`
`IPR2023-00783
`
`
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`Chapter 15
`
`Fluid Mechanics
`
`He
`
`Air
`
`D te
`/
`
`
`
`Ca)
`
`(b)
`
`Figure P15.51
`
`
`
`16
`
`Temperature and the
`Kinetic Theory of Gases
`
`is simple harmonic, and (b) determine the period of the
`motion. Take the density of air to be 1.29 kg/m", and ig-
`any
`lost due to airfri
`
`
` . Torricedli’s Law;
`
`containing a liquid of
`Aank, with a cover,
`
`: y, from the
`density p has a hole in its side at a di
`
`(Fig. P15.52). The diameter of the holeis small com-
`
`pared to the dij
`er af the tank. The air above the liquid
`
`ANSWERS TO CONCEPTUAL PROBLEMS
`
`is maintained at a pressure P, Assume steady, frictionless
`flow, Showthat the speed at which the fluid leaves the hole
`when the liquid level is a distance A above the hole is
`
`“=
`
`ur study thus far has focused mainly on Newtonian mechanics and
`relativity, which explain a wide range of phenomena, such as the mo-
`tion of baseballs, rockets, and planets. We now turn to the study of
`thermodynamics, which is concerned with the concepts of heat and temper-
`ature. As we shall see, thermodynamics is very successful in explaining the
`bulk properties of matter and the correlation between these properties and
`the mechanics ofatoms and
`molecules,
`Have you ever won-
`5. The balance will not be in equilibrium—thelead side will
`She can exert enough pressure on the floor to. dent or pune-
`
`he lower. Despite the fact that the weights on both sides of
`dered how a reftigerator
`ture the floor ©
`Thelarge pressure is caused by the
`
`the balance are the same, the styrofoam, due to its larger
`fact that her weight is distributed over
`the very
`small cross
`cools, or what types of trans-
`
`formations occur in an au-
`onal: a
`of her high heels, Lf you are the homeowner,
`volume, will experience a langer buoyant force from the sur-
`rounding air. Thus, the net force of the weight and buoyant
`you might want
`to suggest that she remove her high heels
`tomobile engine, or what
`force is larger, in the downward direction, for the lead than
`and. put on someslippers.
`for the styrefoam.
`happens to the kinetic en-
`think of the grain stored in the silo as a fluid, the
`
`
`ergy of an object once the
`The level of the pondfalls. This is because the anchor dis-
`pressure the grain exerts
`on the walls of the silo increases
`
`object comes to rest? The
`with increasing depth just as water pressure in a lake in-
`places more water while in the boat, A floating object dis
`laws of
`thermodynamics
`places a volume of water whose weight is equal to the weight
`creases with increasing depth. Thus, the spacing berween
`
`bands is made51
`
`ofthe object.Asubmerged object displaces a volume ofwater
`and the concepts of heat
`ler at the lower portions to overcome the
`and temperature enable us
`equal to the volume of the object, Because the density of the
`larger outward forces on the walls in these regions.
`
`
`anchoris greater than that of water, a volume of water that
`The level of floating of a ship in the water is unaffected by
`to answer such practical
`
`ir exerts ne
`ble buoyant force
`
`the atmospheric pressur
`weighs the same as the anchor will be greater
`than the vol-
`questions,
`ume of the anchor
`compared to water, Th
`vant
`for
`the water results
`
`
`Manythings can hap-
`7. As the truck passes, the air between your car ane the truck
`from the pressure differential in the fluid. Ona high-pressure
`pen to an object whenits
`
`
`is compressed into the channel-between you and the truck
`day, the pressureat all points in the
`ter is higher than on
`
`“1 is
`
`temperature is
`raised,
`Its
`
`a low-pressure day. Since
`and moves at a higher speed than when your car is in the
`
`incompressible,
`nost
`size changesslightly, but
`it
`open. According to Bernoulli's principle, this high-speedair
`
` sure with depth is the
`however, the
`rate of changeof pt
`
`
`nt force.
`side of your
`may also melt, boil, ignite,
`resulting in no change in the bu
`has a lower pressure than the air on the out
`
`
`vant force from
`
`ran, the ship floats due to the
`car, The differcnce in pressure provides a net force on your
`
` eris denser than fresh water. As the ship is
`car toward the truck.
