College Physics Explore and Apply

Eugenia Etkina; Alan Van Heuvelen; Gorazd Planinši?

Chapter 12

Gases - all with Video Answers

Educators

Chapter Questions

Problem 1

What are the molar masses of molecular and atomic hydrogen, helium, oxygen, and nitrogen? What are their molecular masses?

Zulfiqar Ali

Zulfiqar Ali

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Problem 2

Estimate the number of hydrogen atoms in the Sun. The mass of the Sun is $2 \times 10^{30} \mathrm{kg}$. About $70 \%$ of it by mass is hydrogen, $30 \%$ is helium, and there is a negligible amount of other elements.

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Problem 3

The average particle density in the Milky Way galaxy is about one particle
per cubic centimeter. Express this number in SI units 1kg>m3. Indicate any assumptions you made

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Problem 4

(a) What is the concentration (number per cubic meter) of the molecules in air at normal conditions? (b) What is the average distance between molecules compared to the dimensions of the molecules?
(c) Can you consider air to be an ideal gas? Explain your answer.

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Problem 5

What is the mass of a water molecule in kilograms? What is the mass of an average air molecule in kilograms?

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Problem 6

You find that the average gauge pressure in your car tires is about 35 psi. (a) How many newtons per square meter is it? What is gauge pressure? (b) Determine the absolute pressure in the tires.

Zulfiqar Ali

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Problem 7

Forced vital capacity Physicians use a machine called a spirometer to measure the maximum amount of air a person can exhale (called the forced vital capacity). Suppose you can exhale $4.8 \mathrm{L} .$ How many kilograms of air do you exhale? What assumptions did you make to answer the question? How do these assumptions affect the result?

Farhanul Hasan

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Problem 8

A container is at rest with respect to a desk. Inside the container a particle is moving horizontally at a speed $v$ with respect to the desk. It collides with a vertical wall of the container elastically and rebounds. Compare the direction and the speed of the particle if the wall is (a) at rest with respect to the desk; (b) moving in the same direction as the particle at a speed smaller than the particle's; and (c) moving in the direction opposite to the motion of the particle at a smaller speed.

Zachary Warner

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Problem 9

Oxygen tank for mountains Consider an oxygen tank for a mountain climbing trip. The mass of one molecule of oxygen is $5.3 \times 10^{-26} \mathrm{kg}$. What is the pressure that oxygen exerts on the inside walls of the tank if its concentration is $10^{25}$ particles/m and its rms speed is $600 \mathrm{m} / \mathrm{s} ?$ What assumptions did you make?

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Problem 10

You have five molecules with the following speeds: $300 \mathrm{m} / \mathrm{s}, 400 \mathrm{m} / \mathrm{s}$, $500 \mathrm{m} / \mathrm{s}, 450 \mathrm{m} / \mathrm{s},$ and $550 \mathrm{m} / \mathrm{s} .$ (a) What is their average speed?
(b) What is their rms speed? Compare it with the average speed.

Zulfiqar Ali

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Problem 11

Two gases in different containers have the same concentration and same rms speed. The mass of a molecule of the first gas is twice the mass of a molecule of the second gas. What can you say about their pressures? Explain.

Zulfiqar Ali

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Problem 12

Four molecules are moving with the following velocities: $300 \mathrm{m} / \mathrm{s}$ south, $300 \mathrm{m} / \mathrm{s}$ north $, 400 \mathrm{m} / \mathrm{s}$ east, and $400 \mathrm{m} / \mathrm{s}$ west.
(a) What is their average velocity? (b) What is their rms speed?

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Problem 13

Hitting tennis balls against a wall A 0.058-kg tennis ball, traveling at $25 \mathrm{m} / \mathrm{s},$ hits a wall, rebounds with the same speed in the opposite direction, and is hit again by another player, causing the ball to return to the wall at the same speed. The collision of the ball with the wall lasts $1 \mathrm{ms}$. The ball returns to the wall once every $0.60 \mathrm{s}$. (a) Determine the average force exerted on the ball during a single collision and the force that the ball exerts on the wall averaged over the time between collisions. State the assumptions that you made. (b) If 10 people are practicing against a wall with an area of $30 \mathrm{m}^{2},$ what is the average pressure of the 10 tennis balls against the wall?

