Physics

Robert Coleman Richardson; Betty McCarthy Richardson; Alan Giambattista

Chapter 14

Heat - all with Video Answers

Educators

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Chapter Questions

Problem 1

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

Surjit Tewari

Surjit Tewari

Numerade Educator

Problem 2

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

Surjit Tewari

Numerade Educator

Problem 3

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

Surjit Tewari

Numerade Educator

Problem 4

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

Surjit Tewari

Numerade Educator

Problem 5

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

Surjit Tewari

Numerade Educator

Problem 6

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

Surjit Tewari

Numerade Educator

Problem 7

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

Surjit Tewari

Numerade Educator

Problem 8

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

Surjit Tewari

Numerade Educator

Problem 9

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

Surjit Tewari

Numerade Educator

Problem 10

What is the heat capacity of a $30.0 \mathrm{kg}$ block of ice?

Surjit Tewari

Numerade Educator

Problem 11

What is the heat capacity of $1.00 \mathrm{m}^{3}$ of aluminum?

Vipender Yadav

Numerade Educator

Problem 12

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

Surjit Tewari

Numerade Educator

Problem 13

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

Surjit Tewari

Numerade Educator

Problem 14

Rank these six situations in order of the temperature increase, largest to smallest.
(a) $1 \mathrm{kJ}$ of heat into $400 \mathrm{g}$ of steel with $c=0.45 \mathrm{kJ} /(\mathrm{kg} \cdot \mathrm{K})$
(b) $2 \mathrm{kJ}$ of heat into $400 \mathrm{g}$ of steel
(c) $2 \mathrm{kJ}$ of heat into $800 \mathrm{g}$ of steel
(d) $1 \mathrm{kJ}$ of heat into $400 \mathrm{g}$ of aluminum with $c=$ $0.90 \mathrm{kJ} /(\mathrm{kg} \cdot \mathrm{K})$
(e) $2 \mathrm{kJ}$ of heat into $400 \mathrm{g}$ of aluminum
(f) $2 \mathrm{kJ}$ of heat into $800 \mathrm{g}$ of aluminum

Vipender Yadav

Numerade Educator

Problem 15

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

Vipender Yadav

Numerade Educator

Problem 16

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

Surjit Tewari

Numerade Educator

Problem 17

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

Surjit Tewari

Numerade Educator

Problem 18

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

Surjit Tewari

Numerade Educator

Problem 19

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

Vipender Yadav

Numerade Educator

Problem 20

An experiment is conducted with a Joule apparatus (see Fig. 14.2). The hanging objects descend through a distance of $1.25 \mathrm{m}$ each time. After 30 descents, a total of $1.00 \mathrm{kJ}$ has been delivered to the water. What is the total mass of the hanging objects?

Vipender Yadav

Numerade Educator

Problem 21

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

Surjit Tewari

Numerade Educator

Problem 22

An 83 kg man eats a banana of energy content $418 \mathrm{kJ}(100 \mathrm{kcal}) .$ If all of the energy from the banana is converted into kinetic energy of the man, how fast is he moving, assuming he starts from rest?

Vipender Yadav

Numerade Educator

Problem 23

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

Surjit Tewari

Numerade Educator

Problem 24

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

Surjit Tewari

Numerade Educator

Problem 25

A bit of space debris penetrates the hull of a spaceship traversing the asteroid belt and comes to rest in a container of water that was at $20.0^{\circ} \mathrm{C}$ before being hit. The mass of the debris is $1.0 \mathrm{g}$ and the mass of the water is $1.0 \mathrm{kg} .$ If the space rock traveled at $8.4 \times 10^{3} \mathrm{m} / \mathrm{s}$ with respect to the spaceship and if all of its kinetic energy is used to heat the water, what is the final temperature of the water?

Vipender Yadav

Numerade Educator

Problem 26

A $7.30 \mathrm{kg}$ steel ball at $15.2^{\circ} \mathrm{C}$ is dropped from a height of $10.0 \mathrm{m}$ into an insulated container with $4.50 \mathrm{L}$ of water at $10.1^{\circ} \mathrm{C} .$ If no water splashes, what is the final temperature of the water and steel?