`salt water, Salt w
`hucvant force from the fresh water
`
`pulled uptheriver, the
`in the river is not sufficie
`
`nt to support the weight of the ship,
`and it sinks.
`
`CHAPTER OUTLINE
`
`16,1 Temperature and the Zeroth
`Law of Thermodynamics
`16.2 Thermometers and
`Temperature Scales
` 3 Thermal Expansion of Solids
`andLiquids
`16.4 Macroscopic Description
`of an Ideal Gas
`
`5 The Kinetic Theory of Gases
`
`
`
`The glass vessel contains dry
`ice (solid carbon dioxide). The
`white cloud is corbon dioxide
`vapor, which is denser than
`gir and hence fallsfrom the
`vessel,
`(R. Folwell//Science
`Library/Phota Researchers)
`
`
`
`
`439
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`IPR2023-00783
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`IPR2023-00783
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`Chapter 16
`
`Temperature and the Kinetic Theory ofGases
`
`16.3
`
`Thermal Expansion of Solids and Liquids
`
`445
`
`16.3 + THERMAL EXPANSION OF SOLIDS AND LIQUIDS
`
`
`
`The most common temperature scale in everyday use in the United States is
`the Fahrenheit scale, This scale sets the temperature of the ice point at 32°F and
`Qurdiscussion of the liquid thermometer made use of one of the best-known
`the temperature of the steam point at 212°F. The relationship between the Celsius
`changes that occurs in a substance: As its temperature increases, its volume in-
`
`and Fahrenheit temperature scales is
`creases. (As we shall see shortly, in some materials the volume dec
`s when the
`(16.2)
`Ty = $1, + 32°F
`temperature increases.) This phenomenon, known as thermal expansion,plays
`Equation 16.2 can easily be used to find a relationship between changes in
`an important role in numerousapplications, For example, thermal expansionjoints
`
`temperature on the Celsius and Fahrenheit scales. [tis left as a problem for you to
`must be included in buildings, concrete highways, and bridges to compensate for
`show that if the Celsius temperature changes by AT,., the Fahrenheit temperature
`changes in dimensions with temperature variations.
`
`changes by an amount 47), given by
`The overall thermal expansion ofan object is a consequence of the changein
`the average separation between its constituent atoms or molecules. Consider how
`AT, = 2AT¢
`[16.3]
`the atoms in a solid substance behave. At ordinary temperatures, the atoms vibrate
`about their equilibrium positions with an amplitude of about 10-' m, and the
`
`Thermal expansionjoints are used
`average spacing between the atoms is about 10-' m. As the temperature of the
`to separate sections of roadways on
`solid increases, the average separation between atoms increases. The increase in
`A groupof future astronauts lands on an inhabited planet. They strike up a conver-
`bridges. Without these joints, the
`sation with the life forms about temperature scales. It turns out that the inhabitants of
`
`average separation with increasing temperature (and subsequent thermal expan-
`surfaces would buckle duetother-
`
`this planet have a temperature scale based on the freezing and boiling pomts ofwater
`sion) is due to the asymmetry of the potential energy betweenatoms, If the thermal
`
`
`mal expansion on very hot days or
`separated by 100 of the inhabitants’
`. Would these two temperatures on this
`expansion of an object is sufficiently small compared with the object's initial di-
`crack de to contraction on very
`planet be the sameas those on Earth? Wouldthe size ofthe planct inhabitants’ degrees
`cold days.
`(Frank Siteman,
`mensions, then the change in any dimension is, to a good approximation, depen-
`be the same as ours? Suppose that the inhabitants have also devised a scale similar to
`‘Mock,Boston)
`dent on the first power of the temperature change.
`the Kelvin scale, Would their absolute zero be the same as ours?
`Suppose an object has aninitial length of Ly along some direction at some
`
`Reasoning The values of (°C and 100°C for the freezing and boiling points of water
`temperature, The length increases by AM. for the change in temperature AT. Ex-
`are defined at atmospheric pressure. On another planet, it is unlikely that atmospheric
`periments show that. when AT is small enough. AL.