Zulfiqar Ali

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Problem 14

Friends throw snowballs at the wall of a $3.0 \mathrm{m} \times 6.0 \mathrm{m}$ barn. The snowballs have mass $0.10 \mathrm{kg}$ and hit the wall moving at an average speed of $6.0 \mathrm{m} / \mathrm{s} .$ They do not rebound. Determine the average pressure exerted by the snowballs on the wall if 40 snowballs hit the wall each second. Which problem, this or the previous problem, resembles the actions of the molecules of an ideal gas hitting the walls of their container?

Zulfiqar Ali

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Problem 15

A ball moving at a speed of $3.0 \mathrm{m} / \mathrm{s}$ with respect to the ground hits a stationary wall at a $30^{\circ}$ angle with respect to the surface of the wall. Determine the direction and the magnitude of the velocity of the ball after it rebounds. Explain carefully what physics principles you used to find the answer. What assumptions did you make? How will the answer change if one or more of them are not valid?

Zachary Warner

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Problem 16

Oxygen tank for mountain climbing An oxygen container used by mountain climbers has a 90 -min oxygen supply at a rate of $6 \mathrm{L} / \mathrm{min}$ (with the volume measured at atmospheric pressure). Determine everything you can about the gas in the container. Make reasonable assumptions.

Zachary Warner

Numerade Educator

Problem 17

Your temperature, when taken orally, is $98.6^{\circ} \mathrm{F} .$ When taken under your arm, it's $36.6^{\circ} \mathrm{C} .$ Are these results consistent? Explain.

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Problem 18

Air consists of many different molecules, for example, $\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{H}_{2} \mathrm{O},$ and $\mathrm{CO}_{2} .$ Which molecules are the fastest on average? The slowest on average? Explain.

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Problem 19

What is the average kinetic energy of a particle of air at standard conditions?

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Problem 20

Air is a mixture of molecules of different types. Compare the rms speeds of the molecules of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and $\mathrm{CO}_{2}$ at standard conditions. What assumptions did you make?

Farhanul Hasan

Numerade Educator

Problem 21

How many moles of air are in a regular $1-\mathrm{L}$ water bottle when you finish drinking the water? What assumptions did you make? How do these assumptions affect your result?

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Problem 22

At approximately what temperature does the average translational kinetic energy of a $\mathrm{N}_{2}$ molecule in an ideal gas equal the macroscopic translational kinetic energy of a copper atom in a penny that is dropped from the height of $1.0 \mathrm{m} ?$

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Problem 23

A molecule moving at speed $v_{1}$ collides head-on with a molecule of the same mass moving at speed $v_{2}$. Compute the speeds of the molecules after the collision. What assumptions did you make? How does the answer to this problem explain why the mixing of hot and cold gases causes the cold gas to become warmer and the hot gas to become cooler?

Zulfiqar Ali

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Problem 24

Balloon flight For a balloon ride, the balloon must be inflated with helium to a volume of $1500 \mathrm{m}^{3}$ at sea level. The balloon will rise to an altitude of about $12 \mathrm{km},$ where the temperature is about $-52^{\circ} \mathrm{C}$ and the pressure is about $20 \mathrm{kPa}$. How many $\mathrm{kg}$ of helium should be put into the balloon? What assumptions did you make?

Zulfiqar Ali

Numerade Educator

Problem 25

Ears pop The middle ear has a volume of about $6.0 \mathrm{cm}^{3}$ when at a pressure of $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$. Determine the volume of that same air when the air pressure is $0.83 \times 10^{5} \mathrm{N} / \mathrm{m}^{2},$ as it is at an elevation of $1500 \mathrm{m}$ above sea level (assume the air temperature remains constant). If the volume of the middle ear remains constant, some air will have to leave as the
elevation increases. That is why ears "pop."

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Problem 26

Even the best vacuum pumps cannot lower the pressure in a container below $10^{-15}$ atm. How many molecules of air are left in each cubic centimeter in such a "vacuum"? Assume that the temperature is $273 \mathrm{K}$.

