Physics for Scientist and Engineers: A Strategic Approach

Randall Knight

Chapter 16

A Macroscopic Description of Matter - all with Video Answers

Educators

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Chapter Questions

Problem 1

Section 16.1 Solids, Liquids, and Gases
What volume of water has the same mass as $2.0 \mathrm{m}^{3}$ of lead?

Mayukh Banik

Mayukh Banik

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Problem 2

If The nucleus of a uranium atom has a diameter of $1.5 \times 10^{-14} \mathrm{m}$ and a mass of $4.0 \times 10^{-25} \mathrm{kg} .$ What is the density of the nucleus?

Mayukh Banik

Numerade Educator

Problem 3

What is the diameter of a copper sphere that has the same mass as a $10 \mathrm{cm} \times 10 \mathrm{cm} \times 10 \mathrm{cm}$ cube of aluminum?

Mayukh Banik

Numerade Educator

Problem 4

A hollow aluminum sphere with outer diameter $10.0 \mathrm{cm}$ has a mass of $690 \mathrm{g}$. What is the sphere's inner diameter?

Mayukh Banik

Numerade Educator

Problem 5

Section 16.2 Atoms and Moles
How many atoms are in a $2.0 \mathrm{cm} \times 2.0 \mathrm{cm} \times 2.0 \mathrm{cm}$ cube of aluminum?

Mayukh Banik

Numerade Educator

Problem 6

How many moles are in a $2.0 \mathrm{cm} \times 2.0 \mathrm{cm} \times 2.0 \mathrm{cm}$ cube of copper?

Mayukh Banik

Numerade Educator

Problem 7

What is the number density of (a) aluminum and (b) lead?

Mayukh Banik

Numerade Educator

Problem 8

An element in its solid phase has mass density $1750 \mathrm{kg} / \mathrm{m}^{3}$ and number density $4.39 \times 10^{28}$ atoms/m $^{3}$. What is the element's atomic muss number?

Mayukh Banik

Numerade Educator

Problem 9

1.0 mol of gold is shaped into a sphere. What is the sphere's diameter?

Vishal Gupta

Numerade Educator

Problem 10

In What volume of aluminum has the same number of atoms as $10 \mathrm{cm}^{3}$ of mercury?

Mayukh Banik

Numerade Educator

Problem 11

Section 16.4 Phase Changes
The lowest and highest natural temperatures ever recorded on earth are $-127^{\circ} \mathrm{F}$ in Antarctica and $136^{\circ} \mathrm{F}$ in Libya. What are these temperatures in "C and in K?

Mayukh Banik

Numerade Educator

Problem 12

At what temperature does the numerical value in $^{\circ} \mathrm{F}$ match the numerical value in $^{\circ} \mathrm{C} ?$

Mayukh Banik

Numerade Educator

Problem 13

A demented scientist creates a new temperature scale, the $^{*} \mathbf{Z}$ scale." He decides to call the boiling point of nitrogen $0^{\circ} \mathrm{Z}$ and the meluing point of iron $1000^{\circ} \mathrm{Z}$
a. What is the boiling point of water on the Z scale?
b. Convert $500^{\circ} \mathrm{Z}$ to degrees Celsius and to kelvins.

Mayukh Banik

Numerade Educator

Problem 14

What is the temperature in $^{\circ} \mathrm{F}$ and the pressure in $\mathrm{Pa}$ at the triple point of (a) water and (b) carbon dioxide?

Mayukh Banik

Numerade Educator

Problem 15

Section 16.5 Ideal Gases
3.0 mol of gas at a temperature of $-120^{\circ} \mathrm{C}$ fills a $2.0 \mathrm{L}$ container. What is the gas pressure?

Mayukh Banik

Numerade Educator

Problem 16

A cylinder contains $4.0 \mathrm{g}$ of nitrogen gas. A piston compresses the gas to half its initial volume. Afterward,
a. Has the mass density of the gas changed? If so, by what fac. tor? If not, why not?
b. Has the number of moles of gas changed? If so, by what factor? If not, why not?

Mayukh Banik

Numerade Educator

Problem 17

The 3.0-m-long pipe in FIGURE CP16.71 is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the water's surface. What is the length $L$ of the trapped volume of air?
(FIGURE CANNOT COPY)

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 18

A gas at $100^{\circ} \mathrm{C}$ fills volume $V_{0}$. If the pressure is held constant, what is the volume if (a) the Celsius temperature is doubled and (b) the Kelvin temperature is doubled?

