Physics

James S. Walker

Chapter 17

Phases and Phase Changes - all with Video Answers

Educators

Chapter Questions

Problem 1

(a) Is the number of molecules in one mole of $N_{2}$ greater than, less than, or equal to the number of molecules in one mole of $\mathrm{O}_{2} ?(\mathrm{b})$ Is the mass of one mole of $\mathrm{N}_{2}$ greater than, less than, or equal to the mass of one mole of $\mathrm{O}_{2} ?$

Sachin Rao

Sachin Rao

Numerade Educator

Problem 2

Is the number of atoms in one mole of helium greater than, less than, or equal to the number of atoms in one mole of oxygen? Helium consists of individual atoms, He, and oxygen is a diatomic gas, $\mathrm{O}_{2}$

Sachin Rao

Numerade Educator

Problem 3

If you put a helium-filled balloon in the refrigerator, (a) will its volume increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Lowering the temperature of an ideal gas at constant pressure results in a reduced volume.
II. The same amount of gas is in the balloon; therefore, its volume remains the same.
III. The balloon can expand more in the cool air of the refrigerator, giving an increased volume.

Sachin Rao

Numerade Educator

Problem 4

Two containers hold ideal gases at the same temperature. Container A has twice the volume and half the number of molecules as container B. What is the ratio $P_{\mathrm{A}} / P_{B},$ where $P_{A}$ is the pressure in container A and $P_{8}$ is the pressure in container B?

Sachin Rao

Numerade Educator

Problem 5

Standard temperature and pressure (STP) is defined as a temperature of $0^{\circ} \mathrm{C}$ and a pressure of $101.3 \mathrm{kPa}$. What is the volume occupied by one mole of an ideal gas at STP?

HR

Hugh Ross

Numerade Educator

Problem 6

After emptying her lungs, a person inhales 4.1 L of air at $0.0^{\circ} \mathrm{C}$ and holds her breath. How much does the volume of the air increase as it warms to her body temperature of $37^{\circ} \mathrm{C} ?$

Vishal Gupta

Numerade Educator

Problem 7

In the morning, when the temperature is $286 \mathrm{K}$, a bicyclist finds that the absolute pressure in his tires is 501 kPa. That afternoon he finds that the pressure in the tires has increased to 554 kPa. lgnoring expansion of the tires, find the afternoon temperature.

Sachin Rao

Numerade Educator

Problem 8

An automobile tire has a volume of $0.0185 \mathrm{m}^{3} .$ At a temperature of $294 \mathrm{K}$ the absolute pressure in the tire is $212 \mathrm{kPa}$. How many moles of air must be pumped into the tire to increase its pressure to $252 \mathrm{kPa}$, given that the temperature and volume of the tire remain constant?

HR

Hugh Ross

Numerade Educator

Problem 9

Amount of Helium in a Blimp The Goodyear blimp Spirit of Alcron is $62.6 \mathrm{m}$ long and contains $7023 \mathrm{m}^{3}$ of helium. When the temperature of the helium is $285 \mathrm{K}$, its absolute pressure is $112 \mathrm{kPa} .$ Find the mass of the helium in the blimp.

Sachin Rao

Numerade Educator

Problem 10

A compressed-air tank holds $0.500 \mathrm{m}^{3}$ of air at a temperature of $285 \mathrm{K}$ and a pressure of $880 \mathrm{kPa}$. What volume would the air occupy if it were released into the atmosphere, where the pressure is $101 \mathrm{kPa}$ and the temperature is $303 \mathrm{K} ?$

Sachin Rao

Numerade Educator

Problem 11

A typical region of interstellar space may contain $10^{6}$ atoms per cubic meter (primarily hydrogen) at a temperature of $100 \mathrm{K}$. What is the pressure of this gas?

Sachin Rao

Numerade Educator

Problem 12

Four ideal gases have the following pressures, $P$, volumes, $V$, and mole numbers, $n:$ gas $\mathrm{A}, P=100 \mathrm{kPa}, V=1 \mathrm{m}^{3}$,$n=10 \mathrm{mol} ;$ gas $\mathrm{B}, P=200 \mathrm{kPa}, V=2 \mathrm{m}^{3}, n=20 \mathrm{mol} ;$ gas $\mathrm{C}$ $P=50 \mathrm{kPa}, V=1 \mathrm{m}^{3}, n=50 \mathrm{mol} ; g a s \mathrm{D}, P=50 \mathrm{kPa}, V=4 \mathrm{m}^{3}$ $n=5$ mol. Rank these gases in order of increasing temperature. Indicate ties where appropriate.

Sachin Rao

Numerade Educator

Problem 13

A balloon contains 3.7 liters of nitrogen gas at a temperature of $87 \mathrm{K}$ and a pressure of $101 \mathrm{kPa}$. If the temperature of the gas is allowed to increase to $24^{\circ} \mathrm{C}$ and the pressure remains constant, what volume will the gas occupy?

Sachin Rao

Numerade Educator

Problem 14

A balloon is filled with helium at a pressure of $2.4 \times 10^{5} \mathrm{Pa}$. The balloon is at a temperature of $18^{\circ} \mathrm{C}$ and has a radius of $0.25 \mathrm{m} .$ (a) How many helium atoms are contained in the balloon? (b) Suppose we double the number of helium atoms in the balloon, keeping the pressure and the temperature fixed. By what factor does the radius of the balloon increase? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

A gas has a temperature of $310 \mathrm{K}$ and a pressure of $101 \mathrm{kPa}$.
(a) Find the volume occupied by 1.25 mol of this gas, assuming it is ideal.
(b) Assuming the gas molecules can be approximated as small spheres of diameter $2.5 \times 10^{-10} \mathrm{m},$ determine the fraction of the volume found in part (a) that is occupied by the molecules. (c) In determining the properties of an ideal gas, we assume that molecules are points of zero volume. Discuss the validity of this assumption for the case considered here.

