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Essential University Physics

Richard Wolfson

Chapter 16

Temperature and Heat - all with Video Answers

Educators


Chapter Questions

00:54

Problem 1

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

Dading Chen
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04:33

Problem 2

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

Dading Chen
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00:36

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
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00:49

Problem 4

Why does the temperature in a stone building usually vary less than in a wooden building?

Dading Chen
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00:35

Problem 5

Why do large bodies of water exert a temperature-moderating effect on their surroundings?

Dading Chen
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00:51

Problem 6

Stainless-steel cookware often has a layer of aluminum or copper embedded in the bottom. Why?

Dading Chen
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00:26

Problem 7

What method of energy transfer dominates in baking? In broiling?

Dading Chen
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00:30

Problem 8

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

Dading Chen
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00:51

Problem 9

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

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00:57

Problem 10

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

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01:59

Problem 11

A 2017 Stanford University study suggests there's a $50 \%$ chance 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
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00:44

Problem 12

A Canadian meteorologist predicts an overnight low of $-15^{\circ} \mathrm{C}$. How would a U.S. meteorologist express that prediction?

Dading Chen
Dading Chen
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00:42

Problem 13

Normal room temperature is $68^{\circ} \mathrm{F}$. What's this in Celsius?

Dading Chen
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02:38

Problem 14

The outdoor temperature rises by $10^{\circ} \mathrm{C}$. What's that rise in Fahrenheit?

Dading Chen
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01:43

Problem 15

At what temperature do the Fahrenheit and Celsius scales coincide?

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01:52

Problem 16

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

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00:42

Problem 17

A sick child's temperature reads 39.1 on a Celsius thermometer. What's the temperature in Fahrenheit?

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01:53

Problem 18

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

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01:51

Problem 19

Find the energy needed to raise the temperature of a $2.0-\mathrm{kg}$ chunk of aluminum by $18^{\circ} \mathrm{C}$.

Dading Chen
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01:21

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
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01:24

Problem 21

The average human diet contains about 2000 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
Dading Chen
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02:14

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 420 -kcal hamburger?

Dading Chen
Dading Chen
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04:17

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?

Prabhat Tyagi
Prabhat Tyagi
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01:24

Problem 24

Building heat loss in the United States is usually expressed in Btu/h. What's 1 Btu/h in SI units?

Shoukat Ali
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02:45

Problem 25

Find the magnitude of the heat-loss rate per square meter through slabs of (a) wood and (b) Styrofoam, each $2.0 \mathrm{~cm}$ thick, if one surface is at $20^{\circ} \mathrm{C}$ and the other is at $0^{\circ} \mathrm{C}$.

Shoukat Ali
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02:02

Problem 26

You're a builder who's advising a homeowner to have her foundation 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?

Dading Chen
Dading Chen
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01:34

Problem 27

An $8.0 \mathrm{~m}$ by $12 \mathrm{~m}$ house is built on a concrete slab $23 \mathrm{~cm}$ thick. Find the heat-loss rate through the floor if the interior is at $20^{\circ} \mathrm{C}$ while the ground is at $10^{\circ} \mathrm{C}$.

Dading Chen
Dading Chen
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02:32

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
Dading Chen
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02:53

Problem 29

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

Dading Chen
Dading Chen
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01:37

Problem 30

A horseshoe has surface area $50 \mathrm{~cm}^{2},$ and a blacksmith heats it to a red-hot $810^{\circ} \mathrm{C}$. At what rate does it radiate energy?

Dading Chen
Dading Chen
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01:18

Problem 31

An oven loses energy at the rate of $14 \mathrm{~W}$ per ${ }^{\circ} \mathrm{C}$ temperature difference between its interior and the $20^{\circ} \mathrm{C}$ temperature of the kitchen. What average power must be supplied to maintain the nyen at $180^{\circ} \mathrm{C}^{\circ}$

Shoukat Ali
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01:46

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
Dading Chen
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01:37

Problem 33

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

Dading Chen
Dading Chen
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01:41

Problem 34

A typical human body has surface area $1.4 \mathrm{~m}^{2}$ and skin temperature $33^{\circ} \mathrm{C}$. If the body's emissivity is about $1,$ what's the net radiation from the body when the ambient temperature is $18^{\circ} \mathrm{C} ?$

Dading Chen
Dading Chen
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04:57

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
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02:17

Problem 36

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
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 $\mathrm{cool}$ it. What's the minimum amount of water that will keep the equilibrium temperature below $$40^{\circ} \mathrm{C} ?$$

Shoukat Ali
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04:45

Problem 37

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
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 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

Shoukat Ali
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05:00

Problem 38

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
Example 16.2: A manufacturer of brass starts with $755 \mathrm{~kg}$ of molten 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 $497 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K} .$ If the equilibrium temperature of the $\operatorname{mix}$ is $1170^{\circ} \mathrm{C}$
what percent of the alloy's mass is zinc?