`is proportional to ATand
`pressure would be exactly the same as that on Earth. Thus, water would freeze and boil
`to Ly
`at different temperatures on the planet. The inhabiuunts may call these temperatures
`OF and 100", bur they would not be the same temperatures as our 0° and 100°, If the
`inhabitants did assign values of0° and 100° for these temperatures, then their degrees
`would not be the same sizeas our Celsius degrees (unless their atmospheric pressure
`was the same as ours). For a version of the Kelvin scale from this other planet, the
`absolute zero would be the same as ours, because it is based on a natural, universal
`definition, rather than being associated with a particular substance or a given atmo-
`spheric pressure.
`CONCEPTUAL PROBLEM 1———
`In an astronomy class, the temperature at the core of a star is given by the professor as
`1.5 = 10? degrees. A student asks if this is Kelvin or Celsius. How would you respond?
`
`
`
`or
`
`AL = al, AT
`
`L— fo = ah CF — Ty)
`
`16.4]
`
`16.5]
`
`
`
`EXERCISE 1
`The melting point of gold is 1064°C, and the boiling point
`(a) Express these temperatures in kelvin.
`(b) Compute the difference ber
`
`temperatures in Celsius degrees and kebin,
`a)
`1337
`K: 2933 K (b) 1596°C; 1596 K
`
`
`is 2660°C
`
`een these
`
`L= ky + aly Al
`
`Figure 16.6 Thermal expansion
`of a home
`"
`washer
`
`Note tha
`cr
`is heated
`
`all dimensi
`ase.
`(The ex-
`pansion is ¢
`ed in this
`figure.)
`
`length, 7is the final temperature, and the proportionality
`where f is the final
`constant
`is called the average coefficient of linear expansion for a given ma-
`
`and has units of (°C)
`~!,
`It may be helpful to think of the process of thermal expansion as a magnifi-
`
`
`
`her is heated
`n or a photographic enlargement. For example, as a metal wa
`
`Example 16.1 Heating a Pan of Water
`(Fig. 16.6), all dimensions, including the radius of the hole, increase according to
`AT= AT;
`A pan of water is heated from 25°C to 80°C. Whatis the
`
`Equation 16.4. Table 16.1 lists the average coefficient of linear
`expansion for various
`change in its temperature on the Kelvin scale and on the
`From Equation 16.3, we find
`
`
`Fahrenheit scale?
`materials,
`Note that for thesematerials a is positive, indi
`fan increasein length
`with increasing temperature. Thisisnot always the case. For example, some sub-
`
`AT,=FAT, = 1(80 — 25) = 99°F
`=
`Solution
`From Equation 16.1, we see that the changein
`tem-
`
`sion (positive a) and
`stances, such as calcite (CaCO,), expand along one dim
`ature,
`perature onthe Celsius scale equals the change on the Kelvin
`emper
`
`
`scale. Therefore,
`contract along another (negative @) with increasir
`
`ture, it follows
`Because the linear dimensions of an object char
`with tempe
`
`that volume and si also change with t
`uure, Gonsid
`
`racube having
`ime of ¥, = E
`aninitial edge|
`therefore an initial ve
`
`. As the temper-
`
`atureis increased, the length of each side increases to
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`Temperature and the Kinetic Theory of Gases
`
`Chapter 16
`
`TABLE 16.1 Expansion Coefficients for Some Materials
`Near Room Temperature
`
`
`
`1.12 %.10°4
`Alcohol, ethyl
`24% 10%
`Aluminum
`1.24 x 10-4
`Benzene
`19 x 10°*
`Brass and bronze
`15 ™ 1074
`Acetone
`17 *.10*
`Copper
`4.85 x 10-4
`Glycerin
`9x 10%
`Glass (ordinary)
`1.82 x 10™
`Mercury
`$.2 x 10°%
`Glass (Pyrex)
`90 x 10-4
`Turpentine
`29 = 10-*
`Lead
`96x10
`Gasoline
`11 x 1o-*
`Steel
`3.67 x 107"
`Air at OC
`0.9 x 10-*
`Invar (Ni-Fe alloy)
`
`
`
`12 x 10-% Helium at °CConcrete 3.665 x 10-*
`
`V= = 1° + SalAT = Vy + 3aV, AT
`
`16.3.
`
`ThermalExpansion of Solids and Liquids
`
`447
`
`Reasoning Let us imagine lowering the temperature. Liquids tend to have larger co-
`efficients of linear expansion thansolids, so the density of the water will increase more
`rapidly with the dropping temperature than that ofthe solid. If the density ofthe solid
`were initially onlyslightly larger than that ofwater, it would in principle be possible to
`make it float by lowering the temperature, although one faces the possible problem of
`reaching the freezing point of the water before this happens.