Mayukh Banik

Numerade Educator

Problem 19

A 15 -cm-diameter compressed-air tank is $50 \mathrm{cm}$ tall. The pressure at $20^{\circ} \mathrm{C}$ is 150 atm.
a. ow many moles of air are in the tank?
b. What volume would this air occupy at STP?

Mayukh Banik

Numerade Educator

Problem 20

A 20 -cm-diameter cylinder that is $40 \mathrm{cm}$ long contains $50 \mathrm{g}$ of oxygen gas at $20^{\circ} \mathrm{C}.$
a. How many moles of oxygen are in the cylinder?
b. How many oxygen molecules are in the cylinder?
c. What is the number density of the oxygen?
d. What is the reading of a pressure gauge attached to the tank?

Mayukh Banik

Numerade Educator

Problem 21

A 10 -cm-diameter cylinder of helium gas is 30 cm long and at $20^{\circ} \mathrm{C}$. The pressure gauge reads $120 \mathrm{psi}.$
a. How many helium atoms are in the cylinder?
b. What is the mass of the helium?
c. What is the helium number density?
d. What is the helium mass density?

Mayukh Banik

Numerade Educator

Problem 22

Section 16.6 Ideal-Gas Processes
A gas with initial state variables $p_{1}, V_{1},$ and $T_{1}$ expands isothermally until $V_{1}=2 V_{1},$ What are $(a) T_{1}$ and $(b) p_{1} ?$

Mayukh Banik

Numerade Educator

Problem 23

A gas with initial state variables $p_{1}, V_{1},$ and $T_{1}$ is cooled in an isochoric process until $p_{2}=\frac{1}{3} p_{1} .$ What are (a) $V_{2}$ and (b) $T_{2} ?$

Mayukh Banik

Numerade Educator

Problem 24

A rigid container bolds hydrogen gas at a pressure of 3.0 atm and a temperature of $2^{\circ} \mathrm{C}$. What will the pressure be if the temperature is raised to $10^{\circ} \mathrm{C} ?$

Mayukh Banik

Numerade Educator

Problem 25

A rigid sphere has a valve that can be opened or closed. The sphere with the valve open is placed in boiling water in a room where the air pressure is 1.0 atm. After a long period of time has elapsed, the valve is closed. What will be the pressure inside the sphere if it is then placed in (a) a mixture of ice and water and (b) an insulated box filled with dry ice?

Mayukh Banik

Numerade Educator

Problem 26

A 24 -cm-diameter vertical cylinder is sealed at the top by a frictionless $20 \mathrm{kg}$ piston. The piston is $84 \mathrm{cm}$ above the bottom when the gas temperature is $303^{\circ} \mathrm{C}.$
a. What is the gas pressare inside the cylinder?
b. What will the pressure and the height of the piston be if the temperature is lowered to $15^{\circ} \mathrm{C} ?$

Mayukh Banik

Numerade Educator

Problem 27

0.10 mol of argon gas is admitted to an evacuated $50 \mathrm{cm}^{3}$ container at $20^{\circ} \mathrm{C}$. The gas then undergoes an isochoric heating to a temperature of $300^{\circ} \mathrm{C}.$
a. What is the final pressure of the gas?
b. Show the process on a $p V$ diagram. Include a proper scale on both axes.

Mayukh Banik

Numerade Educator

Problem 28

0.10 mol of argon gas is admitted to an evacuated $50 \mathrm{cm}^{3}$ container at $20^{\circ} \mathrm{C}$. The gas then undergoes an isobaric heating to a temperature of $300^{\circ} \mathrm{C}$
a. What is the final volume of the gas?
b. Show the process on a $p V$ diagram. Include a proper scale on both axes.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 29

0.10 mol of argon gas is admitted to an evacuated $50 \mathrm{cm}^{3}$ container at $20^{\circ} \mathrm{C}$. The gas then undergoes an isothermal expansion to a volume of $200 \mathrm{cm}^{3}$.
a. What is the final pressure of the gas?
b. Show the process on a $p V$ diagram. Include a proper scale on both axes.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 30

0.0040 mol of gas undergoes the process shown in FIGURE X16.30.
a. What type of process is this?
b. What are the initial and final temperatures in $^{\circ} \mathrm{C} ?$
(FIGURE CANNOT COPY)