Shoukat Ali
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05:36

Problem 39

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
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 $-10.5^{\circ} \mathrm{F}$.

Shoukat Ali
Shoukat Ali
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05:34

Problem 40

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
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?

Shoukat Ali
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02:05

Problem 41

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
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?

Shoukat Ali
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06:27

Problem 42

The following problems are based on two worked examples from the text. Each set of four problems is designed to help you make connections that enhance your understanding of physics and to build your confidence in solving problems that differ from ones you've seen before. The first problem in each set is essentially the example problem but with different numbers. The second problem presents the same scenario as the example but asks a different question. The third and fourth problems repeat this pattern but with entirely different scenarios.
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.

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01:51

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 $(373 \mathrm{~K}),(\mathrm{b})$ the normal boiling point of oxygen $(90.2 \mathrm{~K}),$ and $(\mathrm{c})$ the normal boiling point of mercury $(630 \mathrm{~K}) ?$

Prabhu Ramji
Prabhu Ramji
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01:30

Problem 44

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

Dading Chen
Dading Chen
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03:20

Problem 45

In Fig. 16.2's gas thermometer, the height $h$ is $60.0 \mathrm{~mm}$ at the triple point of water. When the thermometer is immersed in boiling sulfur dioxide, the height drops to $57.8 \mathrm{~mm} .$ What is the boiling point of $\mathrm{SO}_{2}$ in kelvins and in degrees Celsius?

Shoukat Ali
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01:40

Problem 46

If your mass is $60 \mathrm{~kg}$, what's the minimum number of Calories (kcal) you would "burn off" climbing a 1700 -m-high mountain?

Shoukat Ali
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01:20

Problem 47

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

Dading Chen
Dading Chen
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04:26

Problem 48

A circular lake $1.0 \mathrm{~km}$ in diameter 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 $10^{\circ} \mathrm{C}$
to $20^{\circ} \mathrm{C} ?$

Ren Jie Tuieng
Ren Jie Tuieng
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05:19

Problem 49

How much heat is required to raise an $800-\mathrm{g}$ copper pan from $15^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ if (a) the pan is empty or contains
(b) $1.0 \mathrm{~kg}$ of water and (c) $4.0 \mathrm{~kg}$ of mercury?

Dading Chen
Dading Chen
Numerade Educator
05:13

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 $32^{\circ} \mathrm{C}$ and the other substance at $76^{\circ} \mathrm{C}$. (a) What's the other substance? (b) What's the heating rate?

Dading Chen
Dading Chen
Numerade Educator
02:48

Problem 51

You draw $330 \mathrm{~mL}$ of $10^{\circ} \mathrm{C}$ 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?

Dading Chen
Dading Chen
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05:44

Problem 52

Two neighbors return from Florida to find their houses at a frigid $35^{\circ} \mathrm{F}$. Each house has a furnace that can supply $100,000 \mathrm{Btu} / \mathrm{h}$. One house is made of stone and weighs 75 tons. The other is wood and weighs 15 tons. How long does it take each house to reach $65^{\circ} \mathrm{F}$ ? Neglect heat loss, and assume the entire house mass reaches a uniform temperature.

Dading Chen
Dading Chen
Numerade Educator
07:59

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
Dading Chen
Numerade Educator
02:53

Problem 54

In the 2011 nuclear accident at Fukushima, Japan, an 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 $\mathrm{cool}$ 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 thermal power to bring the water to the boiling point?

Shoukat Ali
Shoukat Ali
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02:06

Problem 55

A $1.2-\mathrm{kg}$ iron tea kettle sits on a $2.0-\mathrm{kW}$ stove burner. If it takes 5.4 min to bring the kettle and the water in it from $20^{\circ} \mathrm{C}$ to the boiling point, how much water is in the kettle?

Shoukat Ali
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02:30

Problem 56

The temperature of the eardrum provides a reliable measure of 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?

Dading Chen
Dading Chen
Numerade Educator
03:39

Problem 57

A $1500-\mathrm{kg}$ car moving at $40 \mathrm{~km} / \mathrm{h}$ is brought to a sudden stop. If all the car's energy is dissipated in heating its four $5.0-\mathrm{kg}$ steel brake disks, by how much do the disk temperatures increase?

Dading Chen
Dading Chen
Numerade Educator
02:22

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
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02:18

Problem 59

A piece of copper at $300^{\circ} \mathrm{C}$ is dropped into $1.0 \mathrm{~kg}$ of water at $20^{\circ} \mathrm{C} .$ If the equilibrium temperature is $25^{\circ} \mathrm{C},$ what's the mass of the conper?

