiling point of nitrogen is $77.3 \mathrm{~K}$. Express this in Celsius and Fahrenheit.

Dading Chen

Numerade Educator

Problem 17

A sick child's temperature reads $39.5$ on a Celsius thermometer. What's the temperature in Fahrenheit?

Dading Chen

Numerade Educator

Problem 18

Find the heat capacity of a 55 -tonne concrete slab.

Shoukat Ali

Other Schools

Problem 19

Find the energy needed to raise the temperature of a $2.2-\mathrm{kg}$ chunk of aluminum by $18^{\circ} \mathrm{C}$.

Dading Chen

Numerade Educator

Problem 20

What's the specific heat of a material if it takes $7.5 \mathrm{~kJ}$ to increase the temperature of a $1-\mathrm{kg}$ sample by $3.0^{\circ} \mathrm{C}$ ?

Dading Chen

Numerade Educator

Problem 21

The average human diet contains about $2000 \mathrm{kcal}$ per day. If all this food energy is released rather than stored as fat, what's the approximate average power output of the human body?

Dading Chen

Numerade Educator

Problem 22

Walking at $3 \mathrm{~km} / \mathrm{h}$ requires an energy expenditure rate of about $200 \mathrm{~W}$. How far would you have to walk to "burn off" a $390-\mathrm{kcal}$ slice of chocolate cake?

Dading Chen

Numerade Educator

Problem 23

(a) How much heat does it take to bring a 3.4-kg iron skillet from $20^{\circ} \mathrm{C}$ to $130^{\circ} \mathrm{C}$ ? (b) If the heat is supplied by a stove burner at the rate of $2.0 \mathrm{~kW}$, how long will it take to heat the pan?

Dading Chen

Numerade Educator

Problem 24

Building heat loss in the United States is usually expressed in Btu/h. What's I Btu/h in SI units?

Shoukat Ali

Other Schools

Problem 25

Find the magnitude of the heat-loss rate per square meter through slabs of (a) wood and (b) Styrofoam, each $5.0 \mathrm{~cm}$ thick, if one surface is at $20^{\circ} \mathrm{C}$ and the other is at $-5^{\circ} \mathrm{C}$.

Shoukat Ali

Other Schools

Problem 26

You're a builder who's advising a homeowner to have her foun-
ENN dation walls insulated with 2 inches of Styrofoam. To make your point, you tell her how thick the concrete walls (normally 8 inches) would have to be to have the same insulating value as 2 inches of Styrofoam. What's this thickness?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 27

A $17 \mathrm{~m}$ by $4.5 \mathrm{~m}$ house is built on a concrete slab $17 \mathrm{~cm}$ thick. Find the heat-loss rate through the floor if the interior is at $30^{\circ} \mathrm{C}$ while the ground is at $20^{\circ} \mathrm{C}$.

Dading Chen

Numerade Educator

Problem 28

Find the $\mathcal{R}$-factor for a wall that loses $0.040$ Btu each hour through each square foot for each ${ }^{\circ} \mathrm{F}$ temperature difference.

Dading Chen

Numerade Educator

Problem 29

Compute the $\mathcal{R}$-factors for 1 -inch thicknesses of air, concrete, fiberglass, glass, Styrofoam, and wood.

Dading Chen

Numerade Educator

Problem 30

A horseshoe has surface area $50 \mathrm{~cm}^{2}$, and a blacksmith heats it to a red-hot $880^{\circ} \mathrm{C}$. At what rate does it radiate energy?

Dading Chen

Numerade Educator

Problem 31

An oven loses energy at the rate of $16 \mathrm{~W}$ per ${ }^{\circ} \mathrm{C}$ temperature difference between its interior and the $18^{\circ} \mathrm{C}$ temperature of the kitchen. What average power must be supplied to maintain the oven at $240^{\circ} \mathrm{C}$ ?