Sachin Rao

Numerade Educator

Problem 16

$A 515-\mathrm{cm}^{3}$ flask contains $0.460 \mathrm{g}$ of a gas at a pressure of $153 \mathrm{kPa}$ and a temperature of $322 \mathrm{K}$. What is the molecular mass of this gas?

Yaqub Khan

Numerade Educator

Problem 17

The Atmosphere of Mars On Mars, the average temperature is $-64^{\circ} \mathrm{F}$ and the average atmospheric pressure is $0.92 \mathrm{kPa} .$ (a) What is the number of molecules per volume in the Martian atmosphere? (b) Is the number of molecules per volume on the Earth greater than, less than, or equal to the number per volume on Mars? Explain your reasoning. (c) Estimate the number of molecules per volume in Earth's atmosphere.

Sachin Rao

Numerade Educator

Problem 18

The air inside a hot-air balloon has an average temperature of $79.2^{\circ} \mathrm{C}$. The outside air has a temperature of $20.3^{\circ} \mathrm{C}$. What is the ratio of the density of air in the balloon to the density of air in the surrounding atmosphere?

Yaqub Khan

Numerade Educator

Problem 19

A cylindrical flask is fitted with an a irtight piston that is free to slide up and down, as shown in Figure $17-24$. A mass rests on top of the piston. The initial temperature of the system is $313 \mathrm{K}$ and the pressure of the gas is held constant at $137 \mathrm{kPa}$. The temperature is now increased until the height of the piston rises from $23.4 \mathrm{cm}$ to $26.0 \mathrm{cm} .$ What is the final temperature of the gas?

Sachin Rao

Numerade Educator

Problem 20

Consider the system described in Problem 19. Contained within the flask is an ideal gas at a constant temperature of $313 \mathrm{K}$. Initially the pressure applied by the piston and the mass is $137 \mathrm{kPa}$ and the height of the piston above the base of the flask is $23.4 \mathrm{cm} .$ When additional mass is added to the piston, the height of the piston decreases to $20.0 \mathrm{cm}$. Find the new pressure applied by the piston.

Sachin Rao

Numerade Educator

Problem 21

One mole of a monatomic ideal gas has an initial pressure of $210 \mathrm{kPa},$ an initial volume of $1.2 \times 10^{-3} \mathrm{m}^{3}$, and an initial temperature of $350 \mathrm{K}$. The gas now undergoes three separate processes: (i) a constant-temperature expansion that triples its volume; (ii) a constant-pressure compression to its initial volume; and (iii) a constant-volume increase in pressure to its initial pressure. At the end of these three processes, the gas is back at its initial pressure, volume, and temperature. Plot these processes on a pressure-versus-volume graph, showing the values of $P$ and $V$ at the end points of each process.

Sachin Rao

Numerade Educator

Problem 22

The air in your room is composed mostly of oxygen $\left(\mathrm{O}_{2}\right)$ and nitrogen $\left(\mathrm{N}_{2}\right)$ molecules. The oxygen molecules are more massive than the nitrogen molecules.
(a) Is the rms speed of the $\mathrm{O}_{2}$ molecules greater than, less than, or equal to the rms speed of the $\mathrm{N}_{2}$ molecules?
(b) Choose the best explanation from among the following:
I. The more massive oxygen molecules have greater momentum and therefore greater speed.
II. Equal temperatures for the oxygen and nitrogen molecules imply they have equal rms speeds.
III. The temperature is the same for both molecules, and hence their average kinetic energies are equal. As a result, the more massive oxygen molecules have lower speeds.

Sachin Rao

Numerade Educator

Problem 23

If the translational speed of molecules in an ideal gas is doubled, by what factor does the Kelvin temperature change? Explain.

Sachin Rao

Numerade Educator

Problem 24

A piston held at the temperature $T$ contains a gas mixture with molecules of three different types; $A, B,$ and $C$. The corresponding molecular masses are $m_{\mathrm{C}}>m_{\mathrm{B}}>m_{\mathrm{A}} .$ Rank these molecular types in order of increasing (a) average kinetic energy and (b) rms speed. Indicate ties where appropriate.

Sachin Rao

Numerade Educator

Problem 25

The molecules in a tank of hydrogen have the same rms speed as the molecules in a tank of oxygen. State whether each of the following statements is true, false, or unknowable with the given information: (a) the pressures are the same; (b) the hydrogen is at the higher temperature; $(c)$ the hydrogen has the higher pressure; (d) the temperatures are the same; (e) the oxygen is at the higher temperature.

Sachin Rao

Numerade Educator

Problem 26

At what temperature is the rms speed of $\mathrm{H}_{2}$ equal to the rms speed that $\mathrm{O}_{2}$ has at $313 \mathrm{K}$ ?

Sachin Rao

Numerade Educator

Problem 27

Suppose a planet has an atmosphere of pure ammonia at $0.0^{\circ} \mathrm{C} .$ What is the rms speed of the ammonia molecules?