Vipender Yadav

Numerade Educator

Problem 27

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

Vipender Yadav

Numerade Educator

Problem 28

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

Vipender Yadav

Numerade Educator

Problem 29

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

Vipender Yadav

Numerade Educator

Problem 30

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

Surjit Tewari

Numerade Educator

Problem 31

Jill takes in $0.021 \mathrm{mol}$ of air in a single breath. The air is taken in at $20^{\circ} \mathrm{C}$ and exhaled at $35^{\circ} \mathrm{C} .$ (a) How much heat leaves her body in a single breath due to the temperature increase of the air? Ignore the humidification of the air in the lungs and treat air as an ideal diatomic gas. (b) Her respiration rate is 14 breaths per minute. At what average rate does heat leave her body due to the temperature increase of the air? Compare this with $72 \mathrm{W}$, the total rate of heat loss from her body.

Vipender Yadav

Numerade Educator

Problem 32

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

Vipender Yadav

Numerade Educator

Problem 33

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

Vipender Yadav

Numerade Educator

Problem 34

Given these data, compute the heat of vaporization of water. The specific heat capacity of water is $4.186 \mathrm{J} /(\mathrm{g} \cdot \mathrm{K})$. $$
\begin{array}{cl}
\hline \text { Mass of calorimeter }= & \text { Specific heat of calorimeter }= \\
3.00 \times 10^{2} \mathrm{g} & 0.380 \mathrm{J} /(\mathrm{g} \cdot \mathrm{K}) \\
\text { Mass of water }= & \text { Initial temperature of water and } \\
2.00 \times 10^{2} \mathrm{g} & \text { calorimeter }=15.0^{\circ} \mathrm{C} \\
\text { Mass of condensed } & \text { Initial temperature of steam }= \\
\text { steam }=18.5 \mathrm{g} & 100.0^{\circ} \mathrm{C} \\
& \text { Final temperature of calorimeter } \\
& =62.0^{\circ} \mathrm{C} \\
\hline
\end{array}
$$

Matthew Baker

Numerade Educator

Problem 35

Given these data, compute the heat of fusion of water. The specific heat capacity of water is $4.186 \mathrm{J} / \mathrm{cg} \cdot \mathrm{K}$ ).
$$
\begin{array}{cl}
\hline \text { Mass of calorimeter }= & \text { Specific heat of calorimeter }= \\
3.00 \times 10^{2} \mathrm{g} & 0.380 \mathrm{J} /(\mathrm{g} \cdot \mathrm{K}) \\
\text { Mass of water }= & \text { Initial temperature of water and } \\
2.00 \times 10^{2} \mathrm{g} & \text { calorimeter }=20.0^{\circ} \mathrm{C} \\
\text { Mass of ice }=30.0 \mathrm{g} & \text { Initial temperature of ice }=0^{\circ} \mathrm{C} \\
& \text { Final temperature of calorimeter }= \\
& 8.5^{\circ} \mathrm{C} \\
\hline
\end{array}
$$

Matthew Baker

Numerade Educator

Problem 36

In an emergency, it is sometimes the practice of medical professionals to immerse a patient who suffers from heat stroke in an ice bath, a mixture of ice and water in equilibrium at $0^{\circ} \mathrm{C},$ in order to reduce her body temperature. (a) If a 75 kg patient whose body temperature is $40.8^{\circ} \mathrm{C}$ must have her temperature reduced to the normal range, how much heat must be removed? (b) If she is placed in a bath containing $7.5 \mathrm{kg}$ of ice, will there be ice remaining in the bath when her body temperature is $37.0^{\circ} \mathrm{C}$ ? If so, how much? If not, what will the final water temperature be?

Manish Jain

Numerade Educator

Problem 37

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

Surjit Tewari

Numerade Educator

Problem 38

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

Vishal Gupta

Numerade Educator

Problem 39

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

Surjit Tewari

Numerade Educator

Problem 40

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

Narayan Hari

Numerade Educator

Problem 41

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

Narayan Hari

Numerade Educator

Problem 42

Repeat Problem 41 without ignoring the temperature change of the glass. The glass has a mass of $350 \mathrm{g}$ and the specific heat of the glass is $0.837 \mathrm{kJ} /(\mathrm{kg} \cdot \mathrm{K}) .$ By what percentage does the answer change from the answer for Problem 41?

Narayan Hari

Numerade Educator

Problem 43

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

Surjit Tewari

Numerade Educator

Problem 44

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

Narayan Hari

Numerade Educator

Problem 45

Is it possible to heat the aluminum of Problem 44 to a high enough temperature so that it melts an equal mass of ice? If so, what temperature must the aluminum have?