Dading Chen

Numerade Educator

Problem 32

You're having your home's heating system replaced, and the heating contractor has specified a new system that supplies energy at the maximum rate of $40 \mathrm{~kW}$. You know that your house loses energy at the rate of $1.3 \mathrm{~kW}$ per ${ }^{\circ} \mathrm{C}$ temperature difference between interior and exterior, and the minimum winter temperature in your area is $-15^{\circ} \mathrm{C}$. You'd like to maintain $20^{\circ} \mathrm{C}\left(68^{\circ} \mathrm{F}\right)$ indoors. Should you go with the system your contractor recommends?

Dading Chen

Numerade Educator

Problem 33

The filament of a 100 -W lightbulb is at $3.0 \mathrm{kK}$. What's the filament's surface area?

Dading Chen

Numerade Educator

Problem 34

A typical human body has surface area $1.4 \mathrm{~m}^{2}$ and skin temBio perature $33^{\circ} \mathrm{C}$. If the body's emissivity is about 1 , what's the net radiation from the body when the ambient temperature is $20^{\circ} \mathrm{C}$ ?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 35

Example 16.2: An iron frying pan of mass $2.65 \mathrm{~kg}$ is at $144^{\circ} \mathrm{C}$ when it's plunged into a sink full of $10.9 \mathrm{~kg}$ of water at $21.0^{\circ} \mathrm{C}$. Assuming no heat loss, what's the equilibrium temperature of the water and pan?

Shoukat Ali

Other Schools

Problem 36

Example 16.2: You've got a 2.33-kg aluminum skillet on a hot stove burner, and the skillet is at a sizzling $286^{\circ} \mathrm{C}$. You plan to plunge the skillet into $25^{\circ} \mathrm{C}$ water to cool it. What's the minimum amount of water that will keep the equilibrium temperature below $40^{\circ} \mathrm{C} ?$

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 37

Example 16.2: During the refueling of a nuclear power plant, 248 spent fuel assemblies are moved from the reactor to a spent fuel pool. Each fuel assembly has mass $322 \mathrm{~kg}$ and specific heat $284 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$, and they come from the reactor at an average temperature of $658^{\circ} \mathrm{C}$. The spent fuel pool contains 1720 tonnes ( 1720 $\mathrm{Mg}$ ) of water initially at $15.0^{\circ} \mathrm{C}$. By how much does the water temperature increase once it comes to equilibrium with the fuel rods? (In this situation, though, the water temperature rises further because of energy generated by radioactive decay in the fuel rods.) Example 16.2: A manufacturer of brass starts with $755 \mathrm{~kg}$ of mol-

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 38

Example 16.2: A manufacturer of brass starts with $755 \mathrm{~kg}$ of mol- ten copper at $1350^{\circ} \mathrm{C}$, then adds molten zinc at $469^{\circ} \mathrm{C}$. The specific ten copper at $1350^{\circ} \mathrm{C}$, then adds molten zinc at $469^{\circ} \mathrm{C}$. The specific heats of molten copper and zinc are respectively $572 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ and heats of molten copper and zinc are respectively $572 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ and $497 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$. If the equilibrium temperature of the mix is $1170^{\circ} \mathrm{C}$, what percent of the alloy's mass is zinc?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 39

Example 16.7: A solar greenhouse has $435 \mathrm{ft}^{2}$ of $\mathcal{R}-45$ walls and $285 \mathrm{ft}^{2}$ of $\mathcal{R}-2.1$ glass that admits solar energy at the average rate of $35.6 \mathrm{Btu} / \mathrm{h} / \mathrm{ft}^{2}$. Find the greenhouse temperature on a day when the outdoor temperature is $-10.5^{\circ} \mathrm{F}$.

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 40

Example 16.7: A solar greenhouse in Europe has $51.5 \mathrm{~m}^{2}$ of walls insulated to $\mathcal{R}=9.56 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}$ and $32.3 \mathrm{~m}^{2}$ of glass with $\mathcal{R}=0.21 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}$ that admits solar energy at the average rate of $112 \mathrm{~W} / \mathrm{m}^{2}$. What's the minimum outdoor temperature for which the greenhouse interior will stay above freezing?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 41

Example 16.7: An asteroid in the belt between Mars and Jupiter absorbs solar energy at the average rate of $96.2 \mathrm{~W}$ for every square meter of its surface. If the asteroid behaves like a blackbody, what's its surface temperature?