Sachin Rao

Numerade Educator

Problem 28

Three moles of oxygen gas (that is, 3.0 mol of $\mathrm{O}_{2}$ ) are placed in a portable container with a volume of $0.0035 \mathrm{m}^{3}$. If the temperature of the gas is $295^{\circ} \mathrm{C}$, find $(a)$ the pressure of the gas and (b) the average kinetic energy of an oxygen molecule.
(c) Suppose the volume of the gas is doubled, while the temperature and number of moles are held constant. By what factor do your answers to parts (a) and (b) change? Explain.

Sachin Rao

Numerade Educator

Problem 29

The rms speed of $\mathrm{O}_{2}$ is $1550 \mathrm{m} / \mathrm{s}$ at a given temperature.
(a) Is the rms speed of $\mathrm{H}_{2} \mathrm{O}$ at this temperature greater than, less than, or equal to $1550 \mathrm{m} / \mathrm{s}$ ? Explain.
(b) Find the rms speed of $\mathrm{H}_{2} \mathrm{O}$ at this temperature.

Sachin Rao

Numerade Educator

Problem 30

An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. (a) If the number of molecules in the gas is doubled, does the rms speed increase, decrease, or stay the same? Explain. (b) If the initial rms speed is $1300 \mathrm{m} / \mathrm{s},$ what is the final rms speed?

Sachin Rao

Numerade Educator

Problem 31

What is the temperature of a gas of $\mathrm{CO}_{2}$ molecules whose rms speed is $329 \mathrm{m} / \mathrm{s}$ ?

Sachin Rao

Numerade Educator

Problem 32

The rms speed of a sample of gas is increased by $1 \%$. (a) What is the percent change in the temperature of the gas? (b) What is the percent change in the pressure of the gas, assuming its volume is held constant?

Yaqub Khan

Numerade Educator

Problem 33

Enriching Uranium In naturally occurring uranium atoms, $99.3 \%$ are $238 \mathrm{U}$ (atomic mass $=238 \mathrm{u},$ where $\mathrm{u}=1.6605 \times \mathrm{m}$ $10^{-27} \mathrm{kg}$ ) and only $0.7 \%$ are ${ }^{235} \mathrm{U}$ (atomic mass $\left.=235 \mathrm{u}\right)$ Uranium-fueled reactors require an enhanced proportion of 235 U. since both isotopes of uranium have identical chemical properties, they can be separated only by methods that depend on their differing masses. One such method is gaseous diffusion, in which uranium hexafluoride (UF $_{6}$ ) gas diffuses through a series of porous barriers. The lighter ${ }^{235} \mathrm{UF}_{6}$ molecules have a slightly higher rms speed at a given temperature than the heavier $^{238}$ Uf $_{6}$ molecules, and this allows the two isotopes to be separated. Find the ratio of the rms speeds of the two isotopes at $23.0^{\circ} \mathrm{C}$

Sachin Rao

Numerade Educator

Problem 34

A 350 -mL spherical flask contains 0.075 mol of an ideal gas at a temperature of $293 \mathrm{K}$. What is the average force exerted on the walls of the flask by a single molecule?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 35

A brick has faces with the following dimensions: face 1 is $1 \mathrm{cm}$ by $2 \mathrm{cm} ;$ face 2 is $2 \mathrm{cm}$ by $3 \mathrm{cm} ;$ face 3 is $1 \mathrm{cm}$ by $3 \mathrm{cm} .$ On which face should the brick be placed if it is to have the smallest change in dimensions due to its own weight? Explain.

Sachin Rao

Numerade Educator

Problem 36

A hollow cylindrical rod (rod 1) and a a solid cylindrical rod (rod 2 ) are made of the same material. The two rods have the same length and the same outer radius. If the same compressional force is applied to each rod, (a) is the change in length of rod 1 greater than, less than, or equal to the change in length of rod $2 ?$ (b) Choose the best explanation from among the following:
I. The solid rod has the larger effective cross-sectional area, since the empty part of the hollow rod doesn't resist compression. Therefore, the solid rod has the smaller change in length.
II. The rods have the same outer radius and hence the same cross-sectional area. As a result, their change in length is the same.
III. The walls of the hollow rod are hard and resist compression more than the uniform material in the solid rod. Therefore the hollow rod has the smaller change in length.

Sachin Rao

Numerade Educator

Problem 37

A rock climber hangs freely from a nylon rope that is $14 \mathrm{m}$ long and has a diameter of $8.3 \mathrm{mm}$. If the rope stretches $4.6 \mathrm{cm}$, what is the mass of the climber?

Sachin Rao

Numerade Educator

Problem 38

To stretch a relaxed biceps muscle $2.5 \mathrm{cm}$ requires a force of $25 \mathrm{N}$. Find the Young's modulus for the muscle tissue, assuming it to be a uniform cylinder of length $0.24 \mathrm{m}$ and crosssectional area $47 \mathrm{cm}^{2}$

Sachin Rao

Numerade Educator

Problem 39

A $22-k g$ chimpanzee hangs from the end of a horizontal, broken branch $1.1 \mathrm{m}$ long, as shown in Figure $\mathrm{T} \rightarrow 25 .$ The branch is a uniform cylinder $4.6 \mathrm{cm}$ in diameter, and the end of the branch supporting the chimp sags downward through a vertical distance of $13 \mathrm{cm}$. What is the shear modulus for this branch?

Sachin Rao

Numerade Educator

Problem 40

The Marianas Trench The deepest place in all the occans is the Marianas Trench, where the depth is $10.9 \mathrm{km}$ and the pressure is $1.10 \times 10^{8} \mathrm{Pa}$. If a copper ball $15.0 \mathrm{cm}$ in diameter is taken to the bottom of the trench, by how much does its volume decrease?