Manish Jain

Numerade Educator

Problem 46

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

Narayan Hari

Numerade Educator

Problem 47

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

Surjit Tewari

Numerade Educator

Problem 48

(a) How much ice at $-10.0^{\circ} \mathrm{C}$ must be placed in $0.250 \mathrm{kg}$ of water at $25.0^{\circ} \mathrm{C}$ to cool the water to $0^{\circ} \mathrm{C}$ and melt all of the ice? (b) If half that amount of ice is placed in the water, what is the final temperature of the water?

Manish Jain

Numerade Educator

Problem 49

A 75 g cube of ice at $-10.0^{\circ} \mathrm{C}$ is placed in $0.500 \mathrm{kg}$ of water at $50.0^{\circ} \mathrm{C}$ in an insulating container so that no heat is lost to the environment. Will the ice melt completely? What will be the final temperature of this system?

Manish Jain

Numerade Educator

Problem 50

A $0.360 \mathrm{kg}$ piece of solid lead at $20^{\circ} \mathrm{C}$ is placed into an insulated container holding $0.980 \mathrm{kg}$ of liquid lead at $420^{\circ} \mathrm{C} .$ The system comes to an equilibrium temperature with no loss of heat to the environment. Ignore the heat capacity of the container. (a) Is there any solid lead remaining in the system? (b) What is the final temperature of the system?

Manish Jain

Numerade Educator

Problem 51

A dog loses a lot of heat through panting. The air rushing over the upper respiratory tract causes evaporation and thus heat loss. A dog typically pants at a rate of around 300 pants per minute. As a rough calculation, assume that one pant causes $0.010 \mathrm{g}$ of water to be evaporated from the respiratory tract. What is the rate of heat loss for the dog through panting?

Narayan Hari

Numerade Educator

Problem 52

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

Narayan Hari

Numerade Educator

Problem 53

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

Matthew Baker

Numerade Educator

Problem 54

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

Surjit Tewari

Numerade Educator

Problem 55

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

Surjit Tewari

Numerade Educator

Problem 56

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

Narayan Hari

Numerade Educator

Problem 57

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

Surjit Tewari

Numerade Educator

Problem 58

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

Narayan Hari

Numerade Educator

Problem 59

A wall that is $2.74 \mathrm{m}$ high and $3.66 \mathrm{m}$ long has a thickness composed of $1.00 \mathrm{cm}$ of wood plus $3.00 \mathrm{cm}$ of insulation (with the thermal conductivity approximately of wool). The inside of the wall is $23.0^{\circ} \mathrm{C}$ and the outside of the wall is at $-5.00^{\circ} \mathrm{C}$.
(a) What is the rate of heat flow through the wall? (b) If half the area of the wall is replaced with a single pane of glass that is $0.500 \mathrm{cm}$ thick, how much heat flows out of the wall now?

Manish Jain

Numerade Educator

Problem 60

Boiling water in an aluminum pan is being converted to steam at a rate of $10.0 \mathrm{g} / \mathrm{s} .$ The flat bottom of the pan has an area of $325 \mathrm{cm}^{2}$ and the pan's thickness is $3.00 \mathrm{mm}$ If $27.0 \%$ of all heat that is transferred to the pan from the flame beneath it is lost from the sides of the pan and the remaining $73.0 \%$ goes into the water, what is the temperature of the base of the pan?

Manish Jain

Numerade Educator

Problem 61

Your hot water tank is insulated, but not very well. To reduce heat loss, you wrap some old blankets around it. With the water at $81^{\circ} \mathrm{C}$ and the room at $21^{\circ} \mathrm{C},$ a thermometer inserted between the outside of the original tank and your blanket reads $36^{\circ} \mathrm{C} .$ By what factor did the blanket reduce the heat loss?

Narayan Hari

Numerade Educator

Problem 62

A copper rod has one end in ice at a temperature of $0^{\circ} \mathrm{C}$ the other in boiling water. The length and diameter of the rod are $1.00 \mathrm{m}$ and $2.00 \mathrm{cm},$ respectively. At what rate in grams per hour does the ice melt? Assume no heat flows out the sides of the rod.

Narayan Hari

Numerade Educator

Problem 63

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

Surjit Tewari

Numerade Educator

Problem 64

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

Surjit Tewari

Numerade Educator

Problem 65

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

Surjit Tewari

Numerade Educator

Problem 66

Find the temperature drop across the epidermis (the outer layer of skin) under these conditions: the rate of heat flow via conduction through a $10.0 \mathrm{cm}^{2}$ area of the epidermis is $50 \mathrm{mW} ;$ the epidermis is $2.00 \mathrm{mm}$ thick and has thermal conductivity $0.45 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$.