Zulfiqar Ali

Numerade Educator

Problem 27

Pressure in interstellar space The concentration of particles (assume neutral hydrogen atoms) in interstellar gas is 1 particle $/ \mathrm{cm}^{3},$ and the average temperature is about $3 \mathrm{K} .$ What is the pressure of the interstellar gas? How does it compare to the best vacuum that can be achieved on Earth (see the previous problem)?

Zulfiqar Ali

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Problem 28

Describe experiments to determine if each of the three gas isoprocess laws works. The experiments should be ones that you could actually carry out.

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Problem 29

The following data were collected for the temperature and volume of a gas. Can this gas be described by the ideal gas model? Explain how you know.
$$
\begin{array}{cc}
\hline \begin{array}{c}
\text { Temperature } \\
\left({ }^{\circ} \mathrm{C}\right)
\end{array} & \text { Volume (mL) } \\
\hline 11 & 95.0 \\
25 & 100.0 \\
47 & 107.5 \\
73 & 116.0 \\
159 & 145.1 \\
233 & 170.0 \\
258 & 177.9 \\
\hline
\end{array}
$$

Zulfiqar Ali

Numerade Educator

Problem 30

Explain the microscopic mechanisms for the relation of macroscopic variables for an isothermal process, an isobaric process, and an isochoric process occurring in an ideal gas.

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Problem 31

Scuba diving The pressure of the air in a diver's lungs when he is $20 \mathrm{m}$ under the water surface is $3.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2},$ and the air occupies a volume of 4.8 L. How many moles of air should he exhale while moving to the surface, where the pressure is $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} ?$

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Problem 32

When surrounded by air at a pressure of $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$, a baskethall has a radius of $0.12 \mathrm{m},$ Compare its volume at this condition with the volume that it would have if you took it $15 \mathrm{m}$ below the water surface, where the pressure is $2.5 \times 10^{3} \mathrm{N} / \mathrm{m}^{2}$. What assumptions did you make?

Zulfiqar Ali

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Problem 33

Some students are given the following problem: "A $5000-\mathrm{cm}^{3}$ cylinder is filled with nitrogen gas at $1.0 \times 10^{5} \mathrm{Pa}$ and $300 \mathrm{K}$ and closed with a movable piston. The gas is slowly compressed at constant temperature to a final
(a) Explain why volume of $5 \mathrm{cm}^{3} .$ Determine the final pressure of the gas." the ideal gas law cannot be applied to solve this problem. Present quantitative arguments. (b) Modify the problem so that it can be solved using the ideal gas law and give your solution.

Zulfiqar Ali

Numerade Educator

Problem 34

" - You have gas in a container with a movable piston. The walls of the container are thin enough so that its temperature stays the same as the temperature of the surrounding medium. You have baths of water of different temperatures, different objects that you can place on top of the piston, etc.
(a) Describe how you could make the gas undergo an isothermal process so that the pressure inside increases by $10 \%$, then undergo an isobaric process so that the new volume decreases by $20 \%$, and finally undergo an isochoric process so that the temperature increases by $15 \%$
(b) Represent this three-step process in $P$ -versus- $T, V$ -versus- $T,$ and $P$ -versus- $V$ graphs.
(c) Express the new pressure, volume, and temperature in terms of their initial values.

Zachary Warner

Numerade Educator

Problem 35

You want to determine the temperature in a freezer using the following equipment: an empty plastic bottle with a cap, a graduated measuring cylinder, and a bowl of water. You also know your room temperature $T_{\mathrm{R}}$.
(a) Which of the procedures described below will give data from which you can determine the temperature in the freezer? (b) For the procedure that you have chosen in part (a), derive the expression for the temperature in the freezer as a function of relevant physical quantities. Indicate any assumptions that you made.
I. Put the open plastic bottle into the freezer for half an hour. Take the bottle out, turn it upside down into the water, and measure the volume of the water sucked into the bottle.
II. Put the open plastic bottle in the freezer for half an hour. Take the bottle out and close it tightly with a cap. Wait until the bottle's shape stops changing. Turn the bottle upside down into the water, open the cap, and measure the volume of the water that entered the bottle.
III. Put the closed plastic bottle in the freezer for half an hour. Take the bottle out, turn it upside down into the water, and then open the cap. Measure the volume of the water sucked into the bottle.
IV. Put the closed plastic bottle in the freezer for half an hour. Take the bottle out, open the cap, and turn the bottle upside down into the water. Measure the volume of the water sucked into the bottle.