Prabhu Ramji

Numerade Educator

Problem 42

Example 16.7: The habitable zone around a given star is defined as the region in which a planet's surface temperature is consistent with the existence of liquid water. The red dwarf star Trappist-1 has a luminosity (total power output) only $0.000522$ that of the Sun. Determine the range of distances from Trappist-1 that mark its habitable zone. Assume terrestrial atmospheric pressure, under which water freezes at $0^{\circ} \mathrm{C}$ and boils at $100^{\circ} \mathrm{C}$. Assume also that any planet in this range behaves like a blackbody and, for the reason described this chapter's Application: The Greenhouse Effect and Global Warming, that a planet absorbs solar energy over its cross-sectional area but radiates from its entire surface. Hint: You'll need to consult the inside back cover and maybe review Section 14.4. (There are, in fact, seven planets in Trappist-1's habitable zone.)

Shoukat Ali

Other Schools

Problem 43

A constant-volume gas thermometer is filled with air whose pressure is $101 \mathrm{kPa}$ at the normal melting point of ice. What would its pressure be at (a) the normal boiling point of water $(373 \mathrm{~K}),(b)$ the normal boiling point of oxygen $(90.2 \mathrm{~K})$, and $(\mathrm{c})$ the normal boiling point of mercury $(630 \mathrm{~K})$ ?

Prabhu Ramji

Numerade Educator

Problem 44

A constant-volume gas thermometer is at $55-\mathrm{kPa}$ pressure at the triple point of water. By how much does its pressure change for each kelvin temperature change?

Dading Chen

Numerade Educator

Problem 45

In Fig. $16.2$ 's gas thermometer, the height $h$ is $60.4 \mathrm{~mm}$ at the triple point of water. When the thermometer is immersed in boiling sulfur dioxide, the height drops to $57.7 \mathrm{~mm}$. What is the boiling point of $\mathrm{SO}_{2}$ in kelvins and in degrees Celsius?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 46

If your mass is $67 \mathrm{~kg}$, what's the minimum number of calories
Bo (kcal) you would "burn off" climbing a 1600 -m-high mountain?
(Note: The actual metabolic energy used would be much greater.)

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 47

Typical fats contain about 9 kcal per gram. If the energy in body fat
Ba could be utilized with $100 \%$ efficiency, how much mass would a runner lose in a $26.2$-mile marathon while consuming $125 \mathrm{kcal} / \mathrm{mile}$ ?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 48

A circular lake $1.0 \mathrm{~km}$ in diameter
ENV is $10 \mathrm{~m}$ deep (Fig. 16.14). Solar energy is incident on the lake at an average rate of $200 \mathrm{~W} / \mathrm{m}^{2}$. If the lake absorbs all this energy and does not exchange heat with its surroundings, how long will it take to warm from $10^{\circ} \mathrm{C}$
$20^{\circ} \mathrm{C}$ ?
FIGURE $16.14$ Problem 48
ergy and does not exchange heat
with its surroundings, how long
will it take to warm from $10^{\circ} \mathrm{C}$ FIGRE $16.14$ Problem 48

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 49

How much heat is required to raise a $770-\mathrm{g}$ copper pan from $14^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ if (a) the pan is empty or contains (b) $1.1 \mathrm{~kg}$ of water and (c) $4.2 \mathrm{~kg}$ of mercury?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 50

Initially, $100 \mathrm{~g}$ of water and $100 \mathrm{~g}$ of another substance listed in Table $16.1$ are at $20^{\circ} \mathrm{C}$. Heat is then transferred to each substance at the same rate for $1.0 \mathrm{~min}$. At the end of that time, the water is at $29^{\circ} \mathrm{C}$ and the other substance at $95^{\circ} \mathrm{C}$. (a) What's the other substance? (b) What's the heating rate?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 51