Manish Jain

Numerade Educator

Problem 67

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

Manish Jain

Numerade Educator

Problem 68

Five walls of a house have different surface areas, insulation materials, and insulation thicknesses. Rank them in order of the rate of heat flow through the wall, greatest to smallest. Assume the same indoor and outdoor temperatures for each wall.
(a) area $=120 \mathrm{m}^{2} ; 10 \mathrm{cm}$ thickness of insulation with thermal conductivity $0.030 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$
(b) area $=120 \mathrm{m}^{2} ; 15 \mathrm{cm}$ thickness of insulation with thermal conductivity 0.045 W/(m-K)
(c) area $=180 \mathrm{m}^{2} ; 10 \mathrm{cm}$ thickness of insulation with thermal conductivity $0.045 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$
(d) area $=120 \mathrm{m}^{2} ; 10 \mathrm{cm}$ thickness of insulation with thermal conductivity $0.045 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$
(e) area $=180 \mathrm{m}^{2} ; 15 \mathrm{cm}$ thickness of insulation with thermal conductivity $0.030 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$

Manish Jain

Numerade Educator

Problem 69

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

Narayan Hari

Numerade Educator

Problem 70

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

Surjit Tewari

Numerade Educator

Problem 71

A brick wall with thermal conductivity $\kappa=1.3 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K})$ is covered completely with a sheet of foam of the same thickness as the brick, but with $\kappa=0.025 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ How is the rate at which heat is conducted through the wall changed by the addition of the foam?

Manish Jain

Numerade Educator

Problem 72

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

Surjit Tewari

Numerade Educator

Problem 73

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

Surjit Tewari

Numerade Educator

Problem 74

Six wood stoves have total surface areas $A$ and surface temperatures $T$ as given. Rank them in order of the power radiated, from greatest to least. Assume they all have the same emissivity.
(a) $A=1.00 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$
(b) $A=1.01 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$
(c) $A=1.05 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$
(d) $A=1.00 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$
(e) $A=0.99 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$
(f) $A=0.98 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$

Manish Jain

Numerade Educator

Problem 75

A sphere with a diameter of $80 \mathrm{cm}$ is initially at a temperature of $250^{\circ} \mathrm{C} .$ If the intensity of the radiation detected at a distance of $2.0 \mathrm{m}$ from the sphere's center is $102 \mathrm{W} / \mathrm{m}^{2},$ what is the emissivity of the sphere?

Narayan Hari

Numerade Educator

Problem 76

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

Surjit Tewari

Numerade Educator

Problem 77

A tungsten filament in a lamp is heated to a temperature of $2600 \mathrm{K}$ by an electric current. The tungsten has an emissivity of 0.32. What is the surface area of the filament if the lamp delivers $40.0 \mathrm{W}$ of power?

Manish Jain

Numerade Educator

Problem 78

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

Surjit Tewari

Numerade Educator

Problem 79

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

Surjit Tewari

Numerade Educator

Problem 80

A student in a lecture hall has $0.25 \mathrm{m}^{2}$ of skin (arms, hands, and head) exposed. The skin is at $34^{\circ} \mathrm{C}$ and has an emissivity of 0.97. The temperature of the room is $20^{\circ} \mathrm{C}$ (air, walls, ceiling, and floor all at the same temperature).
(a) At what rate does the skin emit thermal radiation?
(b) At what rate does the skin absorb thermal radiation?
(c) What is the net rate of heat flow from the body due to thermal radiation? Compare this to the total rate of heat flow from the body, about 100 W.

Narayan Hari

Numerade Educator

Problem 81

B It is often argued that the head is the most important part of the body to cover when out in cold weather. Estimate the total energy loss by radiation if a person's head is uncovered for 15 min on a very cold, $-15^{\circ} \mathrm{C}$ day, assuming he is bald, his skin temperature is $35^{\circ} \mathrm{C},$ and that skin has an emissivity (in the infrared) of $97 \%$.

Narayan Hari

Numerade Educator

Problem 82

Consider the net rate of heat loss by radiation from exposed skin on a cold day. By what factor does the rate for an outdoor temperature of $0^{\circ} \mathrm{C}$ exceed the rate at $5^{\circ} \mathrm{C} ?$ Assume an initial skin temperature of $35^{\circ} \mathrm{C}$.