Sachin Rao

Numerade Educator

Problem 31

0.0040 mol of 8 as undergoes the process shown in $\mathrm{nic}$. FIGURE EX 16.$31 .$
a. What type of process is this?
b. What is the final temperature in $^{\circ} \mathrm{C} ?$
c. What is the final volume $V_{2} ?$

Mayukh Banik

Numerade Educator

Problem 32

A gas with an initial temperature of $900^{\circ} \mathrm{C}$ undergoes the process shown in FIGURE EXI6 $\mathbf{3 2}.$
a. What type of process is this?
b. What is the final temperature in $^{\circ} \mathrm{C} ?$
c. How many moles of gas are there?
(FIGURE CANNOT COPY)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 33

The atomic mass number of copper is $A=64 .$ Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the atoms left behind are in a cubic crystal lattice. What is the smallest distance between two copper atoms?

Mayukh Banik

Numerade Educator

Problem 34

An element in its solid phase forms a cubic crystal lattice (see Problem 33 ) with mass density $7950 \mathrm{kg} / \mathrm{m}^{3} .$ The smallest spacing between two adjacent atoms is $0.227 \mathrm{nm} .$ What is the element's atomic mass number?

Mayukh Banik

Numerade Educator

Problem 35

The molecular mass of water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ is $A=18 .$ How many protons are there in $1.0 \mathrm{L}$ of liquid water?

Mayukh Banik

Numerade Educator

Problem 36

Estimate the number density of gas molecules in the earth's atmosphere at sea level.

Mayukh Banik

Numerade Educator

Problem 37

The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about $2 \times 10^{6} \mathrm{K}$. The gas pressure in the corona is about $0.03 \mathrm{Pa}$. Estimate the number density of particles in the solar corona.

Mayukh Banik

Numerade Educator

Problem 38

Current vacuum technology can achieve a pressure of $1.0 \times 10^{-10} \mathrm{mm}$ of Hg. At this pressure, and at a temperature of $20^{\circ} \mathrm{C},$ how many molecules are in $1 \mathrm{cm}^{3} ?$

Mayukh Banik

Numerade Educator

Problem 39

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is $1.0 \times 10^{-10} \mathrm{mm}$ of Hg.
a. What fraction is this of atmospheric pressure?
b. At $T=20^{\circ} \mathrm{C}$, how many molecules are in a cylindrical chamber $40 \mathrm{cm}$ in diameter and $30 \mathrm{cm}$ tall?

Mayukh Banik

Numerade Educator

Problem 40

A nebula-a region of the galaxy where new stars are forming-contains a very tenuous gas with 100 atoms/cm". This gas is heated to $7500 \mathrm{K}$ by ultraviolet radiation from nearby stars. What is the gas pressure in atm?

Mayukh Banik

Numerade Educator

Problem 41

An inflated bicycle inner tube is $2.2 \mathrm{cm}$ in diameter and $200 \mathrm{cm}$ in circumference. A small leak causes the gauge pressure to decrease from 110 psi to 80 psi on a day when the temperature is $20^{\circ} \mathrm{C}$. What mass of air is lost? Assume the air is pure nitrogen.

Mayukh Banik

Numerade Educator

Problem 42

On average, cach person in the industrialized world is responsible for the emission of $10,000 \mathrm{kg}$ of carbon dioxide $\left(\mathrm{CO}_{2}\right)$ every year. This includes $\mathrm{CO}_{2}$ that you generate directly, by burning fossil fuels to operate your car or your furnace, as well as $\mathrm{CO}_{2}$ generated on your behalf by electric generating stations and manufacturing plants. $\mathrm{CO}_{2}$ is a greenhouse gas that contributes to global warming. If you were to store your yearly $\mathrm{CO}_{2}$ emissions in a cube at STP, how long would each edge of the cube be?

Mayukh Banik

Numerade Educator

Problem 43

A gas at $25^{\circ} \mathrm{C}$ and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with three times the volume, after which the pressure is half the original pressure. What is the new temperature of the gas in $^{\circ} \mathrm{C} ?$

Mayukh Banik

Numerade Educator

Problem 44

On a hot $35^{\circ} \mathrm{C}$ day, you perspire $1.0 \mathrm{kg}$ of water during your workout.
a. What volume is occupied by the evaporated water?
b. By what factor is this larger than the volume occupied by the liquid water?