You draw $300 \mathrm{~mL}$ of $15^{\circ} \mathrm{C}$ water from the tap and pop it into a $900-\mathrm{W}$ microwave oven to heat for tea. How long should you microwave the water so it just reaches the boiling point?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 52

Two families travel to the U.S. during winter and rent two houses for their holidays. Both houses have not been heated and the
temperature inside is a frigid $32^{\circ} \mathrm{F}$. Each house has a furnace that can supply $100,000 \mathrm{Btu} / \mathrm{h}$. One house is made of stone and weighs 70 tons. The other is wood and weighs 17 tons. How long does it take each house to reach $68^{\circ} \mathrm{F}$ ? Neglect heat loss, and assume the entire house mass reaches a uniform temperature.

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 53

You're arguing with your roommate about whether it's quicker to heat water on a stove burner or in a microwave. The burner supplies energy at the rate of $1.0 \mathrm{~kW}$, the microwave at $625 \mathrm{~W}$. You can heat water in the microwave in a paper cup of negligible heat capacity, but the stove requires a pan with heat capacity $1.4 \mathrm{~kJ} / \mathrm{K}$. How much water do you need before it becomes quicker to heat on the stovetop? Neglect energy loss to the surroundings.

Dading Chen

Numerade Educator

Problem 54

In the 2011 nuclear accident at Fukushima, Japan, an EN earthquake-triggered tsunami wiped out emergency generators, leaving three reactors without a source of cooling water. Although safety systems shut down the reactors during the earthquake, radioactive decay continued to generate thermal energy at the rate of some $33 \mathrm{MW}$. In a desperate attempt to cool the reactors, operators used fire engines to pump seawater into the reactors. If $650 \mathrm{~m}^{3}$ of $10^{\circ} \mathrm{C}$ seawater were injected into a reactor, how long would it take that $33 \mathrm{MW}$ of themal power to bring the water to the boiling point?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 55

A $1.0-\mathrm{kg}$ iron tea kettle sits on a $2.2-\mathrm{kW}$ stove burner. If it takes $5.9$ min to bring the kettle and the water in it from $21^{\circ} \mathrm{C}$ to the boiling point, how much water is in the kettle?

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 56

The temperature of the eardrum provides a reliable measure of Bio deep body temperature and is measured quickly with ear thermometers that sense infrared radiation. A thermometer that "views" $1 \mathrm{~mm}^{2}$ of the eardrum requires $100 \mu \mathrm{J}$ of energy for a reliable reading at normal $37^{\circ} \mathrm{C}$ body temperature. How long does the measurement take?

Narayan Hari

Numerade Educator

Problem 57

A $2100-\mathrm{kg}$ car moving at $85 \mathrm{~km} / \mathrm{h}$ is brought to a sudden stop. If all the car's energy is dissipated in heating its four $5.8-\mathrm{kg}$ steel brake disks, by how much do the disk temperatures increase?

Dading Chen

Numerade Educator

Problem 58

A washing machine's "warm" setting calls for water at $34.0^{\circ} \mathrm{C}$. If the cold-water supply is at $12.4^{\circ} \mathrm{C}$ and the hot-water supply is at $51.7^{\circ} \mathrm{C}$, what ratio of hot to cold water should the washing machine's fill valves admit to the machine?

Shoukat Ali

Other Schools

Problem 59

A piece of copper at $260^{\circ} \mathrm{C}$ is dropped into $1.4 \mathrm{~kg}$ of water at $24^{\circ} \mathrm{C}$. If the equilibrium temperature is $29^{\circ} \mathrm{C}$, what's the mass of the copper?