Tianyu Li

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Problem 36

Bubbles While snorkeling, you see air bubbles leaving a crevice at the bottom of a reef. One of the bubbles has a radius of $0.060 \mathrm{m}$. As the bubble rises, the pressure inside it decreases by $50 \% .$ Now what is the bubble's radius? What assumptions did you make to solve the problem?

Zulfiqar Ali

Numerade Educator

Problem 37

Diving bell A cylindrical diving bell, open at the bottom and closed at the top, is $4 \mathrm{m}$ tall. Scientists fill the bell with air at the pressure of $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} .$ The pressure increases naturally by $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ for
each $10 \mathrm{m}$ that the bell is lowered below the surface of the water. If the bell
is lowered $30 \mathrm{m}$ below the ocean surface, how many meters of air space are left inside the bell? Why doesn't water enter the entire bell as it goes under water? Draw several sketches for this problem. Assume the temperature remains constant.

Zachary Warner

Numerade Educator

Problem 38

Mount Everest (a) Determine the number of molecules per unit volume in the atmosphere at the top of Mount Everest. The pressure is $0.31 \times 10^{5} \mathrm{N} / \mathrm{m}^{2},$ and the temperature is $-30^{\circ} \mathrm{C}$ (b) Determine the number of molecules per unit volume at sea level, where the pressure is $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ and the temperature is $20^{\circ} \mathrm{C}$

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Problem 39

Breathing on Mount Everest Using the information from Problem 12.38 , estimate how frequently you need to breathe on top of Mount Everest to inhale the same amount of oxygen as you do at sea level. The pressure is about one-third the pressure at sea level.

Zulfiqar Ali

Numerade Educator

Problem 40

You would like to make homemade beer, but you are concerned about storing it. Your beer is capped into a bottle at a temperature of $27^{\circ} \mathrm{C}$ and a pressure of $1.2 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$. The cap will pop off if the pressure inside the bottle exceeds $1.5 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} .$ At what maximum temperature can you store the beer so the gas inside the bottle does not pop the

Zulfiqar Ali

Numerade Educator

Problem 41

Car tire With a tire gauge, you measure the pressure in a car tire as 2.1 $\times 10^{5} \mathrm{N} / \mathrm{m}^{2}$. How can this be if you know that absolute pressure in the tire is three times higher than atmospheric? The tire looks okay. What's the deal?

Zulfiqar Ali

Numerade Educator

Problem 42

Car tire dilemma Imagine a car tire that contains 5.1 moles of air when at a gauge pressure of $2.1 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ (the pressure above atmospheric pressure) and a temperature of $27^{\circ} \mathrm{C}$. The temperature increases to $37^{\circ} \mathrm{C}$, the volume decreases to 0.8 times the original volume, and the gauge pressure decreases to $1.6 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$. Can these measurements be correct if the tire did not leak? If it did leak, then how many moles of air are left in the tire?

Zulfiqar Ali

Numerade Educator

Problem 43

There is a limit to how much gas can pass through a pipeline, because the pipes can only tolerate so much pressure on the walls. To increase the amount of gas going through the pipeline, engineers decide to cool the gas (to reduce its pressure). Suggest how much they should lower the temperature of the gas if they want to increase the mass per unit time by 1.5 times.

Zulfiqar Ali

Numerade Educator

Problem 44

Explain how you know that the volume of one mole of gas at standard conditions is $22.4 \mathrm{L}$.

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Problem 45

At what pressure is the density of $-50^{\circ} \mathrm{C}$ nitrogen gas $\left(\mathrm{N}_{2}\right)$ equal to
0.01 times the density of water?

Zulfiqar Ali

Numerade Educator

Problem 46

In the morning, the gauge pressure in your car tires is 35 psi. During the day, the air temperature increases from $20^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ and the pressure increases to 36.5 psi. By how much did the volume of one of the tires increase? What assumptions did you make?