`
`
`Thinking Physics 3
`A homeowneris painting the ceiling. and a drop of paint falls fromthe brush onto an
`operating incandescent light bulb, The bulb breaks. Why?
`Reasoning The glass envelope of an incandescentlight bulb receives energy on the
`inside surface by radiation from the very hotfilament and movement ofthe gas filling
`the bulb, Thus, the glass can become very hot. If a drop of paintfalls onto the glass,
`that portion of the glass envelope will suddenly become cold, and the contraction of
`this region could cause thermal stresses that would break the glass,
`
`The new volume, V = £4,is
`CONCEPTUAL PROBLEM 2FeNO
`1 = (lq + alg AT) = 1,3 + SalAT + Se(AT)? + aL(AT)?
`The last
`two terms in this expression contain the quantity a ATraised to
`Common thermometers are made of a mercury column in a glass tube. Based on the oper-
`ation ofthese common thermometers, which hasthe larger coefficient of linear expansion —
`the second and third powers. Because a AT’ is much less than one, squaring it
`makes it even smaller. Therefore, we can neglect these two terms to get a simpler
`glass or mercury? (Don't answer this by looking in a table!)
`expression:
`CONCEPTUAL PROBLEM 3TT
`Thermal expansion: The extreme
`or
`heat of a July day in Asbury Park,
`Two spheres are made of the same metal and have the same radius, but one is hollow and
`[16.6]
`AV=V- = 8aT
`New Jersey, caused these railroad
`the other is solid. The spheres are taken through the same temperature increase. Which
`tracks to buckle.
`(Wide World Photox)
`sphere expands more?
`where 8 = Sa, The quantityfis called the average coefficient ofvolume expan-
`sion. We considered a solid cube in deriving it, but Equation 16,6 describes a
`sample of any shape of solid, liquid, or gas at constant pressure.
`
`Bya similar
`procedure, we can showthat the increase in area of an object accom-
`Example 16.2 Does the Hole Get Bigger or Smaller?
`panying an increase in temperature is
`A hole ofcross-sectional area 100 cm* is. cut in a piece of steel
`AA = yA, AT
`at 20°C. Whar is the change in area of the hole ifthe steel is
`heated from 20°C to 100°C?
`where y, the average coefficient ofarea expansion,is given by y = 2a,
`As Table 16.1 indicates, each substance has its own characteristic coefficients
`Solution A hole in a substance expands in exactly the same
`
`of expansion, For example, when the temperatures of a brass rod and a steel rod
`way as would a piece of the substance having the same shape
`of equal length are raised by the same amount from some common initial value,
`as the hole, The change in the area of the hole can be found
`the brass red expands more than the steel rod because brass has a larger coefficient
`by using Equation 16.7.
`
`of expansion than steel. A simple device called a bimetallic strip that uses this
`
`
`principleisfound in practical devices such as thermostats, The strip is made by
`securely bonding two different metals together. As the temperature ofthe strip
`Figure 16.7) The two metals that
`increases, the two metals expand bydifferent amounts, and the strip bends as in
`form this bimetallic strip are
`Figure 16.7.
`bonded along their longest dir
`sion. The stripin this phow
`was straight before being hea
`
`ind bends when heated, Which
`it were
`
`way would it bend
`if
`Courtesy of Cemirat Sci
`
`
`
`
`
`[16.7]
`
`AA
`
`Ao AT
`[22 x 10-®(°C)-"] (100 em*) (80°C)
`= (0.18 cm*
`
`Thinking Physics 2
`Suppose a solic object slightly denser thanwater is sitting on the bottomof a container
`of water. Can the temperature of this system be changed in any way to make the object
`float to the surface?
`
`The Unusual Behavior of Water
`Liquids generally increase in volumewith increasing temperature and have volume
`
`
`expansion coefficients about ten times greater
`than those of solids. Water is an
`
`
`exception to this rule,
`as we can see fro’
`ts clensily-versus-temperature curve in
`Figure 16.8. As the temperatureincreases from 0°C to 4°C, water contracts and thus
`
`
`its density increases. Above 4°C, water expands with increasing temperature,
`In
`other words, the density of water reaches a maximumvalue of 1000 kg/m? at 4°C.