Dading Chen

Numerade Educator

Problem 60

While camping, you boil water to make spaghetti. Your pot contains $2.1 \mathrm{~kg}$ of water initially at $10^{\circ} \mathrm{C}$. You stoke up the campfire, and as a result the water gains energy at an increasing rate: $P=a+b t$, where $a=1.1 \mathrm{~kW}, b=2.5 \mathrm{~W} / \mathrm{s}$, and $t$ is the time in $\mathrm{s}$. To the nearest minute, how long will it take to bring the water to a boil?

Dading Chen

Numerade Educator

Problem 61

A biology lab's walk-in cooler measures $3.0 \mathrm{~m}$ by $2.0 \mathrm{~m}$ by $2.3 \mathrm{~m}$ and is insulated with $8.0$-cm-thick Styrofoam. If the surrounding building is at $20^{\circ} \mathrm{C}$, at what average rate must the cooler's refrigeration unit remove heat in order to maintain $4.0^{\circ} \mathrm{C}$ in the cooler?

Dading Chen

Numerade Educator

Problem 62

One end of an iron rod $36 \mathrm{~cm}$ long and $2.8 \mathrm{~cm}$ in diameter is in ice water, the other in boiling water (Fig. $16.15$ ). The rod is well insulated so no heat is lost out the sides. Find the heat-flow rate along the rod.

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 63

You arrive for a party on a lice water Boiling water night when it's $8^{\circ} \mathrm{C}$ outside.
night when it's $8^{\circ} \mathrm{C}$ outside. FIGURE 16.15 Problem 62 Your hosts meet you at the
door and say the party may need to be cancelled, because the heating system has failed and they don't want to discomfort their guests. You say, "Not so fast!" A total of 36 people are expected, the average power output of a human body is $100 \mathrm{~W}$, and the house loses energy at the rate $320 \mathrm{~W} /{ }^{\circ} \mathrm{C}$. Will the house remain comfortable?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 64

An electric stove burner has surface area $325 \mathrm{~cm}^{2}$ and emissivity $e=1$. The burner consumes $1500 \mathrm{~W}$ and is at $900 \mathrm{~K}$. If room temperature is $300 \mathrm{~K}$, what fraction of the burner's heat loss is from radiation?

Dading Chen

Numerade Educator

Problem 65

In a low-temperature physics experiment, a metal block is sur$\mathrm{CH}$ rounded on five faces by near-perfect insulation that prevents any conductive heat loss, and it's coated on those faces with a perfect reflector that prevents radiation. The remaining face is painted black so it behaves like a blackbody of emissivity 1 , and it's covered with a slab of material with themal conductivity $k$ and thickness $d$ that's transparent to radiation. The other side of the slab is in contact with liquid helium at nearly $0 \mathrm{~K}$. (a) Find an expression for the temperature of the metal block if it loses energy equally by radiation and conduction. You can assume that heat flows straight through the slab, perpendicular to its interface with the metal block, with no heat loss out its sides. (b) Evaluate your expression when the slab is $2.85$ $\mathrm{cm}$ thick and is made of insulating foam with $k=0.0166 .$

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 66

You're considering purchasing a new sleeping bag whose man-
Bio ufacturer claims it will keep you warm to $-10^{\circ} \mathrm{F}$. The bag has down insulation with $4.0$-cm loft (thickness). Your body produces heat at the rate of $100 \mathrm{~W}$ and has area $1.5 \mathrm{~m}^{2}$. Considering only conductive heat loss, will you be able to maintain normal body temperature in the bag at $-10^{\circ} \mathrm{F}$ ?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 67

A blacksmith heats a $1.1-\mathrm{kg}$ iron horseshoe to $550^{\circ} \mathrm{C}$, then plunges it into a bucket containing $15 \mathrm{~kg}$ of water at $20^{\circ} \mathrm{C}$. What's the equilibrium temperature?

Dading Chen

Numerade Educator

Problem 68

What's the power output of a microwave oven that can heat 430 $\mathrm{g}$ of water from $20^{\circ} \mathrm{C}$ to the boiling point in $2.5 \mathrm{~min}$ ? Neglect the container's heat capacity.