Mayukh Banik

Numerade Educator

Problem 45

$10,000 \mathrm{cm}^{3}$ of $200^{\circ} \mathrm{C}$ steam at a pressure of 20 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in $\mathrm{cm}^{3}$.

Mayukh Banik

Numerade Educator

Problem 46

An electric generating plant boils water to produce high pressure steam. The steam spins a turbine that is connected to the generator.
a. How many liters of water must be boiled to fill a $5.0 \mathrm{m}^{3}$ boiler with 50 atm of steam at $400^{\circ} \mathrm{C} ?$
b. The steam has dropped to 2.0 atm pressure at $150^{\circ} \mathrm{C}$ as it exits the turbine. How much volume does it now occupy?

Mayukh Banik

Numerade Educator

Problem 47

On a cool morning, when the temperature is $15^{\circ} \mathrm{C}$, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is $45^{\circ} \mathrm{C}$ What pressure will your tire gauge now show?

Mayukh Banik

Numerade Educator

Problem 48

The air temperature and pressure in a laboratory are $20^{\circ} \mathrm{C}$ and
1.0 atm. A $1.0 \mathrm{L}$ container is open to the air. The container is then sealed and placed in a bath of boiling water. After reaching thermal equilibrium, the container is opened. How many moles of air escape?

Mayukh Banik

Numerade Educator

Problem 49

The volume in a constant-pressure gas thermometer is directly proportional to the absolute temperature. A constant pressure thermometer is calibrated by adjusting its volume to $1000 \mathrm{mL}$ while it is in contact with a reference cell at the triple point of water. The volume increases to 1638 mL when the thermometer is placed in contact with a sample. What is the sample's temperature?

Prabhu Ramji

Numerade Educator

Problem 50

The mercury manometer shown in FIGURE P16.50 so is attached to
a gas cell. The mercury height $h$ is 120 mm when the cell is placed in an ice-water mixture. The mercury height drops to $30 \mathrm{mm}$ when the device is carried into an industrial freezer. What is the freezer temperature? Hint: The right tube of the manometer is much narrower than the left tube. What reasonable assumption can you make about the gas volume?
(FIGURE CANNOT COPY)

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 51

The U-shaped tube in FIGURE CP16.51 crissi has a total length of 1.0 $\mathrm{m}$. It is open at one end, closed at the other, and is initially filled with air at $20^{\circ} \mathrm{C}$ and 1.0 atm pressure. Mercury is poured slowly into the open end without letting any air escape, thus compressing the air. This is continued until the open side of the tube is completely filled with mercury. What is the length $L$ of the column of mercury?

Mayukh Banik

Numerade Educator

Problem 52

A diver 50 m deep in $10^{\circ} \mathrm{C}$ fresh water exhales a $1.0-\mathrm{cm}-$ diameter bubble. What is the bubble's diameter just as it reaches the surface of the lake, where the water temperature is $20^{\circ} \mathrm{C} ?$ Hint: Assume that the air bubble is always in thermal equilibrium with the surrounding water.

Mayukh Banik

Numerade Educator

Problem 53

A compressed-air cylinder is known to fail if the pressure exceeds 110 atm. A cylinder that was filled to 25 atm at $20^{\circ} \mathrm{C}$ is stored in a warehouse. Unfortunately, the warehouse catches fire and the temperature reaches $950^{\circ} \mathrm{C}$. Does the cylinder blow?

Mayukh Banik

Numerade Educator

Problem 54

Reproduce FIGURE P16.54 on a piece of paper. A gas starts with pressure $p_{1}$ and volume $V_{1} .$ Show on the figure the process in which the gas undergoes an isochoric process that doubles the pressure, then an isobaric process that doubles the volume, followed by an isothermal process that doubles the volume again. Label each of the three processes.
(FIGURE CANNOT COPY)

Mayukh Banik

Numerade Educator

Problem 55

Reproduce FIGURE P16.55 on a piece of paper. A gas starts with pressure $p_{1}$ and volume $V_{1} .$ Show on the figure the process in which the gas undergoes an isothermal process during which the volume is halved, then an isochoric process during which the pressure is halved, followed by an isobaric process during which the volume is doubled. Label each of the three processes.
(FIGURE CANNOT COPY)