Narayan Hari

Numerade Educator

Problem 83

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

Surjit Tewari

Numerade Educator

Problem 84

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

Surjit Tewari

Numerade Educator

Problem 85

Consider the leaf of Problem $84 .$ Assume that the top surface of the leaf absorbs $70.0 \%$ of $9.00 \times$ $10^{2} \mathrm{W} / \mathrm{m}^{2}$ of radiant energy, while the bottom surface absorbs all of the radiant energy incident on it due to its surroundings at $25.0^{\circ} \mathrm{C} .$ (a) If the only method of heat loss for the leaf is thermal radiation, what would be the temperature of the leaf? (Assume that the leaf radiates like a blackbody.) (b) If the leaf is to remain at a temperature of $25.0^{\circ} \mathrm{C},$ how much power per unit area must be lost by other methods such as transpiration (evaporative heat loss)?

Narayan Hari

Numerade Educator

Problem 86

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

Narayan Hari

Numerade Educator

Problem 87

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

Narayan Hari

Numerade Educator

Problem 88

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

Surjit Tewari

Numerade Educator

Problem 89

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

Narayan Hari

Numerade Educator

Problem 90

A scientist working late at night in her lowtemperature physics laboratory decides to have a cup of hot tea, but discovers the lab hot plate is broken. Not to be deterred, she puts about 8 oz of water, at $12^{\circ} \mathrm{C}$, from the tap into a lab dewar (essentially a large thermos bottle) and begins shaking it up and down. With each shake the water is thrown up and falls back down a distance of $33 \mathrm{cm} .$ If she can complete 30 shakes per minute, how long will it take for the water to reach $87^{\circ} \mathrm{C} ?$ Would this really work? If not, why not?

Narayan Hari

Numerade Educator

Problem 91

Small animals eat much more food per kilogram of body mass than do larger animals. The basal metabolic rate (BMR) is the minimal energy intake necessary to sustain life in a state of complete inactivity. The table lists the BMR in kilocalories per day, the mass, and the surface area for five animals.
(a) Calculate the BMR per kilogram of body mass for each animal. Is it true that smaller animals must consume much more food per kilogram of body mass?
(b) Calculate the BMR per square meter of surface area. (c) Can you explain why the BMR per square meter is approximately the same for animals of different sizes? Consider what happens to the food energy metabolized by an animal in a resting state.
$$
\begin{array}{lccc}
\hline & \text { BMR } & & \text { Surface } \\
\text { Animal } & \text { (kcal/d) } & \text { Mass (kg) } & \text { Area (m }^{2} \text { ) } \\
\text { Mouse } & 3.80 & 0.018 & 0.0032 \\
\text { Dog } & 770 & 15 & 0.74 \\
\text { Human } & 2050 & 64 & 2.0 \\
\text { Horse } & 4900 & 440 & 5.1 \\
\hline
\end{array}
$$

Manish Jain

Numerade Educator

Problem 92

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

Manish Jain

Numerade Educator

Problem 93

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

Manish Jain

Numerade Educator

Problem 94

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

Narayan Hari

Numerade Educator

Problem 95

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

Surjit Tewari

Numerade Educator

Problem 96

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

Surjit Tewari

Numerade Educator

Problem 97

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

Narayan Hari

Numerade Educator

Problem 98

If the temperature surrounding the sunbather in Problem 78 is greater than the normal body temperature of $37^{\circ} \mathrm{C}$ and the air is still, so that radiation, conduction, and convection play no part in cooling the body, how much water (in liters per hour) from perspiration must be given off to maintain the body temperature? The heat of vaporization of water is $2430 \mathrm{J} / \mathrm{g}$ at normal skin temperature.

Narayan Hari

Numerade Educator

Problem 99

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

Narayan Hari

Numerade Educator

Problem 100

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

Narayan Hari

Numerade Educator

Problem 101

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

Surjit Tewari

Numerade Educator

Problem 102

If $4.0 \mathrm{g}$ of boiling water at $100.0^{\circ} \mathrm{C}$ was splashed onto a burn victim's skin and if it cooled to $45.0^{\circ} \mathrm{C}$ on the $37.0^{\circ} \mathrm{C}$ skin, (a) how much heat is given up by the water? (b) How much tissue mass, originally at $37.0^{\circ} \mathrm{C}$, was involved in cooling the water? See Table $14.1 .$ Compare the result with that found in Problem 101 .