Dading Chen

Numerade Educator

Problem 69

A cylindrical log $15 \mathrm{~cm}$ in diameter and $65 \mathrm{~cm}$ long is glowing red hot in a fireplace. The log's emissivity is essentially 1 . If it's emitting radiation at the rate of $34 \mathrm{~kW}$, what's its temperature?

Dading Chen

Numerade Educator

Problem 70

A blue giant star whose surface temperature is $23 \mathrm{kK}$ radiates energy at the rate of $3.4 \times 10^{30}$ W. Find the star's radius, assuming it behaves like a blackbody.

Shoukat Ali

Other Schools

Problem 71

Rework Example $16.4$, now assuming the house has 10 ENV single-glazed windows, each measuring $2.5 \mathrm{ft}$ by $5.0 \mathrm{ft}$. Four of the windows are on the south, and each admits solar energy at the average rate of $30 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}$. All the windows lose heat; their $\mathcal{R}$-factor is $0.90$. (a) Find the total heating cost for the month. (b) How much is the solar gain worth?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 72

In 2014 the European Space Agency's Rosetta spacecraft was $5000 \mathrm{~km}$ from the comet 67 P/Churyumov-Gerasimenko. Rosetta turned its infrared sensors toward the comet and measured a flux of $96.3 \mathrm{~W}$ per square meter of cometary surface. Assuming the dark, dusty comet radiated like a blackbody, what was its temperature?

Shoukat Ali

Other Schools

Problem 73

Estimate the average temperature on Pluto, treating the dwarf planet as a blackbody whose great distance from the Sun means that it receives energy from the Sun at the rate of only $0.876 \mathrm{~W} / \mathrm{m}^{2}$.

Shoukat Ali

Other Schools

Problem 74

The table below shows temperature versus time for $500 \mathrm{~g}$ of waDATA ter heated in a microwave oven. In a microwave, essentially all the microwave energy goes into the water-containing food in the oven. Plot the data, determine a best-fit line, and use the slope of your line to determine the microwave power of this particular oven. Assume that water's specific heat is independent of temperature (which is only approximately true; see Problem 75 ).
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Time (s) & 0 & 25 & 60 & 95 & 125 & 160 & 190 \\
\hline Temperature $\left({ }^{\circ} \mathrm{C}\right)$ & 12 & 20 & 39 & 53 & 64 & 83 & 93 \\
\hline
\end{tabular}

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 75

Water's specific heat in the range from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ varies with tem$\mathrm{CH}$ perature according to the equation $c(T)=c_{0}+a T+b T^{2}$, where $c_{0}=4207.9 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}, a=-1.292 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}^{2}$, and $b=0.01330 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}^{3}$.
Use this expression to find the heat required to raise the temperature of $1.000 \mathrm{~kg}$ of water from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$. By what percentage does this differ from the result you would get using the value of $c$ in Table $16.1$ over the entire temperature range?

Umar Sohail Qureshi

Umar Sohail Qureshi

Numerade Educator

Problem 76

At low temperatures, the specific heats of solids are approximately cH proportional to the cube of the temperature: $c(T)=a\left(T / T_{0}\right)^{3}$. For copper, $a=31 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K}$ and $T_{0}=343 \mathrm{~K}$. Find the heat required to bring $33 \mathrm{~g}$ of copper from $13.0 \mathrm{~K}$ to $29.0 \mathrm{~K}$.

Dading Chen

Numerade Educator

Problem 77

The Application on global warming (page 322 ) gives $960 \mathrm{~W} / \mathrm{m}^{2}$ ENV as the average rate at which solar energy reaches Earth. You can approximate the solar energy rate reaching other planets by scaling this quantity by the inverse square of the planet's distance from the Sun (see Appendix E)-although what you'll get is only an approximation because that $960 \mathrm{~W} / \mathrm{m}^{2}$ includes effects of clouds and reflection that are unique to Earth and, more importantly, it neglects the greenhouse effect. Follow the procedure used in the Application to find approximations to the temperatures of Mars and Venus, and compare with their mean measured surface temperatures (you'll have to research those). Your results suggest that Mars has very little greenhouse effect, while Venus exhibits a "runaway" greenhouse effect resulting in a very high surface temperature.