Shoukat Ali
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07:10

Problem 60

While camping, you boil water to make spaghetti. Your pot contains $2.5 \mathrm{~kg}$ 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 $a=1.1 \mathrm{~kW}, b=2.3 \mathrm{~W} / \mathrm{s},$ 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
Dading Chen
Numerade Educator
02:46

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 $8.0-\mathrm{cm}$ -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
Dading Chen
Numerade Educator
02:52

Problem 62

One end of an iron rod $40 \mathrm{~cm}$ long and $3.0 \mathrm{~cm}$ 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.

Dading Chen
Dading Chen
Numerade Educator
03:12

Problem 63

You arrive for a party on a night when it's $8^{\circ} \mathrm{C}$ outside. 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 $320 \mathrm{~W} / \mathrm{C}$. Will the house remain comfortable?

Dading Chen
Dading Chen
Numerade Educator
02:12

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
Dading Chen
Numerade Educator
03:39

Problem 65

In a low-temperature physics experiment, a metal block is surrounded 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 thermal 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 $k=0.0166$.

Shoukat Ali
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05:02

Problem 66

You're considering purchasing a new sleeping bag whose manufacturer claims it will keep you warm to $-10^{\circ} \mathrm{F}$. The bag has down insulation with $4.0-\mathrm{cm}$ 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 $-10^{\circ} \mathrm{F}$ ?

Dading Chen
Dading Chen
Numerade Educator
03:50

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
Dading Chen
Numerade Educator
01:34

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
Dading Chen
Numerade Educator
03:06

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
Dading Chen
Numerade Educator
02:30

Problem 70

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

Shoukat Ali
Shoukat Ali
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09:30

Problem 71

Rework Example 16.4, now assuming the house has 10 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
01:54

Problem 72

In 2014 the European Space Agency's Rosetta spacecraft was $5000 \mathrm{~km}$ from the comet $67 \mathrm{P} /$ 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
Shoukat Ali
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01:45

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 $0.876 \mathrm{~W} / \mathrm{m}^{2}$.

Supratim Pal
Supratim Pal
Numerade Educator
03:26

Problem 74

The table below shows temperature versus time for $500 \mathrm{~g}$ of water 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). $$
\begin{array}{|l|l|l|l|l|l|l|l|}
\hline \text { Time (s) } & 0 & 25 & 60 & 95 & 125 & 160 & 190 \\
\hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & 12 & 20 & 39 & 53 & 64 & 83 & 93 \\
\hline
\end{array}
$$

Shoukat Ali
Shoukat Ali
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06:14

Problem 75

Water's specific heat in the range from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ varies with temperature 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
02:18

Problem 76

At low temperatures the specific heats of solids are approximately 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 40 g of copper from $10.0 \mathrm{~K}$ to $25.0 \mathrm{~K}$.

Dading Chen
Dading Chen
Numerade Educator
07:39

Problem 77

The Application on global warming (page 305 ) gives $960 \mathrm{~W} / \mathrm{m}^{2}$ 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.

Shoukat Ali
Shoukat Ali
Other Schools
05:56

Problem 78

In a cylindrical pipe where area isn't constant, Equation 16.5 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, respectively. (Hint: Consider the heat flow through a thin section of pipe, with thickness $d r$, as shown in Fig. 16.16 . Then integrate.)

Dading Chen
Dading Chen
Numerade Educator
05:30

Problem 79

A friend who's skeptical about climate change argues that the 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?

Dading Chen
Dading Chen
Numerade Educator
02:16

Problem 80

Your family is winterizing its lakefront camp, and you want at least $\mathcal{R}-19$ insulation in the walls. You've got some Europeanmade insulation with $\mathcal{R}$ -factor $3.5 \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W}$. Will it do?

Dading Chen
Dading Chen
Numerade Educator
01:26

Problem 81

A passive solar house has south-facing windows that, in winter, admit solar energy at an average rate of $2.2 \mathrm{~kW}$. The house is well insulated, losing only $55 \mathrm{~W}$ for every ${ }^{\circ} \mathrm{C}$ temperature difference between inside and outside. What's the minimum outdoor temperature for which the house can maintain $21^{\circ} \mathrm{C}$ inside?

Shoukat Ali
Shoukat Ali
Other Schools
05:20

Problem 82

A more realistic approach to the solar greenhouse of Example 16.7 considers the time dependence of the solar input. A function that approximates 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,

Morgan Cheatham
Morgan Cheatham
Numerade Educator
00:36

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
Shoukat Ali
Other Schools
00:30

Problem 84

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

Dading Chen
Dading Chen
Numerade Educator
01:25

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
Dading Chen
Numerade Educator
01:04

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
Dading Chen
Numerade Educator