Sachin Rao

Numerade Educator

Problem 41

Four cylindrical rods with various cross-sectional areas and initial lengths are stretched by an applied force, as in Figure $17-10 .$ The resulting change in length of each rod is given in the following table. Rank these rods in order of increasing Young's modulus. Indicate ties where appropriate.

Brandy Heflin

Numerade Educator

Problem 42

A steel wire $4.7 \mathrm{m}$ long stretches $0.11 \mathrm{cm}$ when it is given a tension of $360 \mathrm{N}$. (a) What is the diameter of the wire? (b) If it is desired that the stretch be less than $0.11 \mathrm{cm},$ should its diameter be increased or decreased? Explain.

Sachin Rao

Numerade Educator

Problem 43

An orb weaver spider with a mass of 0.26 g hangs vertically by one of its threads. The thread has a Young's modulus of $4.7 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$ and a radius of $9.8 \times 10^{-6} \mathrm{m}$.
(a) What is the fractional increase in the thread's length caused by the spider? (b) Suppose a $76-\mathrm{kg}$ person hangs vertically from a nylon rope. What radius must the rope have if its fractional increase in length is to be the same as that of the spider's thread?

Sachin Rao

Numerade Educator

Problem 44

Two rods of equal length $(0.55 \mathrm{m})$ and diameter $(1.7 \mathrm{cm})$ are placed end to end. One rod is aluminum, the other is brass. If a compressive force of $8400 \mathrm{N}$ is applied to the rods, (a) how much does their combined length decrease? (b) Which of the rods changes its length by the greatest amount? Explain.

Sachin Rao

Numerade Educator

Problem 45

A piano wire $0.82 \mathrm{m}$ long and $0.93 \mathrm{mm}$ in diameter is fixed on one end. The other end is wrapped around a tuning peg $3.5 \mathrm{mm}$ in diameter. Initially the wire, whose Young's modulus is $2.4 \times 10^{10} \mathrm{N} / \mathrm{m}^{2},$ has a tension of $14 \mathrm{N} .$ Find the tension in the wire after the tuning peg has been turned through one complete revolution.

Yaqub Khan

Numerade Educator

Problem 46

The formation of ice from water is accompanied by which of the following: (a) an absorption of heat by the water; (b) an increase in temperature; $(c)$ a decrease in volume; $(d)$ a removal of heat from the water; (e) a decrease in temperature?

Sachin Rao

Numerade Educator

Problem 47

Figure $T 7-26$ shows a portion of the vapor-pressure curve for water. Referring to the figure, estimate the pressure that would be required for water to boil at $30^{\circ} \mathrm{C}$.

Sachin Rao

Numerade Educator

Problem 48

Using the vapor-pressure curve given in Figure $17-26,$ find the temperature at which water boils when the pressure is $1.5 \mathrm{kPa}$.

Yaqub Khan

Numerade Educator

Problem 49

The Vapor Pressure of $C O_{2}$ A portion of the vapor pressure curve for carbon dioxide is given in Figure $17-27$
(a) Estimate the pressure at which $\mathrm{CO}_{2}$ boils at $0^{\circ} \mathrm{C}$.
(b) If the temperature is increased, does the boiling pressure increase, decrease, or stay the same? Explain.

Sachin Rao

Numerade Educator

Problem 50

Referring to the vapor-pressure curve for carbon dioxide given in Figure $17-27$
(a) estimate the temperature at which $\mathrm{CO}_{2}$ boils when the pressure is $1.5 \times 10^{6} \mathrm{Pa} .$ (b) If the pressure is increased, does the boiling temperature increase, decrease, or stay the same? Explain.

Sachin Rao

Numerade Educator

Problem 51

The phase diagram for water is shown in Figure $\nabla-28$. phase diagram? (b) What is the temperature $T_{2}$ on the phase diagram? (c) What happens to the melting/freezing temperature of water if atmospheric pressure is decreased? Justify your answer by referring to the phase diagram. (d) What happens to the boiling/condensation temperature of water if atmospheric pressure is increased? Justify your answer by referring to the phase diagram.(a) What is the temperature $T_{1}$ on the

Sachin Rao

Numerade Educator

Problem 52

The phase diagram for $\mathrm{CO}_{2}$ is shown in Figure $T-29 .$
(a) What is the phase of $\mathrm{CO}_{2}$ at $T=20^{\circ} \mathrm{C}$ and $P=500 \mathrm{kPa} ?$ (b) What is the phase of $\mathrm{CO}_{2}$ at $T=-80^{\circ} \mathrm{C}$ and $P=120 \mathrm{kPa} ?$ (c) For reasons of economy and convenience, bulk $\mathrm{CO}_{2}$ is often transported in liquid form in pressurized tanks. Using the phase diagram, determine the minimum pressure required to keep $\mathrm{CO}_{2}$ in the liquid phase at $20^{\circ} \mathrm{C}$.

Sachin Rao

Numerade Educator

Problem 53

A sample of water ice at atmospheric pressure has a temperature just below the freezing point. Refer to Figure $17-28$ to answer the following questions.
(a) What phase changes occur if the temperature of the system is increased while the pressure is held constant? (b) Suppose, instead, that the temperature of the system is held constant just below the freezing point while the pressure is decreased. What phase changes occur now?

Sachin Rao

Numerade Educator

Problem 54

A sample of liquid water at atmospheric pressure has a temperature just above the freezing point. Refer to Figure $17-28$ to answer the following questions.
(a) What phase changes occur if the temperature of the system is increased while the pressure is held constant? (b) Suppose, instead, that the temperature of the system is held constant just above the freezing point while the pressure is decreased. What phase changes occur now?