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 78

In a cylindrical pipe where area isn't constant, Equation $16.5$ CH takes the form $H=-k A(d T / d r)$, where $r$ is the radial coordinate measured from the pipe axis. Use this equation to show that the heat-loss rate from a cylindrical pipe of radius $R_{1}$ and length $L$ is
$$
H=\frac{2 \pi k L\left(T_{1}-T_{2}\right)}{\ln \left(R_{2} / R_{1}\right)}
$$
where the pipe is surrounded by insulation of outer radius $R_{2}$ and thermal conductivity $k$ and where $T_{1}$ and $T_{2}$ are the temperatures at the pipe surface and the outer surface of the insulation, respec-
tively_ (Hint: Consider the heat - FIGURE $16.16$ Problem 78

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 79

A friend who's skeptical about climate change argues that the ENV roughly $0.85^{\circ} \mathrm{C}$ increase in Earth's temperature during the industrial era could be caused by an increase in the Sun's power output. The Sun's average power has, in fact, increased by about $0.05 \%$ during this time. Could your friend be right?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 80

You are planning to insulate the walls in your home, and you are told that the minimum insulation level needed is $\mathcal{R}$-factor $3.5 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}$.
You've got some U.S.-made $\mathcal{R}-19$ fiberglass insulation. Will it do?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 81

A passive solar house has south-facing windows that, in winter, ENV admit solar energy at an average rate of $2.1 \mathrm{~kW}$. The house is well insulated, losing only $60 \mathrm{~W}$ for every ${ }^{\circ} \mathrm{C}$ temperature difference between inside and outside. What's the minimum outdoor temperature for which the house can maintain $20^{\circ} \mathrm{C}$ inside?

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 82

A more realistic approach to the solar greenhouse of Example $16.7$ comp considers the time dependence of the solar input. A function that apEN proximates the solar input is $\left(40 \mathrm{Btu} / \mathrm{h} / \mathrm{ft}^{2}\right) \sin ^{2}(\pi t / 24)$, where $t$ is the time in hours, with $t=0$ at midnight. Then the greenhouse is no longer in energy balance, but is described instead by the differential form of Equation $16.3$ with $Q$ the time-varying energy input. Use computer software or a calculator with differential-equation-solving capability to find the time-dependent temperature of the greenhouse, and determine the maximum and minimum temperatures. Assume the same numbers as in Example $16.7$, along with a heat capacity $C=1500 \mathrm{Btu} /{ }^{\circ} \mathrm{F}$ for the greenhouse. You can assume any reasonable value for the initial temperature, and after a few days your greenhouse temperature should settle into a steady oscillation independent of the initial value.

Morgan Cheatham

Morgan Cheatham

Numerade Educator

Problem 83

Fiberglass insulation owes its insulating quality primarily to
a. the low thermal conductivity of glass.
b. its ability to block cold air infiltration.
c. the low thermal conductivity of air trapped between the glass fibers.

Shoukat Ali

Other Schools

Problem 84

One purpose of foil facing on fiberglass insulation is to reduce heat loss by
a. conduction.
b. convection.
c. radiation.

Dading Chen

Numerade Educator

Problem 85

Fiberglass insulation for attics is available in 12 -inch thickness. Its $\mathcal{R}$-factor is
a. 38 .
b. 76 .
c. $29 .$

Dading Chen

Numerade Educator

Problem 86

Since fiberglass insulation is readily compressible, you could squash two slabs initially 6 inches wide into a 6 -inch wall space.
This would
a. double the overall $\mathcal{R}$-factor.
b. increase the overall $\mathcal{R}$-factor but not double it.
c. decrease the overall $\mathcal{R}$-factor.
d. not change the overall $\mathcal{R}$-factor.

Dading Chen

Numerade Educator