`
`
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`
`
`Figure 16.8 The variation ofdensity with temperature for water at aumospheric pressure. The
`inset at the right shows that the maximum density ofwater occurs at 4°C.
`
`Wecan use this unusual thermal expansion behaviorof water to explain why a
`pondfreezes at the surface. When the atmospheric temperature drops from, say,
`7C to 6°C, the water at the surface of the pond also cools and consequently de-
`creases in volume, This means that the surface water is denser than the water below
`it, which has not cooled and decreased in volume. As a result, the surface water
`sinks and warmer water from below is forced to the surface to be cooled, When the
`atmospheric temperature is between 4°C and (°C, however, the surface water ex-
`pands as it cools, becoming less dense than the water below it, The mixing process
`stops, and eventually the surface water freezes, As the water freezes, the ice remains
`on the surface because ice is less dense than water. The ice continues to build up
`on the surface, and water near the bottom of the pool remains at 4°C. If this did
`not happen, fish and other forms of marinelife would not survive.
`2 An automobile fuel tank is filled to the brim with 45 L. of gasoline at 10°C,
`Immediately afterward, the vehicle is parked in a location where the temperature is 35°C.
`How much gasoline overflows from the tank as a result ofexpansion? (Neglect the expansion
`of the tank.)
`Answer
`1,08 L
`
`16.4 +» MACROSCOPIC DESCRIPTION OF AN IDEAL GAS
`
`
`
`16.4
`
`Macroscopic Description ofan Ideal Gas
`
`It is convenient to express the ammountof gas in a given volume in terms of the
`number of moles, » As we learned in Section 1.2, one mole ofany substance is
`that mass of the substance that contains Avogadro's number, N, = 6.022 * 10°,
`of molecules, The number of moles, n, of a substance is relatect to its mass, m,
`through the expression
`
`mm
`
`(16.8)
`
`eae
`where Mis the molar mass of the substance, usually expressed in grams per mole.
`For example, the molar mass of molecular oxygen, O,, is 32.0 g/mol. Therefore,
`the mass of one mole of oxygen is 32.0 g,
`Now suppose an ideal gas is confined to a cylindrical container the volume of
`which can be varied by meansof a movablepiston,as in Figure 16.9, We shall assume
`that the cylinder does not leak, and so the mass (or the number of moles) remains
`constant. For such a system, experiments provide the following information.First,
`whenthe gas is kept at a constant temiperature,its pressure is inversely proportional
`to the volume (Boyle's law). Second, when the pressure of the gas is kept constant,
`the volume is directly proportional to the temperature (the law ofCharles and Gay-
`Lussac). These observations can be summarized bythe following equation ofstate
`for an ideal gas:
`
`
`In this expression, called the ideal gas law, fis a constant for a specific gas that
`can be determined from experiments, and Tis the absolute temperature in kelvin,
`Experiments on several gases show that as the pressure approaches zero, the quan-
`tity PV/nTapproachesthe same value of R forall gases. For this reason, Ris called
`the universal gas constant. In 5! units, where pressure is expressed in pascals and
`volume in cubic meters, the product PVhas units of newton-meters, or joules, and
`R has the value
`
`[16.9]
`
`(16.10)
`R=8.31 J/mol-K
`lf the pressure is expressed in atmospheres and the volume im liters (1 L. =
`10° cm* = 10-7 m"), then R has thevalue
`R= 0.0821 L-atm/mol: kK
`
`
`
`These colorful balloons rise as a
`gas burner heats the air insede
`them, Because warm air is bess
`dense than coolair, the buoyant
`force upward can exceed the total
`force downward, causing the bal-
`loon to rise. The vertical motion
`can also be controlled by venting
`hot air at the top ofthe balloon.
`(Richard Magna, FundamentalPhote-
`gmiphs, NYC)
`
`* The universal gas constant
`
`Using this value of A and Equation 16.9, one finds that the volume occupied by
`1 mol of any gas at atmospheric pressure and (°C (275 RK)is 22.4 L.