Narayan Hari

Numerade Educator

Problem 103

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

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 104

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

Surjit Tewari

Numerade Educator

Problem 105

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

Surjit Tewari

Numerade Educator

Problem 106

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

Narayan Hari

Numerade Educator

Problem 107

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

Surjit Tewari

Numerade Educator

Problem 108

The student from Problem 79 realizes that standing naked in a cold room will not give him the desired weight loss results since it is much less efficient than simply exercising. So he decides to "burn" calories through conduction. He fills the bathtub with $16^{\circ} \mathrm{C}$ water and gets in. The water right next to his skin warms up to the same temperature as his skin, $35^{\circ} \mathrm{C},$ but the water only $3.0 \mathrm{mm}$ away remains at $16^{\circ} \mathrm{C}$. At what rate (in kcal/h) would he "burn" calories? The thermal conductivity of water at this temperature is $0.58 \mathrm{W} /(\mathrm{m} \cdot \mathrm{K}) .$ [Warning: Do not try this. Sitting in water this cold can lead to hypothermia and even death. $]$

Narayan Hari

Numerade Educator

Problem 109

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

Manish Jain

Numerade Educator

Problem 110

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

Manish Jain

Numerade Educator

Problem 111

On a hot summer day, Daphne is off to the park for a picnic. She puts $0.10 \mathrm{kg}$ of ice at $0^{\circ} \mathrm{C}$ in a thermos and then adds tea initially at $25^{\circ} \mathrm{C}$. How much tea will just melt all the ice?

Narayan Hari

Numerade Educator

Problem 112

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

Narayan Hari

Numerade Educator

Problem 113

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

Manish Jain

Numerade Educator

Problem 114

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

Narayan Hari

Numerade Educator

Problem 115

A 20.0 g lead bullet leaves a rifle at a temperature of $47.0^{\circ} \mathrm{C}$ and travels at a speed of $5.00 \times 10^{2} \mathrm{m} / \mathrm{s}$ until it hits a $6.0 \mathrm{kg}$ block of ice at $0^{\circ} \mathrm{C}$ that is initially at rest on a frictionless surface. The bullet becomes embedded in
the ice. (a) How fast is the the block of ice moving after the bullet is embedded?
(b) How much ice melts?

Supratim Pal

Numerade Educator

Problem 116

A star's spectrum emits more radiation with a wavelength of $700.0 \mathrm{nm}$ than with any other wavelength.
(a) What is the surface temperature of the star? (b) If the star's radius is $7.20 \times 10^{8} \mathrm{m},$ what power does it radiate? (c) If the star is 9.78 ly from Earth, what will an Earth-based observer measure for this star's inten-
sity? Stars are nearly perfect blackbodies. [Note: ly stands for light-years.]

Narayan Hari

Numerade Educator

Problem 117

A $3.0 \mathrm{L}$ container of nitrogen gas $\left(\mathrm{N}_{2}\right)$ and a $5.0 \mathrm{L}$ container of oxygen gas $\left(\mathrm{O}_{2}\right)$ are both at $20^{\circ} \mathrm{C}$ and 1.0 atm. (a) Which gas has the larger rms speed? Explain.
(b) At what temperature will oxygen gas have the same rms speed as nitrogen when the nitrogen is at $20^{\circ} \mathrm{C} ?(\mathrm{c})$ How much heat must flow into or out of the container of oxygen to change its temperature from $20^{\circ} \mathrm{C}$ to the temperature you found in part (b)?

Manish Jain

Numerade Educator

Problem 118

Two aluminum blocks are in thermal contact.
(a) Are the blocks necessarily in physical contact? Explain. (b) If they have the same temperature, do they necessarily have the same internal energy? Explain.
(c) If their internal energies are not equal, is there necessarily a net energy transfer between the two blocks? Explain. (d) One block has mass $1.00 \mathrm{kg}$ and temperature $40.0^{\circ} \mathrm{C} .$ The other has mass $3.00 \mathrm{kg}$ and temperature $20.0^{\circ} \mathrm{C}$. Find the final equilibrium temperature and the changes in internal energy of each block.

Manish Jain

Numerade Educator

Problem 119

A 60.0 g piece of ice slides 5.00 m down an icy roof inclined at $27.0^{\circ}$ to the horizontal. The magnitude of its acceleration is $4.10 \mathrm{m} / \mathrm{s}^{2} .$ All the ice is at $0^{\circ} \mathrm{C}$. How much ice melts?

Manish Jain

Numerade Educator

Problem 120

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

Narayan Hari

Numerade Educator