Mayukh Banik

Numerade Educator

Problem 56

$8.0 \mathrm{g}$ of helium gas follows the process $1 \rightarrow 2 \rightarrow 3$ shown in FIGURE P16.56. Find the values of $V_{1}, V_{3}, p_{2},$ and $T_{3}$
(FIGURE CANNOT COPY)

Prashant Bana

Numerade Educator

Problem 57

FIGURE P16.57 shows two different processes by which $1.0 \mathrm{g}$ of nitrogen gas moves from state 1 to state $2 .$ The temperature of state 1 is $25^{\circ} \mathrm{C}$. What are (a) pressure $p_{1}$ and (b) temperatures (in $\left.^{\circ} \mathrm{C}\right) T_{2}, T_{3},$ and $T_{4} ?$

Mayukh Banik

Numerade Educator

Problem 58

FIGURE P16.58 shows two different processes by which 80 mol of gas move from state 1 to state $2 .$ The dashed line is an isotherm.
a. What is the temperature of the isothermal process?
b. What maximum temperature is reached along the straight line process?
(FIGURE CANNOT COPY)

Ze-Han Lee

Numerade Educator

Problem 59

0.10 mol of gas undergoes the process $1 \rightarrow 2$ shown in $\mathrm{Fic}$. FIGURE PI6.59.
a. What are temperatures $T_{1}$ and $T_{2}\left(\text { in }^{\circ} \mathrm{C}\right)$ ?
b. What type of process is this?
c. The gas undergoes an isochoric beating from point 2 until the pressure is restored to the value it had at point $1 .$ What is the final temperature of the gas?

Mayukh Banik

Numerade Educator

Problem 60

0.0050 mol of gas undergoes the process $1 \rightarrow 2 \rightarrow 3$ shown in FIGURE P16.60. What are (a) temperature $T_{1},$ (b) pressure $p_{2}$. and (c) volume $V_{3} ?$

Mayukh Banik

Numerade Educator

Problem 61

$4.0 \mathrm{g}$ of oxygen gas, starting at $20^{\circ} \mathrm{C},$ follow the process $1 \rightarrow 2$ shown in FIGURE P16.61. What is temperature $T_{2}$ (in $^{\circ} \mathrm{C}$ )?

Mayukh Banik

Numerade Educator

Problem 62

$10 \mathrm{g}$ of dry ice (solid $\mathrm{CO}_{2}$ ) is placed in a $10,000 \mathrm{cm}^{3}$ container, then all the air is quickly pumped out and the container sealed. The container is warmed to $0^{\circ} \mathrm{C}$, a temperature at which $\mathrm{CO}_{2}$ is a gas.
a. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is $1000 \mathrm{cm}^{3}.$
b. What is the final temperature of the gas (in $^{\circ} \mathrm{C}$ )?
c. Show the process on a $p V$ diagram.

Mayukh Banik

Numerade Educator

Problem 63

A container of gas at 2.0 atm pressure and $127^{\circ} \mathrm{C}$ is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again.
a. What are the final pressure and temperature of the gas?
b. Show this process on a $p V$ diagram.

Mayukh Banik

Numerade Educator

Problem 64

Five grams of nitrogen gas at an initial pressure of 3.0 atm and
at $20^{\circ} \mathrm{C}$ undergo an isobaric expansion until the volume has tripled.
a. What is the gas volume after the expansion?
b. What is the gas temperature after the expansion (in $^{\circ} \mathrm{C}$ ) $?$ The gas pressure is then decreased at constant volume until the original temperature is reached.
c. What is the gas pressure after the decrease? Finally, the gas is isothermally compressed until it returns to its initial volume.
d. What is the final gas pressure?
e. Show the full three-step process on a $p V$ diagram. Use appropriate scales on both axes.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 65

In Problems 65 through 68 you are given the equation(s) used to solve
a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation(s).
b. Draw a $p V$ diagram.
c. Finish the solution of the problem.
$$p_{2}=\frac{300 \mathrm{cm}^{3}}{100 \mathrm{cm}^{3}} \times 1 \times 2 \mathrm{atm}$$

Mayukh Banik

Numerade Educator

Problem 66

In Problems 65 through 68 you are given the equation(s) used to solve
a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation(s).
b. Draw a $p V$ diagram.
c. Finish the solution of the problem.
$$\left(T_{2}+273\right) \mathrm{K}=\frac{200 \mathrm{kPa}}{500 \mathrm{kPa}} \times 1 \times(400+273) \mathrm{K}$$