Zulfiqar Ali

Numerade Educator

Problem 47

Equation Jeopardy 1 The equation below describes a process. Construct a word problem for a process that is consistent with the equations (there are many possibilities). Provide as much detailed information as possible about your proposed process.
$$
\frac{1.2 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}}{293 \mathrm{K}}=\frac{2.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}}{T}
$$

Zulfiqar Ali

Numerade Educator

Problem 48

Equation Jeopardy 2 The equation below describes a process. Construct a word problem for a process that is consistent with the equations (there are many possibilities). Provide as much detailed information as possible about your proposed process.
$$
\begin{aligned}
\Delta n=\frac{\left(0.67 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}\right)\left(0.60 \times 10^{-6} \mathrm{m}^{3}\right)}{(8.3 \mathrm{J} / \mathrm{mole} \cdot \mathrm{K})(303 \mathrm{K})} \\
-& \frac{\left(1.00 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}\right)\left(0.60 \times 10^{-6} \mathrm{m}^{3}\right)}{(8.3 \mathrm{J} / \mathrm{mole} \cdot \mathrm{K})(310 \mathrm{K})}
\end{aligned}
$$

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Numerade Educator

Problem 49

"The P-versus-T graph in Figure $P 12.49$ describes a cyclic process comprising four hypothetical parts. (a) What happens to the pressure of the gas in each part? (b) What happens to the temperature of the gas in each part? (c) What happens to the volume of the gas in each part?
(d) Explain each part microscopically.
(e) Use the information from (a)-(c) to represent the same parts in $P$ -versus- $V$ and $V$ -versus-T graphs. (Hint: It helps to align the $P$ -versus- $V$ graph beside the $P$ -versus- $T$ graph using the same $P$ values on the ordinate (vertical axis) and to place the $V$ -versus-T graph below the $P$ -versus-T graph using the same $T$ values on the abscissa (horizontal axis). This helps keep the same scale for the variables.)

Zachary Warner

Numerade Educator

Problem 50

the $V$ -versus- $T$ graph in Figure $P 12.50$ describes a cyclic process comprising four hypothetical parts. (a) What happens to the pressure of the gas in each part?
(b) What happens to the temperature of the gas in each part?
(c) What happens to the volume of the gas in each part?
(d) Explain cach part microscopically.
(e) Use the information from (a)-(c) to represent the same process in a $P$ -versus- $T$ graph (below the $V$ -versus- $T$ graph) and a P-versus- $V$ graph (beside the $P$ -versus- $T$.gee the hint in the previous problem about the graph alignments.

Zachary Warner

Numerade Educator

Problem 51

Breathing You are breathing heavily while hiking up the mountain. To inhale, you expand your diaphragm and lungs. Explain, using your knowledge of gas pressure, why this mechanical movement leads to the air flowing into your nose or mouth. Support your reasoning with diagrams if necessary.

Zulfiqar Ali

Numerade Educator

Problem 52

The temperature of the Sun's atmosphere near the surface is about $6000 \mathrm{K},$ and the concentration of atoms is about $10^{15}$ particles $/ \mathrm{m}^{3} .$ What are the average pressure and density of its atmosphere? What assumptions did you make to solve the problem?

Zulfiqar Ali

Numerade Educator

Problem 53

Breathing and metabolism We need about $0.7 \mathrm{L}$ of oxygen per minute to maintain our resting metabolism and about $2 \mathrm{L}$ when standing and walking. Estimate the number of breaths per minute for a person to satisfy this need when resting and when standing and walking. What assumptions did you make? Remember that oxygen is about $21 \%$ of the air.

Zulfiqar Ali

Numerade Educator

Problem 54

Sun's life expectancy (a) Estimate the average kinetic energy of the particles in the Sun. Assume that it is made of atomic hydrogen and that its average temperature is $100,000 \mathrm{K} .$ The mass of the Sun is $2 \times 10^{30} \mathrm{kg}$ (b) For how long would the Sun shine using this energy if it radiates $4 \times 10^{26} \mathrm{W} / \mathrm{s} ?$ Is your answer reasonable? Explain.