`Theideal gas lawis often expressed in terms of the total number of molecules,
`N. Because the total number of molecules equals the product of the number of
`moles and Avogadro's number, N,, we can write Equation 16.9 as
`In this section we shall be concerned with the properties of a gas of mass m confined
`= 4 =—R
`py=ar=~rr
`to a container of volume V, pressure P, and temperature 7. It is useful to know how
`M
`Figure 16.9 An ideal gas con-
`these quantities are related. In general, the equation that interrelates these quan-
`fined to a cylinder the volume of
`which can be varied with a mov-
`tities, called the equation ofstate, is very complicated. However, if the gas is main-
`able piston. The state of the gas is
`tained at a very low pressure (or low density), the equation ofstate is found exper-
`imentally to be quite simple. Such a low-density gas is commonly referred to as an
`defined by any twoproperties,
`such as pressure, volume, amd tem-
`ideal gas. Most gases at room temperature and atmospheric pressure behave ap-
`proximately as ideal gases.
`
`
`
`PV = NigT
`wherei, is called Boltzmann's constant and bias the value
`R
`aie?
`= —— = 1.58 x
`|/K
`Ny
`
`dy
`
`10
`
`[16.11]
`
`[16.12]
`
`* Boltzmann's constant
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

` Petitioner Intel Corp., Ex. 1038
`
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`
`
`IPR2023-00783
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`454
`
`Chapter 16
`
`Temperature and the Kinetic Theory of Gases
`s
`:
`:
`By
`anging Equation 16.14, we can relate the average translational molec-
`ular kinetic energyto the temperature:
`
`Average kinetic energy per
`molecule
`
`*
`
`EMERY
`
`a2
`
`(b) Fromthepoint ofviewof kinetic theory, a moleculecolliding withthe piston
`
`
`causes the piston to rebound with somevelocity. According to conservation of mo-
`
`mentum, then, the molecule must rebound with less velocity than it had before the
`collision. Thus, as these collisions occur,
`the averagevelocity of the collection of mol-
` uced. Because temperatureis related to the average velocity of molecules,
`ecules is
`the temperatureof the gas drops.
`
`dmv?=dag [16.16] CONCEPTUAL PROBLEM 6
`
`16.15]
`l dim? = aT
`=
` Thatis, average translational kinetic energy per molecule is jk,7. Because v=
`dv", it follows that
`
`
`Small pl
`tend to havelitte or no atmosphere, Why is this?
`
`
`ilar manner, for the y and 2 motions we find
`dmv? =1h,7
`and
`Linu? = SkyT
`Example 16.5 A Tank of Helium
`al,
`iL
`‘
`Thus, each translational degree of freedom contributes an equal amount of energy
`Solution From Equation 16.15, we see that the averageki-
`A tank of volume 0.300 m* contains 2.00 mol of helium gas
`to the gas, namely, dh T. (In general, the phrase “degrees offreedom” refers to the
`netic energy per moleculeis
`at 20.0°C. Assuming the helium behaves like an ideal gas,
`numberof independent means by which a molecule can possess energy.) A gen-
`
`
`Theorem ofequipartition of *—cralization of thi It, known as the theorem of equipartition of energy, says (a) find the total thermal energy of the system.
`
`beer = Shy T= 31.38 x 10 J/K) (293 K)
`energy
`that the energy of a system in thermal equilibrium is equally divided among
`Solution Using Equation 16.17 with n= 2.00 and T=
`all degrees of freedom.
`295 K, we get
`6.07 * 10°71]
`Thetotal translational kinetic energy of N molecules of gas is simply Ntimes
`
` 2.00 mol) (8.31 J//mol-K) (293 K)
`
`ct that the molar mass of helium
`the average energy per molecule, whichis giv
`
`a by Equation 16,15;
`EXERCISE 6 Using the
`116.17]
`E=
`N(dmv?) = 4NkyT= SnRT
`is 4.00 * 10°“ kg/mol, determinethe rmsspeedof the atoms
`= 7.50 x 10°]
`
`S
`;
`at 200°C.
`Mes
`1.35 * 10° m/s
`bh) What
`is
`the average kinetic ene:
`“f
`molecule?