Yaqub Khan

Numerade Educator

Problem 55

A sample of solid carbon dioxide at a pressure of $5707 \mathrm{kPa}$ has a temperature just below the freezing point. Refer to Figure $17-29$ to answer the following questions.
(a) What phase changes occur if the temperature of the system is increased while the pressure is held constant? (b) Suppose, instead, that the temperature of the system is held constant just below the freezing point while the pressure is decreased. What phase changes OCCur now?

Sachin Rao

Numerade Educator

Problem 56

Four liquids are at their freezing temperature. Heat is now removed from each of the liquids until it becomes completely solidified. The amount of heat that must be removed, $Q$, and the mass, $m$, of each of the liquids are as follows: liquid $A, Q=33,500 \mathrm{J}, m=0.100 \mathrm{kg} ;$ liquid $\mathrm{B}, Q=166,000 \mathrm{J}$ $m=0.500 \mathrm{kg}$; liquid $\mathrm{C}, \mathrm{Q}=31,500 \mathrm{J}, \mathrm{m}=0.250 \mathrm{kg}$; liquid $\mathrm{D}$$Q=5400 \mathrm{J}, \mathrm{m}=0.0500 \mathrm{kg} .$ Rank these liquids in order of in creasing latent heat of fusion. Indicate ties where appropriate.

Sachin Rao

Numerade Educator

Problem 57

How much heat must be removed from $0.96 \mathrm{kg}$ of water at $0^{\circ} \mathrm{C}$ to make ice cubes at $0^{\circ} \mathrm{C} ?$

Sachin Rao

Numerade Educator

Problem 58

A heat transfer of $9.5 \times 10^{5}$ J is required to convert a block of ice at $-15^{\circ} \mathrm{C}$ to water at $15^{\circ} \mathrm{C} .$ What was the mass of the block of ice?

Yaqub Khan

Numerade Educator

Problem 59

How much heat must be added to $1.75 \mathrm{kg}$ of copper to change it from a solid at $1358 \mathrm{K}$ to a liquid at $1358 \mathrm{K}$ ?

Sachin Rao

Numerade Educator

Problem 60

A $1.1-\mathrm{kg}$ block of ice is initially at a temperature of $-5.0^{\circ} \mathrm{C} .$ (a) If $5.2 \times 10^{5} \mathrm{J}$ of heat are added to the ice, what is the final temperature of the system? Find the amount of ice, if any, that remains. (b) Suppose the amount of heat added to the ice block is doubled. By what factor must the mass of the ice be increased if the system is to have the same final temperature? Explain.

Sachin Rao

Numerade Educator

Problem 61

Referring to the previous problem, suppose the amount of heat added to the block of ice is reduced by a factor of 2 to $2.6 \times 10^{5} \mathrm{J} .$ Note that this amount of heat is still sufficient to melt at least some of the ice. (a) Do you expect the temperature increase in this case to be one-half that found in the previous problem? Explain. (b) What is the final temperature of the system in this case? Find the amount of ice, if any, that remains.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 62

Figure $17-21$ shows a temperature-versus-heat plot for $1.000 \mathrm{kg}$ of water. $(\mathrm{a})$ Calculate the heat corresponding to the points $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D} .$ (b) Calculate the slope of the line from point $B$ to point $C$. Show that this slope is equal to $1 / c,$ where $c$ is the specific heat of liquid water.

Yaqub Khan

Numerade Educator

Problem 63

Suppose the $1.000 \mathrm{kg}$ of water in Figure $17-21$ starts at point $A$ at time zero. Heat is added to this system at the rate of $12,250 \mathrm{J} / \mathrm{s} .$ How long does it take for the system to reach (a) point $\mathrm{B},$ (b) point $\mathrm{C},$ and $(\mathrm{c})$ point $\mathrm{D} ?$ (d) Describe the physical state of the system at time $t=63.00 \mathrm{s}$.

Anand Jangid

Numerade Educator

Problem 64

shows a temperature-versus-heat plot for $0.550 \mathrm{kg}$ of water.
(a) Calculate the slope of the line from point A to point B. Show that the slope is equal to $1 / m c,$ where $c$ is the specific heat of ice. (b) Calculate the slope of the line from point C to point D. Show that the slope is equal to $1 / m c,$ where $c$ is the specific heat of liquid water.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 65

In Conceptual Checkpoint $17-5$ we pointed out that steam can cause more serious burns than water at the same temperature. Here we examine this effect quantitatively, noting that flesh becomes badly damaged when its temperature reaches $50.0^{\circ} \mathrm{C}$. (a) Calculate the heat released as $12.5 \mathrm{g}$ of liquid water at $100^{\circ} \mathrm{C}$ is cooled to $50.0^{\circ} \mathrm{C}$. (b) Calculate the heat released when $12.5 \mathrm{g}$ of steam at $100^{\circ} \mathrm{C}$ is condensed and cooled to $50.0^{\circ} \mathrm{C}$. (c) Find the mass of flesh that can be heated from $37.0^{\circ} \mathrm{C}$ (normal body temperature) to $50.0^{\circ} \mathrm{C}$ for the cases con sidered in parts (a) and (b). (The average specific heat of flesh is $3500 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K} .)$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

When you go out to your car one cold winter morning you discover a 0.58 -cm-thick layer of ice on the windshield, which has an area of $1.6 \mathrm{m}^{2}$. If the temperature of the ice is $-2.0^{\circ} \mathrm{C}$ and its density is $917 \mathrm{kg} / \mathrm{m}^{3}$, find the heat required to melt all the ice.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 67