Zulfiqar Ali

Numerade Educator

Problem 55

A gas that can be described by the ideal gas model is contained in a cylinder of volume $V$. The temperature of the gas is $T$. The mass of the gas is $m,$ and the molar mass is $M .$ Write an expression for the total thermal energy of the gas. Now, imagine that the exact same gas has been placed in a container of volume $2 V .$ What happens to its pressure? What happens to its temperature? What happens to its thermal energy?

Zulfiqar Ali

Numerade Educator

Problem 56

Equation Jeopardy 3 The three equations below describe a physical situation. Construct a word problem for a situation that is consistent with the equations (there are many possibilities), Provide as much detailed information as possible about the situation.
$$
\begin{aligned}
m &=\left(1.3 \mathrm{kg} / \mathrm{m}^{3}\right)(3.0 \mathrm{m} \times 5.0 \mathrm{m} \times 2.0 \mathrm{m}) \\
N &=m /\left[\left(29 \times 10^{-3} \mathrm{kg}\right) /\left(6.0 \times 10^{23} \text { particles }\right)\right] \\
U_{\mathrm{th}} &=N(3 / 2)\left(1.38 \times 10^{-23} \mathrm{J} / \mathrm{K}\right)(273 \mathrm{K})
\end{aligned}
$$

Zulfiqar Ali

Numerade Educator

Problem 57

A simple experimental setup for performing isobaric processes can be made with a thin glass tube filled with a gas and closed with a drop of water (Figure $P 12.57$ ). If the pressure of the gas changes, the drop moves until the sum of the forces exerted on the drop is zero (there is no friction between the drop and the tube). The inner diameter of the glass tube is $3.0 \mathrm{mm}$ and the length of the tube is $200.0 \mathrm{mm} .$ At normal room temperature, a $5.0-\mathrm{mm}-$ long water drop is $30.0 \mathrm{mm}$ from the open end of the tube. Estimate the temperature range in which this setup can be used to show isobaric processes. (Hint: What happens to water at low temperature?)

Zulfiqar Ali

Numerade Educator

Problem 58

See the previous problem. Explain how the force exerted by Earth on the water drop and the orientation of the tube affects the performance of the setup.

Zulfiqar Ali

Numerade Educator

Problem 59

Jeff and Natalie notice that a rubber balloon, which is first in a warm room, shrinks when they take it into the garden on a cold winter day. They propose two different explanations for the observed phenomenon:
(a) the balloon is slowly leaking; (b) the balloon shrinks due to decreased temperature while the pressure in the balloon remains constant (isobaric compression). In order to test their proposed explanations, Jeff and Natalie perform three consecutive experiments: they measure the volume of the balloon and the temperature of the air near the balloon (1) in the room, ( 2) in the garden, and (3) again in the room. Their measurements, including uncertainties, are presented in the table below. $$
\begin{array}{clcc}
\hline \text { Exp. # } & \text { Location } & \text { Temperature } & \text { Volume of the balloon } \\
\hline 1 & \text { Room } & 26.2^{\circ} \mathrm{C} \pm 0.1^{\circ} \mathrm{C} & 7500 \mathrm{cm}^{3} \pm 400 \mathrm{cm}^{3} \\
2 & \text { Garden } & -15.3^{\circ} \mathrm{C} \pm 0.1^{\circ} \mathrm{C} & 6400 \mathrm{cm}^{3} \pm 400 \mathrm{cm}^{3} \\
3 & \text { Room } & 26.2^{\circ} \mathrm{C} \pm 0.1^{\circ} \mathrm{C} & 7300 \mathrm{cm}^{3} \pm 400 \mathrm{cm}^{3} \\
\hline
\end{array}
$$ Based on the data, can Jeff and Natalie reject any of their hypotheses? Explain. Make sure you include uncertainties in your answer.

Vidhi Bhatt

Numerade Educator

Problem 60

Different planet compositions Explain why planets closer to the Sun have low concentrations of light elements, but light elements are relatively abundant in giant planets such as Jupiter, Uranus, and Saturn, which are far from the Sun.

Zulfiqar Ali

Numerade Educator

Problem 61

Density of our galaxy Estimate the average density of particles in our galaxy, assuming that the most abundant element is atomic hydrogen. There are about $10^{11}$ stars in the galaxy and the size of the galaxy is about $10^{5}$ light-years. A light-year is the distance light travels in 1 year moving at a speed of $3 \times 10^{8} \mathrm{m} / \mathrm{s} .$ What do you need to assume about the stars in order to answer this question?