Mayukh Banik

Numerade Educator

Problem 67

In Problems 65 through 68 you are given the equation(s) used to solve
a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation(s).
b. Draw a $p V$ diagram.
c. Finish the solution of the problem.
$$V_{2}=\frac{(400+273) K}{(50+273) K} \times 1 \times 200 \mathrm{cm}^{3}$$

Mayukh Banik

Numerade Educator

Problem 68

In Problems 65 through 68 you are given the equation(s) used to solve
a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation(s).
b. Draw a $p V$ diagram.
c. Finish the solution of the problem.
$$\begin{array}{l} (2.0 \times 101,300 \mathrm{Pa})\left(100 \times 10^{-6} \mathrm{m}^{3}\right)=n(8.31 \mathrm{J} / \mathrm{mol} \mathrm{K}) T_{1} \\
n=\frac{0.12 \mathrm{g}}{20 \mathrm{g} / \mathrm{mol}} \\ T_{2}=\frac{200 \mathrm{cm}^{3}}{100 \mathrm{cm}^{3}} \times 1 \times T_{1} \end{array}$$

Mayukh Banik

Numerade Educator

Problem 69

The 50 kg lead piston shown in Rounk cels.69 floats on 0.12 mol of compressed air.
a. What is the piston height $h$ if the temperature is $30^{\circ} \mathrm{C} ?$
b. How far does the piston move if the temperature is increased by $100^{\circ} \mathrm{C} ?$
(FIGURE CANNOT COPY)

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 70

A diving bell is a 3.0 -m-tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is $20^{\circ} \mathrm{C} .$ The bell is lowered into the ocean until its lower end is $100 \mathrm{m}$ deep. The temperature at that depth is $10^{\circ} \mathrm{C}.$
a. How high does the water rise in the bell after enough time has passed for the air inside to reach thermal equilibrium?
b. A compressed-air hose from the surface is used to expel all the water from the bell. What minimum air pressure is needed to do this?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 71

The 3.0 -m-long pipe in FIGURE P16.71$ is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the water's surface. What is the length $L$ of the trapped volume of air?
(FIGURE CANNOT COPY)

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 72

The cylinder in FIGURE P16.72 has a move able piston attached to a spring. The cylinder'scross section area is $10 \mathrm{cm}^{2},$ it contains 0.0040 mol of gas, and the spring constant is $1500 \mathrm{N} / \mathrm{m}$. At $20^{\circ} \mathrm{C}$ the spring is neither compressed nor stretched. How far is the spring compressed if the gas temperature is raised to $100^{\circ} \mathrm{C} ?$
(FIGURE CANNOT COPY)

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 73

Containers $A$ and $B$ in FIGURE $P16.73$ hold the same gas. The volume of $\mathrm{B}$ is four times the volume of $\mathrm{A}$. The two containers are connected by a thin tube (negligible volume) and a valve that is closed. The gas in A is at $300 \mathrm{K}$ and pressure of $1.0 \times 10^{5} \mathrm{Pa}$. The gas in $B$ is at $400 \mathrm{K}$ and pressure of $5.0 \times 10^{5} \mathrm{Pa}$. Heaters will maintain the temperatures of A and B even after the valve is opened.
a. After the valve is opened, gas will flow one way or the other until A and B have equal pressure. What is this final pressure?
b. Is this a reversible or an irreversible process? Explain.
(FIGURE CANNOT COPY)

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 74

The closed cylinder of FIGURE P16.74 has a tight-fitting but friction less piston of mass $M .$ The piston is in equilibrium when the left chamber has pressure $p_{0}$ and length $L_{0}$ while the spring on the right is compressed by $\Delta L.$
a. What is $\Delta L$ in terms of $p_{0}, L_{0}, A, M,$ and $k ?$
b. Suppose the piston is moved a small distance $x$ to the right. Find an expression for the net force $\left(F_{x}\right)_{\infty \text { et }}$ on the piston. Assume all motions are slow enough for the gas to remain at the same temperature as its surroundings.
c. If released, the piston will oscillate around the equilibrium position. Assuming $x \ll L_{0}$ find an expression for the oscillation period $T$ Hint: Use the binomial approximation.

Eric Mockensturm

Eric Mockensturm

Numerade Educator