A large punch bowl holds $3.99 \mathrm{kg}$ of lemonade (which is essentially water) at $20.5^{\circ} \mathrm{C} .$ A $0.0550-\mathrm{kg}$ ice cube at $-10.2^{\circ} \mathrm{C}$ is placed in the lemonade. What is the final temperature of the system, and the amount of ice (if any) remaining? Ignore any heat exchange with the bowl or the surroundings.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 68

A 155-g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to $-196^{\circ} \mathrm{C}$. The cylinder is immediately placed in an insulated cup containing 80.0 g of water at $15.0^{\circ} \mathrm{C}$. What is the equilibrium temperature of this system? If your answer is $0{ }^{\circ} \mathrm{C}$, determine the amount of water that has frozen. The average specific heat of aluminum over this temperature range is $653 \mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$.

Yaqub Khan

Numerade Educator

Problem 69

An 825 -g iron block is heated to $352^{\circ} \mathrm{C}$ and placed in an insulated container (of negligible heat capacity) containing $40.0 \mathrm{g}$ of water at $20.0^{\circ} \mathrm{C}$. What is the equilibrium temperature of this system? If your answer is $100^{\circ} \mathrm{C}$, determine the amount of water that has vaporized. The average specific heat of iron over this temperature range is $560 \mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$

Yaqub Khan

Numerade Educator

Problem 70

A $35-g$ ice cube at $0.0 ~^{\circ} \mathrm{C}$ is added to $110 \mathrm{g}$ of water in a $62-g$ aluminum cup. The cup and the water have an initial temperature of $23^{\circ} \mathrm{C} .$ (a) Find the equilibrium temperature of the cup and its contents. (b) Suppose the aluminum cup is replaced with one of equal mass made from silver. Is the equilibrium temperature with the silver cup greater than, less than, or the same as with the aluminum cup? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 71

$A$ 48-g block of copper at $-12^{\circ} \mathrm{C}$ is added to $110 \mathrm{g}$ of water in a $75-g$ aluminum cup. The cup and the water have an initial temperature of $4.1^{\circ} \mathrm{C}$
(a) Find the equilibrium temperature of the cup and its contents. (b) What mass of ice, if any, is present when the system reaches equilibrium?

Yaqub Khan

Numerade Educator

Problem 72

A $0.075-\mathrm{kg}$ ice cube at $0.0^{\circ} \mathrm{C}$ is dropped into a Styrofoam cup holding $0.33 \mathrm{kg}$ of water at $14^{\circ} \mathrm{C} .$ (a) Find the final temperature of the system and the amount of ice (if any) remaining. Assume the cup and the surroundings can be ignored. (b) Find the initial temperature of the water that would be enough to just barely $y$ melt all of the ice.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 73

To help keep her barn warm on cold days, a farmer stores $865 \mathrm{kg}$ of warm water in the barn. How many hours would a 2.00-kilowatt electric heater have to operate to provide the same amount of heat as is given off by the water as it cools from $20.0^{\circ} \mathrm{C}$ to $0^{\circ} \mathrm{C}$ and then freezes at $0^{\circ} \mathrm{C} ?$

Yaqub Khan

Numerade Educator

Problem 74

Plastic bubble wrap is used as a protective packing material. Is the bubble wrap more effective on a cold day or on a warm day? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 75

Two adjacent rooms in a hotel are equal in size and connected by an open door. Room 1 is warmer than room $2 .$ Which room contains more air? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 76

As you go up in altitude, do you expect the ratio of oxygen to nitrogen in the atmosphere to increase, decrease; or stay the same? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 77

Suppose the Celsius temperature of an ideal gas is doubled from $100^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$. (a) Does the average kinetic energy of the molecules in this gas increase by a factor that is greater than, less than, or equal to $2 ?$ (b) Choose the best explanation from among the following:
I. Changing the temperature from $100^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$ goes beyond the boiling point, which will increase the kinetic energy by more than a factor of $2 .$
II. The average kinetic energy is directly proportional to the temperature, so doubling the temperature doubles the kinetic energy.
III. Doubling the Celsius temperature from $100^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$ changes the Kelvin temperature from $373.15 \mathrm{K}$ to $473.15 \mathrm{K}$ which is an increase of less than a factor of 2 .

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 78

Suppose the absolute temperature of an ideal gas is doubled from $100 \mathrm{K}$ to $200 \mathrm{K}$. (a) Does the average speed of the molecules in this gas increase by a factor that is greater than, less than, or equal to $2 ?$ (b) Choose the best explanation from among the following:
I. Doubling the Kelvin temperature doubles the average kinetic energy, but this implies an increase in the average speed by a factor of $\sqrt{2}=1.414 \ldots$ which is less than 2 .
II. The Kelvin temperature is the one we use in the ideal-gas law, and therefore doubling it also doubles the average speed of the molecules.
III. The change in average speed depends on the mass of the molecules in the gas, and hence doubling the Kelvin temperature generally results in an increase in speed that is greater than a factor of 2

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 79

Largest Raindrops Atmospheric scientists studying clouds in the Marshall Islands have observed what they believe to be the world's largest raindrops, with a radius of $0.52 \mathrm{cm}$. How many molecules are in these monster drops?

Yaqub Khan

Numerade Educator

Problem 80

Cooling Computers Researchers are developing "heat exchangers" for laptop computers that take heat from the laptop - to keep it from being damaged by overheating - and use it to vaporize methanol. Given that 5100 J of heat is removed from the laptop when $4.6 \mathrm{g}$ of methanol is vaporized, what is the latent heat of vaporization for methanol?