`a
`
`() Se ane nee Enengy pet tmolewule
`where we have used ky = R/N, for Bolumann’s constant and n = N/N, for the
`number of moles of gas, From this result, we see that the total kinetic energy
`of a system of molecules is proportional to the absolute temperature of the
`system,
`;
`
`Thesquare root of vis called the root-mean-square (rms) speed of the molecules,
`From Equation 16,15 weget, for the rms speed,
`
`3
`me
`f
`
`‘
`m
`[16,18]
`~ wr
`tim =V¥= vf
`
`
`where Mis the molar mass
`in kg/mol. ‘This expression shows that, ata given tem-
`perature, lighter molecules move faster, on the average, than heavier molecules,
`
`
`For example, hydrogen, with a ms
`ass of 2% 10°" kg/mol, moves four times
`
`as fast
`his 32 x 10° kg/mol. Table 16.2 lists the
`as oxygen, the molar mass €
`Some rms
`rmsspeeds forvarious molecules at 20°C
`Speeds
`The relationship beween the Fahrenheit and Celsius temperatures is
`
`
`1 Ty=27, + 32°F [16.2]
`
`
`Molar
`at
`inking
`Physics
`
`
`M.
`2c
`Thin ng Physics4 =. ae ;
`fests : subs
`c
`is eee it Se Sass U ea an a ae of
`
`
`9 it
`some temperature and undergoes a change
`in
`Jesol)
`tras)
`ie
`E
`mr
`’ bap
`re
`of
`AT,
`its length changes
`Cu
`amount A, whichis proportional to the object's initial length andthe temperature
`by the
`(g
`Imagine a gas in an insulated eylinder with a movable piston. The piston is pushed
`
`
`tans
`» (19
`1"
`inward, compressing thegy
`d then released. As the molecules of the gas strike the
`He
`they moveit outward, From the points of view of (a) energy principles, and
`piston,
`4.0.
`|
`HO
`aly AT
`AL=
`18
`(b) kinetic theory, explain how the expansion of this gas causes its temperanine to
`:
`-
`drop
`Ne
`as
`20.1
`
`xpansion.
`The parameter & is called the average coefficient of line
`‘
`
`
`
`
`
`Ny or CO hange in area ofasubstance28 Reasoning (a) From the point of view of encrgy principles, the molecules strike the I is given by
`
`
`
`
`
`
`
`
`NO ules do workonthe piston,30 piston and move it throughadistance. Thus, ¢ fee ee es
`
`
`
`
`
`
`
`
`
`
`CO, 44 which represents a transfer of energy out AA=yA,aresult, the internal energy of A [16.7]
`
`
`
`
`gas drops. Because temperature
`» internal energy, the temperature of
`so,
`64
`the
`the gas drops
`where y is the average coefficient of area expansionand is equal to Zer
`
`Total kinetic energy ofN *
`olecules
`es
`
`Root-meansquare speed *
`
`TABLE 16.2
`
`
`
`
`
`SUMMARY
`
`if wwo objects, A and B, are separately in
`The zeroth law of thermodynamics states that
`other
`thermal equilibriumwith a third object, then A andB arein thermal equilibriumwith each
`Therelationship between 7,,, the Celsius temperature, and 7. the Kelvin (absolute)
`temperature,is
`
`T= T—
`
`278.15
`
`
`
`[16.1]
`
`[16.4]
`
`
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`IPR2023-00783
`
`
`
`
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`
`IPR2023-00783
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`
`
`IPR2023-00783
`
`Petitioner Intel Corp., Ex. 1038
`IPR2023-00783
`
`

`

`CHAPTER OUTLINE
`17.1 Heat, Thermal Energy, and
`Internal Energy
`17.2 Specific Heat
`17.4 Larent Heat and Phase
`Changes
`Work and Thermal Energyin
`Thermodynamic Processes
`17.5 The First Law of
`‘Thermodynamics
`
`17,7 Heat Transfer (Optional)
`
`ie
`
`Heat andthe First Law
`of Thermodynamics
`
`ntl about 1850, the fields of heat and mechanics were considered to
`be two distinct branches of science, and the law of conservation of
`energy seemedto describe only certain kinds of mechanical systems.
`Mid—nineteenth-century
`experiments performed by the Englishman James
`Joule (1818-1889)
`others showed that energy may be added to (or re-
`moved from) a system either as heat or as work done on (or by) the system,
`Now thermal energy is treated as a form of energy that can be transformed
`into mechanical energy. Once the concept of energy was broadened to in-
`clude thermal energy, thelawofconservation ofenergy emerged as a universal
`law of nature.