Zulfiqar Ali

Numerade Educator

Problem 62

Breathing During each breath you probably inhale about $0.50 \mathrm{L}$ of air. How many oxygen molecules do you inhale if you are at sea level?

Zulfiqar Ali

Numerade Educator

Problem 63

Car engine During a compression stroke of a cylinder in a diesel engine, the air pressure in the cylinder increases from $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ to $50 \times 10^{5} \mathrm{N} / \mathrm{m}^{2},$ and the temperature increases from $26^{\circ} \mathrm{C}$ to $517^{\circ} \mathrm{C} . \mathrm{A}$
typical compression ratio (the ratio of the largest and the smallest volume of a cylinder) for a diesel engine is $20: 1 .$ Using this information, how would you convince your friends that knowledge about ideal gases can help explain how hot gases burned in the car engine affect the motion of the car?

Zulfiqar Ali

Numerade Educator

Problem 64

How can the pressure of air in your house stay constant during the day if the temperature rises? Estimate the volume of your house and the number of moles of air that leave the house during the daytime. Assume that nighttime temperature and daytime temperature differ by about $10^{\circ} \mathrm{C}$. List all other assumptions that are necessary to answer the question.

Zulfiqar Ali

Numerade Educator

Problem 65

Tell-all problem Tell everything you can about a process that was performed with $2 \times 10^{-3}$ moles of a gas and that is described by the pressure-versus-volume graph shown in Figure $P 12.65$

Osman Elomda

Numerade Educator

Problem 66

Two massless, frictionless pistons are inside a horizontal tube opened at both ends. A $10-\mathrm{cm}$ -long thread connects the pistons. The cross-sectional area of the tube is $20 \mathrm{cm}^{2} .$ The pressure and temperature of gas between the pistons and the outside air are the same and are equal to $P=1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ and $T=24^{\circ} \mathrm{C} .$ At what temperature of the gas will the thread break if it breaks when the tension reaches $30 \mathrm{N}$ ?

Zulfiqar Ali

Numerade Educator

Problem 67

A closed cylindrical container is divided into two parts by a light, movable, frictionless piston. The container's total length is $100 \mathrm{cm} .$ Where is the piston located when one side is filled with nitrogen $\left(\mathrm{N}_{2}\right)$ and the other side with the same mass of hydrogen $\left(\mathrm{H}_{2}\right)$ at the same temperature?

Zulfiqar Ali

Numerade Educator

Problem 68

How many molecules are there in 1 g of air at normal conditions? If these molecules were distributed uniformly on Earth's surface, estimate the number that would be under your feet right now. The radius of Earth is about $6400 \mathrm{km}$

Zulfiqar Ali

Numerade Educator

Problem 69

The speed of sound in an ideal gas is given by the relationship
$$
v=\sqrt{\frac{\gamma R T}{M}}
$$
where $R=$ the universal gas constant $=8.314 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K} ; T=$ the absolute temperature; $M=$ the molar mass of the gas in $\mathrm{kg} / \mathrm{mol} ;$ and $\gamma$ is a characteristic of the specific gas. For air, $\gamma=1.4$ and the average molar mass for dry air is $28.95 \mathrm{g} / \mathrm{mol}$. (a) Show that the equation gives you correct units. (b) Give reasons why the temperature of the gas is in the numerator and the molar mass of the gas is in the denominator.

Zulfiqar Ali

Numerade Educator

Problem 70

Using the information from problem $12.69,$ calculate the speed of sound in the air. What assumptions are you making?

Zulfiqar Ali

Numerade Educator

Problem 71

Speed of sound in summer and winter Using the information in problem $12.69,$ estimate how much faster sound travels in summer than in winter. Explain how you arrived at your answer and the assumptions that you made.