Yaqub Khan

Numerade Educator

Problem 81

In scuba diving circles, "an $80^{\prime \prime \prime}$ refers to a a scuba tank that holds 80 cubic feet of air, a standard amount for recreational diving. Given that a scuba tank is a cylinder 2 feet long and half a foot in diameter, determine (a) the volume of a tank and (b) the pressure in a tank when 80 cubic feet of air is compressed into its relatively small volume. (c) What is the mass of air in a tank that holds 80 cubic feet of air. Assume the temperature is $21^{\circ} \mathrm{C}$ and that the walls of the tank are of negligible thickness.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 82

A reaction vessel contains 8.06 g of $\mathrm{H}_{2}$ and $64.0 \mathrm{g}$ of $\mathrm{O}_{2}$ at a temperature of $125^{\circ} \mathrm{C}$ and a pressure of $101 \mathrm{kPa}$.
(a) What is the volume of the vessel? (b) The hydrogen and oxygen are now ignited by a spark, initiating the reaction $2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}$
This reaction consumes all the hydrogen and oxygen in the vessel. What is the pressure of the resulting water vapor when it returns to its initial temperature of $125^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 83

A bicycle tire with a radius of $0.68 \mathrm{m}$ has a gauge pressure of $42 \mathrm{lb} / \mathrm{in}^{2}$. Treating the tire as a hollow hoop with a crosssectional area of $0.0028 \mathrm{m}^{2}$, find the number of air molecules in the tire when its temperature is $24^{\circ} \mathrm{C}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 84

Peter catches a $4.8-\mathrm{kg}$ striped bass on a fishing line $0.54 \mathrm{mm}$ in diameter and begins to reel it in. He fishes from a pier well above the water, and his fish hangs vertically from the line out of the water. The fishing line has a Young's modulus of $5.1 \times 10^{9} \mathrm{N} / \mathrm{m}^{2} .$ (a) What is the fractional increase in length of the fishing line if the fish is at rest? (b) What is the fractional increase in the fishing line's length when the fish is pulled upward with a constant speed of $1.5 \mathrm{m} / \mathrm{s} ?$ (c) What is the fractional increase in the fishing line's length when the fish is pulled upward with a constant acceleration of $1.5 \mathrm{m} / \mathrm{s}^{2} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 85

You use a steel socket wrench $28 \mathrm{cm}$ long to loosen a rusty bolt, applying a force $F$ at the end of the handle. The handle undergoes a shear deformation of $0.11 \mathrm{mm}$.
(a) If the cross sectional arca of the handle is $2.3 \mathrm{cm}^{2},$ what is the magnitude of the applied force $F ?$ (b) If the cross-sectional area of the handle is doubled, by what factor does the shear deformation change? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 86

A steel ball (density $=7860 \mathrm{kg} / \mathrm{m}^{3}$ ) with a diameter of $6.4 \mathrm{cm}$ is tied to an aluminum wire $82 \mathrm{cm}$ long and $2.5 \mathrm{mm}$ in diameter. The ball is whirled about in a vertical circle with a tangential speed of $7.8 \mathrm{m} / \mathrm{s}$ at the top of the circle and $9.3 \mathrm{m} / \mathrm{s}$ at the bottom of the circle. Find the amount of stretch in the wire (a) at the top and (b) at the bottom of the circle.

Yaqub Khan

Numerade Educator

Problem 87

A lead brick with the dimensions shown in Figure $17-30$ rests on a rough solid surface. A force of $2400 \mathrm{N}$ is applied as indicated. Find (a) the change in height of the brick and (b) the amount of shear deformation.

Yaqub Khan

Numerade Educator

Problem 87

A lead brick with the dimensions shown in Figure $17-30$ rests on a rough solid surface. A force of $2400 \mathrm{N}$ is applied as indicated. Find (a) the change in height of the brick and (b) the amount of shear deformation.

Yaqub Khan

Numerade Educator

Problem 88

Five molecules have the following specds: $221 \mathrm{m} / \mathrm{s}$ $301 \mathrm{m} / \mathrm{s}, 412 \mathrm{m} / \mathrm{s}, 44.0 \mathrm{m} / \mathrm{s},$ and $182 \mathrm{m} / \mathrm{s}$
(a) Find $v_{a v}$ for these molecules. (b) Do you expect $\left(v^{2}\right)_{a v}$ to be greater than, less than, or equal to $\left(v_{a v}\right)^{2}$ ? Explain. (c) Calculate $\left(v^{2}\right)_{a v}$ and comment on your results. (d) Calculate $v_{\text {rms and compare with }}$ vav.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 88

Five molecules have the following speeds: $221 \mathrm{m} / \mathrm{s}$ $301 \mathrm{m} / \mathrm{s}, 412 \mathrm{m} / \mathrm{s}, 44.0 \mathrm{m} / \mathrm{s},$ and $182 \mathrm{m} / \mathrm{s}$
(a) Find $v_{a r}$ for these molecules. (b) Do you expect $\left(v^{2}\right)_{a x}$ to be greater than, less than, or equal to $\left(v_{a v}\right)^{2}$ ? Explain. (c) Calculate $\left(v^{2}\right)_{a v}$ and comment on your results.
(d) Calculate $v_{\text {rms }}$ and compare with $v_{a v}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 89