`‘This chapter focuses on
`the concept of heat,
`the
`first law of thermodynam-
`ics, and some important ap-
`plications. The first law of
`thermodynamics is merely
`the law of conservation of
`energy. [t tells us only that
`an increase in one form of
`energy must be accompa-
`nied by a decrease in some
`other form of energy. The
`first law places no restric-
`tions on the types of energy
`conversions that can occur,
`Furthermore,
`the first
`law
`makes no distinction be-
`tween the results of heat
`
`Schlieren photographof a tea-
`kcettle showing steam and tur-
`bulent convection currents.
`(Gory Setiles,/Science Source/Phote
`Researchers)
`
`SteeS|
`
`
`
`
`
`17.1
`
`Heat, Thermal Energy, and Internal Energy
`
`463
`
`and work—achange in internal energy. According to thefirst law, a system's in-
`
`ternal energy can be increased cither by transfer of thermal energy to the system
`or by work done on the system. An important difference between thermal energy
`and mechanical energyis not evident from the first law: Energy transferred to a
`
`
`system as work can bestored completely as internal energy,
`but it is impossible for
`internal energy to completelyleave a system only by the mechanismof work.
`
`17.1 + HEAT, THERMAL ENERGY, AND INTERNAL ENERGY
`
`A major distinction must be made between internal energy and heat. Internal
` nary (neither
`
`energy is all of the energy belonging to a system while it
`is sta
`translating nor rotating), including nuclear energy, chemical energy, and strain
`energy (asin a compressedor stretchedspring), as well as thermal energy associated
`with the random motionof atoms or molecules. Heat is the energy that is trans-
`ferred between the system and its surroundings because of a temperature dif-
`ference between them.
`In the previous chapter we showed that the thermal energy of a monatomic
`
`
`ideal gas is associated with the internal motionofits atoms. In this
`special case,
`the
`thermal energyis simply the kinetic energy on a microscopicscale; the higher the
`
`temperature of thegas, the greater the kinetic energy of the atoms
`and thegreater
`the thermal energy of the gas. More generally, however, thermal energy includes
`other forms of molecular energy, such as rotational energy and vibrational kinetic
`and potential energy
`
`rgy that we dis-
`As an analogy, consider the distinction between work and en
`cussed in Chapter 7. The work done on (or by) a systemis a measureof the energy
`transferred between the system and its surroundings, whereas the mechanical en-
`
`ergy of the system(kinetic or potential) is a consequence of its motion and coor
`
`dinates, Thus, when a person does work on a system, energy is transferred from the
`It makes no sense to talk about the work ofa system—one
`person to the system.
` 5
`should instead refer only to the work done on or by a system when some proc
`
`
`
`erred to or
`f
`
`has occurred in which energy has been transf
`omthe system, Likew
`it makes no sense to use the term heat unless energy has been transferred as a
`
`ure difference.
`result of a temper:
`
`It is also imp
`ant to recognize that energy can be transferred between two
`systems even when no thermal energy transfer occurs. For example, when a gas is
`
`compressed by a piston, the gas is warmed and its thermal energy increases, but
`
`there is no transfer of thermal energy from the surroundings; if the gas then ex-
`pands rapidly, it cools andits thermal energy decreases, but there is no transfer of
`
`thermal energy to the surroundings.
`Ir
`ach case, energy 1s transferred to or from
`
`the system as work but appears within the system as an increase or decrease of
`thermale
`gy. The changes in internal ener
`i these examples are eq
`to the
`
`
`
`
`changes in thermal energy and are measured by corresponding changes
`in
`tem-
`pe rature,
`
`Units of Heat
`Early in the development of thermodynamics, beforescientists realized that heat is
`transferred energy, heat was defined in term
`the
`temperature changes it pro
` > defined as the amount of heat
`duced in a body. Hence,
`the calorie (cal
`
`
`
`James Prescott Joule
`(1818-1889)
`A British physicist, Joule received
`somef
`al education in mathemal-
`ics, philosophy, and
`chemistry from
`John Dalton but wasin large port salt
`educated. Joule’s mos! active resear
`
`period,
`from 1837 through 1847,
`le
`to the establishment ofthe principle of
`conservation of energy
`
` olence of heat and other for
`lationship amang elec
`
`ergy. His4
`dy of the quo
`mechanical, and chemic
`
`heat culmin