Zulfiqar Ali

Numerade Educator

Problem 72

A chamber of unknown volume is filled with an unknown amount of ideal gas. A cylinder with an open bottom and calibrated volume is connected to the chamber and is closed with a movable piston. A gas pressure sensor is also mounted on the chamber (Figure $P 12.72$ ). The whole experimental setup is kept at a constant temperature of $300 \mathrm{K}$. Doris moves the piston from mark 0 to mark $200 \mathrm{mL}$ in steps of $50 \mathrm{mL}$ and records the corresponding pressure in the chamber. She moves the piston very slowly and waits several minutes before recording the pressure values. Use Doris's data in the table to determine the volume of the chamber and the number of moles of gas. (Note: This is a problem that requires linearization of data.)
$$
\begin{array}{cc}
\hline V_{\text {Cy }}(\mathrm{mL}) & P\left(10^{5} \mathrm{N} / \mathrm{m}^{2}\right) \\
\hline 0 & 4.35 \\
50 & 3.85 \\
100 & 3.50 \\
150 & 3.15 \\
200 & 2.90 \\
\hline
\end{array}
$$

Zulfiqar Ali

Numerade Educator

Problem 73

Why is the wall tension in capillaries so small?
(a) There are so many capillaries.
(b) Their radii are so small.
(c) The outward pressure of the blood inside is so small.
(d) $b$ and $c$
(e) $a, b,$ and $c$

Zulfiqar Ali

Numerade Educator

Problem 74

Which answer below is closest to the wall tension in a typical arteriole of radius $0.15 \mathrm{mm}$ and $60 \mathrm{mm}$ Hg blood pressure?
(a) $0.001 \mathrm{N} / \mathrm{m}$
(b) $0.01 \mathrm{N} / \mathrm{m}$
(c) $0.1 \mathrm{N} / \mathrm{m}$
(d) $1 \mathrm{N} / \mathrm{m}$
(e) $10 \mathrm{N} / \mathrm{m}$

Zulfiqar Ali

Numerade Educator

Problem 75

According to Laplace's law, elevated blood pressure in an artery should cause the wall tension in the artery to do what?
(a) Increase
(b) Remain unchanged
(c) Decrease
(d) Impossible to decide

Zulfiqar Ali

Numerade Educator

Problem 76

As a person ages, the fibers in arteries become less elastic and the wall tension increases. According to Laplace's law, this will cause the blood pressure to do what?
(a) Increase
(b) Remain unchanged
(c) Decrease
(d) Impossible to decide

Zulfiqar Ali

Numerade Educator

Problem 77

Aortic blowout occurs when part of the wall of the aorta becomes weakened. What does this cause?
(a) A bulge and increased radius of the aorta when the blood pressure inside increases
(b) An increased radius of the aorta, which causes increased tension in
the wall
(c) An increased tension in the aorta, which causes the radius to increase
(d) a and b
(e) $a, b,$ and $c$

Zulfiqar Ali

Numerade Educator

Problem 78

What is closest to the volume of the Gamow bag?
(a) $50 \mathrm{L}$
(b) $100 \mathrm{L}$
(c) $200 \mathrm{L}$
(d) $500 \mathrm{L}$
(c) $1000 \mathrm{L}$

Zulfiqar Ali

Numerade Educator

Problem 79

What is closest to the temperature at the $6450-\mathrm{m}$ elevation on the day described in the problem?
(a) $37 \mathrm{K}$
(b) $253 \mathrm{K}$
(c) $20 \mathrm{K}$
(d) $-20 \mathrm{K}$
(e) $273 \mathrm{K}$

Zulfiqar Ali

Numerade Educator

Problem 80

What is closest to the number $n$ of moles of air in the filled bag when at $4400 \mathrm{m} ?$
(a) 3 moles
(b) 10 moles
(c) 13 moles
(d) 110 moles
(e) 170 moles

Zulfiqar Ali

Numerade Educator

Problem 81

What is closest to the number $n$ of moles of air in the bag if its pressure is at the $6450-\mathrm{m}$ level?
(a) 3 moles
(b) 10 moles
(c) 13 moles
(d) 110 moles
(c) 170 moles

Zulfiqar Ali

Numerade Educator

Problem 82

Estimate the fraction of the air in the Gamow bag that an occupant would inhale in $1 \mathrm{h},$ assuming no replacement of the air.
(a) 0.01
(b) 0.1
(c) 0.3
(d) 0.5
(c) 1.0

Zulfiqar Ali

Numerade Educator