(a) Find the amount of heat that must be extracted from $1.5 \mathrm{kg}$ of steam at $110^{\circ} \mathrm{C}$ to convert it to ice at $0.0^{\circ} \mathrm{C}$. (b) What speed would this $1.5-\mathrm{kg}$ block of ice have if its translational kinetic energy were equal to the thermal energy calculated in part (a)?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 90

When water freezes into ice it expands in volume by $9.05 \%$ Suppose a volume of water is in a houschold water pipe or a cavity in a rock. If the water freezes, what pressure must be exerted on it to keep its volume from expanding? (If the pipe or rock cannot supply this pressure, the pipe will burst and the rock will split.)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 91

Suppose the $0.550 \mathrm{kg}$ of ice in Figure $17-22$ starts at point A. How much ice is left in the system after
(a) $5.00 \times 10^{4} J$
(b) $1.00 \times 10^{5} \mathrm{J},$ and
(c) $1.50 \times 10^{5}$ J of heat are added to the system?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 92

Students on a spring break picnic bring a cooler that contains $5.1 \mathrm{kg}$ of ice at $0.0^{\circ} \mathrm{C} .$ The cooler has walls that are $3.8 \mathrm{cm}$ thick and are made of Styrofoam, which has a thermal conductivity of $0.030 \mathrm{W} / \mathrm{m} \cdot \mathrm{C}^{\circ}$ ). The surface area of the cooler is $15 \mathrm{m}^{2}$, and it rests in the shade where the air temperature is $21^{\circ} \mathrm{C}$. (a) Find the rate at which heat flows into the cooler. (b) How long does it take for the ice in the cooler to melt?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 93

A 5.5-kg block of ice at $-15^{\circ} \mathrm{C}$ slides on a horizontal surface with a coefficient of kinetic friction equal to $0.062 .$ The initial speed of the block is $6.9 \mathrm{m} / \mathrm{s}$ and its final speed is $5.5 \mathrm{m} / \mathrm{s}$. Assuming that all the energy dissipated by kinetic friction goes into melting a small mass $m$ of the ice, and that the rest of the ice block remains at $-1.5^{\circ} \mathrm{C}$, determine the value of $m$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 94

A cylindrical copper rod $37 \mathrm{cm}$ long and $7.5 \mathrm{cm}$ in diameter is placed upright on a hot plate held at a constant temperature of $120^{\circ} \mathrm{C}$, as indicated in Figure $\mathrm{T}-3 \mathrm{l}$. A small depression on top of the rod holds a $25-g$ ice cube at an initial temperature of $0.0^{\circ} \mathrm{C} .$ How long does it take for the ice cube to melt? Assume there is no heat loss through the vertical surface of the rod, and that the thermal conductivity of copper is $390 \mathrm{W} /\left(\mathrm{m} \cdot \mathrm{C}^{\circ}\right)$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 95

What pressure did the bathysphere experience at its record depth?
A. 9.37 atm
B. 89.6 atm
C. 91.9 atm
D. $92.9 \mathrm{atm}$

Yaqub Khan

Numerade Educator

Problem 96

How many moles of air did the bathysphere contain when it was sealed at the surface, assuming a temperature of $297 \mathrm{K}$ and ignoring the thickness of the metal shell? (Note: A resting person breathes roughly 0.5 mol of air per minute.)
A. $65.2 \mathrm{mol}$
B. 270 mol
C. $392 \mathrm{mol}$
D. 523 mol

Yaqub Khan

Numerade Educator

Problem 97

How much did the volume of the bathysphere decrease as it was lowered to its record depth? (For simplicity, treat the bathysphere as a solid metal sphere.)
A. $9.0 \times 10^{-5} \mathrm{m}^{3}$
B. $9.2 \times 10^{-5} \mathrm{m}^{3}$
C. $1.1 \times 10^{-4} \mathrm{m}^{3}$
D. $3.8 \times 10^{-4} \mathrm{m}^{3}$

Yaqub Khan

Numerade Educator

Problem 98

Suppose the bathysphere and its occupants had a combined mass of $12,700 \mathrm{kg}$. How much did the cable stretch when the bathysphere was at a depth of $923 \mathrm{m} ?$ (Neglect the weight of the cable itself, but include the effects of the bathysphere's buoyancy.)
$\mathbf{A}, 47 \mathrm{cm}$
B. $48 \mathrm{cm}$
$\mathrm{C} \cdot 52 \mathrm{cm}$
D. $53 \mathrm{cm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 99

Referring to Example $17-6$ (a) Find the final temperature of the system if two $0.0450-\mathrm{kg}$ ice cubes are added to the warm lemonade. The temperature of the ice is $0^{\circ} \mathrm{C} ;$ the temperature and mass of the warm lemonade are $20.0^{\circ} \mathrm{C}$ and $3.95 \mathrm{kg}$, respectively.
(b) How many $0.0450-\mathrm{kg}$ ice cubes at $0^{\circ} \mathrm{C}$ must be added to the original warm lemonade if the final temperature of the system is to be at least as cold as $15.0^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 100

Referring to Example $17-6$ (a) Find the final temperature of the system if a single $0.045-\mathrm{kg}$ ice cube at $0^{\circ} \mathrm{C}$ is added to $2.00 \mathrm{kg}$ of lemonade at $1.00^{\circ} \mathrm{C} .$ (b) What initial temperature of the lemonade will be just high enough to melt all of the ice in a single ice cube and result in an equilibrium temperature of $0^{\circ} \mathrm{C}$ ? The mass of the lemonade is $2.00 \mathrm{kg}$ and the temperature of the ice cube is $0^{\circ} \mathrm{C}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator