Chapter 19Chapter 19

TemperatureTemperature

TemperatureTemperature

• We associate the concept of temperature with We associate the concept of temperature with how hot or cold an objects feelshow hot or cold an objects feels

• Our senses provide us with a qualitative Our senses provide us with a qualitative indication of temperatureindication of temperature

• Our senses are unreliable for this purposeOur senses are unreliable for this purpose

• We need a technical definition of temperatureWe need a technical definition of temperature

Thermal ContactThermal Contact

• Two objects are in Two objects are in thermal contactthermal contact with with each other if energy can be exchanged each other if energy can be exchanged between thembetween them– The exchanges we will focus on will be in the The exchanges we will focus on will be in the

form of heat or electromagnetic radiationform of heat or electromagnetic radiation– The energy is exchanged due to a The energy is exchanged due to a

temperature differencetemperature difference

Thermal EquilibriumThermal Equilibrium

• Thermal equilibriumThermal equilibrium is a situation in is a situation in which two objects would not exchange which two objects would not exchange energy by heat or electromagnetic energy by heat or electromagnetic radiation if they were placed in thermal radiation if they were placed in thermal contactcontact– The thermal contact does not have to also be The thermal contact does not have to also be

physical contactphysical contact

Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics

• If objects If objects AA and and BB are separately in are separately in thermal equilibrium with a third object thermal equilibrium with a third object CC, , then then AA and and BB are in thermal equilibrium are in thermal equilibrium with each otherwith each other– Let object Let object CC be the thermometerbe the thermometer– Since the objects are in thermal equilibrium Since the objects are in thermal equilibrium

with each other, there is no energy with each other, there is no energy exchanged among themexchanged among them

Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics

• Object Object CC (thermometer) is placed in contact with (thermometer) is placed in contact with AA until they until they achieve thermal equilibriumachieve thermal equilibrium– The reading on The reading on CC is recorded is recorded

• Object Object CC is then placed in contact with object is then placed in contact with object BB until they until they achieve thermal equilibriumachieve thermal equilibrium– The reading on The reading on C C is recorded againis recorded again

• If the two readings are the same, If the two readings are the same, AA and and BB are also in thermal are also in thermal equilibriumequilibrium

Temperature (Technical)Temperature (Technical)

• Temperature Temperature can be thought of as the can be thought of as the property that determines whether an property that determines whether an object is in thermal equilibrium with other object is in thermal equilibrium with other objects objects

• Two objects in thermal equilibrium with Two objects in thermal equilibrium with each other are at the same temperatureeach other are at the same temperature– If two objects have different temperatures, If two objects have different temperatures,

they are not in thermal equilibrium with each they are not in thermal equilibrium with each otherother

ThermometersThermometers

• A A thermometerthermometer is a device that is used to is a device that is used to measure the temperature of a systemmeasure the temperature of a system

• Thermometers are based on the principle Thermometers are based on the principle that some physical property of a system that some physical property of a system changes as the system’s temperature changes as the system’s temperature changeschanges

ThermometersThermometers

• These properties include:These properties include:– The volume of a liquidThe volume of a liquid– The dimensions of a solidThe dimensions of a solid– The pressure of a gas at a constant volumeThe pressure of a gas at a constant volume– The volume of a gas at a constant pressureThe volume of a gas at a constant pressure– The electric resistance of a conductorThe electric resistance of a conductor– The color of an objectThe color of an object

• A temperature scale can be established on A temperature scale can be established on the basis of any of these physical the basis of any of these physical propertiesproperties

Thermometer, Liquid in GlassThermometer, Liquid in Glass

• A common type of A common type of thermometer is a thermometer is a liquid-in-glassliquid-in-glass

• The material in The material in the capillary tube the capillary tube expands as it is expands as it is heatedheated

• The liquid is The liquid is usually mercury or usually mercury or alcoholalcohol

Calibrating a ThermometerCalibrating a Thermometer

• A thermometer can be calibrated by A thermometer can be calibrated by placing it in contact with some natural placing it in contact with some natural systems that remain at constant systems that remain at constant temperaturetemperature

• Common systems involve waterCommon systems involve water– A mixture of ice and water at atmospheric A mixture of ice and water at atmospheric

pressure called the pressure called the ice pointice point of water. of water.– A mixture of water and steam in equilibrium A mixture of water and steam in equilibrium

called the called the steam pointsteam point of water. of water.

Celsius ScaleCelsius Scale

• The ice point of water is defined to be The ice point of water is defined to be 00ooCC

• The steam point of water is defined to be The steam point of water is defined to be 100100o o CC

• The length of the column between these The length of the column between these two points is divided into two points is divided into 100100 increments, increments, called degrees.called degrees.

Problems with Liquid-in-Glass Problems with Liquid-in-Glass ThermometersThermometers

• An alcohol thermometer and a mercury An alcohol thermometer and a mercury thermometer may agree only at the calibration thermometer may agree only at the calibration pointspoints

• The discrepancies between thermometers are The discrepancies between thermometers are especially large when the temperatures being especially large when the temperatures being measured are far from the calibration pointsmeasured are far from the calibration points

• The thermometers also have a limited range of The thermometers also have a limited range of values that can be measuredvalues that can be measured– Mercury cannot be used under Mercury cannot be used under –30–30oo C C– Alcohol cannot be used above Alcohol cannot be used above 8585oo C C

Constant Volume Gas ThermometerConstant Volume Gas Thermometer

• The physical change The physical change exploited is the variation exploited is the variation of pressure of a fixed of pressure of a fixed volume gas as its volume gas as its temperature changestemperature changes

• The volume of the gas is The volume of the gas is kept constant by raising kept constant by raising or lowering the reservoir or lowering the reservoir BB to keep the mercury to keep the mercury level at level at A A constantconstant

Constant Volume Gas ThermometerConstant Volume Gas Thermometer

• The thermometer is calibrated by using an The thermometer is calibrated by using an ice water bath and a steam water bathice water bath and a steam water bath

• The pressures of the mercury under each The pressures of the mercury under each situation are recordedsituation are recorded– The volume is kept constant by adjusting The volume is kept constant by adjusting AA

• The information is plottedThe information is plotted

Constant Volume Gas ThermometerConstant Volume Gas Thermometer

• To find the temperature To find the temperature of a substance, the gas of a substance, the gas flask is placed in flask is placed in thermal contact with thermal contact with the substancethe substance

• The pressure is found The pressure is found on the graphon the graph

• The temperature is The temperature is read from the graphread from the graph

Absolute ZeroAbsolute Zero

• The thermometer The thermometer readings are virtually readings are virtually independent of the gas independent of the gas usedused

• If the lines for various If the lines for various gases are extended, the gases are extended, the pressure is always zero pressure is always zero when the temperature is when the temperature is ––273.15273.15oo C C..

• This temperature is This temperature is called called absolute zeroabsolute zero

A constant-volume gas thermometer is calibrated in dry ice A constant-volume gas thermometer is calibrated in dry ice (that is, carbon dioxide in the solid state, which has a (that is, carbon dioxide in the solid state, which has a temperature of temperature of –80.0°C–80.0°C) and in boiling ethyl alcohol ) and in boiling ethyl alcohol ((78.0°C78.0°C). The two pressures are ). The two pressures are 0.900 atm0.900 atm and and 1.635 atm1.635 atm. . (a) What Celsius value of absolute zero ((a) What Celsius value of absolute zero (P = 0P = 0) does the ) does the calibration yield? What is the pressure at (b) the freezing calibration yield? What is the pressure at (b) the freezing point of water and (c) the boiling point of water?point of water and (c) the boiling point of water?

Problem 1.Problem 1.

A constant-volume gas thermometer is calibrated in dry ice A constant-volume gas thermometer is calibrated in dry ice (that is, carbon dioxide in the solid state, which has a (that is, carbon dioxide in the solid state, which has a temperature of temperature of –80.0°C–80.0°C) and in boiling ethyl alcohol ) and in boiling ethyl alcohol ((78.0°C78.0°C). The two pressures are ). The two pressures are 0.900 atm0.900 atm and and 1.635 atm1.635 atm. . (a) What Celsius value of absolute zero ((a) What Celsius value of absolute zero (P = 0P = 0) does the ) does the calibration yield? What is the pressure at (b) the freezing calibration yield? What is the pressure at (b) the freezing point of water and (c) the boiling point of water?point of water and (c) the boiling point of water?

Problem 1.Problem 1.

Since we have a linear graph, the pressure is related to the temperature asSince we have a linear graph, the pressure is related to the temperature as

, where , where AA and and B B are constants. To find are constants. To find AA and and BB, we use the , we use the data data P A BT

0.900 atm 80.0 CA B

1.635 atm 78.0 CA B

(1)

(2)

A constant-volume gas thermometer is calibrated in dry ice (that is, carbon A constant-volume gas thermometer is calibrated in dry ice (that is, carbon dioxide in the solid state, which has a temperature of dioxide in the solid state, which has a temperature of –80.0°C–80.0°C) and in boiling ) and in boiling ethyl alcohol (ethyl alcohol (78.0°C78.0°C). The two pressures are ). The two pressures are 0.900 atm0.900 atm and and 1.635 atm1.635 atm. (a) . (a) What Celsius value of absolute zero (What Celsius value of absolute zero (P = 0P = 0) does the calibration yield? What is ) does the calibration yield? What is the pressure at (b) the freezing point of water and (c) the boiling point of water?the pressure at (b) the freezing point of water and (c) the boiling point of water?

Solving (1) and (2) simultaneously, we find:Solving (1) and (2) simultaneously, we find:

1.272 atmA34.652 10 atm CB

Therefore, Therefore, 31.272 atm 4.652 10 atm CP T

(a) At absolute zero:(a) At absolute zero: 30 1.272 atm 4.652 10 atm CP T 274 CT

(b) At the freezing point of water: (b) At the freezing point of water: 1.272 atm 0 1.27 atmP

(c) And at the boiling point:(c) And at the boiling point:

31.272 atm 4.652 10 atm C 100 C 1.74 atmP

Absolute Temperature ScaleAbsolute Temperature Scale

• Absolute zero is used as the basis of the Absolute zero is used as the basis of the absolute temperature scaleabsolute temperature scale

• The size of the degree on the absolute The size of the degree on the absolute scale is the same as the size of the degree scale is the same as the size of the degree on the Celsius scaleon the Celsius scale

• To convert:To convert:TTCC = = TT – 273.15 – 273.15

• The absolute temperature scale is now The absolute temperature scale is now based on two new fixed points:based on two new fixed points:

Adopted by in 1954 by the International Adopted by in 1954 by the International Committee on Weights and Measures one point Committee on Weights and Measures one point is absolute zero; the other point is the triple is absolute zero; the other point is the triple point of water (this is the combination of point of water (this is the combination of temperature and pressure where ice, water, temperature and pressure where ice, water, and steam can all coexist).and steam can all coexist).

Absolute Temperature ScaleAbsolute Temperature Scale

Absolute Temperature ScaleAbsolute Temperature Scale

• The triple point of water occurs at The triple point of water occurs at

0.010.01oo C C and and 4.58 mm4.58 mm of mercury of mercury

• This temperature was set to be This temperature was set to be 273.16273.16 on on the absolute temperature scalethe absolute temperature scale– This made the old absolute scale agree closely This made the old absolute scale agree closely

with the new onewith the new one– The units of the absolute scale are The units of the absolute scale are kelvinskelvins

Absolute Temperature ScaleAbsolute Temperature Scale

• The absolute scale is also called the The absolute scale is also called the kelvin kelvin scalescale, named for William Thomson, Lord , named for William Thomson, Lord KelvinKelvin

• The triple point temperature is The triple point temperature is 273.16 K273.16 K– No degree symbol is used with kelvinsNo degree symbol is used with kelvins

• The The kelvin kelvin is defined as is defined as 11//273.16 273.16 of the of the difference between absolute zero and the difference between absolute zero and the temperature of the triple point of watertemperature of the triple point of water

Some Examples of Absolute Some Examples of Absolute

TemperaturesTemperatures

• The figure at right gives The figure at right gives some absolute some absolute temperatures at which temperatures at which various physical processes various physical processes occuroccur

• The scale is logarithmicThe scale is logarithmic• The temperature of The temperature of

absolute zero cannot be absolute zero cannot be achieved, experiments achieved, experiments have come close.have come close.

Energy at Absolute ZeroEnergy at Absolute Zero

• According to classical physics, the kinetic According to classical physics, the kinetic energy of the gas molecules would become energy of the gas molecules would become zero at absolute zerozero at absolute zero

• The molecular motion would cease, The molecular motion would cease, therefore, the molecules would settle out on therefore, the molecules would settle out on the bottom of the container.the bottom of the container.

• Quantum theory modifies this statement and Quantum theory modifies this statement and shows some residual energy would remainshows some residual energy would remain– This energy is called the This energy is called the zero-pointzero-point energy energy

Fahrenheit ScaleFahrenheit Scale

• A common scale in everyday use in the US A common scale in everyday use in the US named for Daniel named for Daniel FahrenheitFahrenheit

• Temperature of the ice point is Temperature of the ice point is 3232ooFF

• Temperature of the steam point is Temperature of the steam point is 212212ooFF

• There are There are 180 180 divisions (degrees) between divisions (degrees) between the two reference pointsthe two reference points

Comparison of ScalesComparison of Scales

• Celsius Celsius and and Kelvin Kelvin have the same size have the same size degrees, but different starting pointsdegrees, but different starting points

TTCC = = TT – 273.16 – 273.16

• CelsiusCelsius and and FahrenheitFahrenheit have different have different sized degrees and different starting pointssized degrees and different starting points

F C

932

5T T F

Comparison of ScalesComparison of Scales

• To compare changes in temperatureTo compare changes in temperature

• Ice point temperaturesIce point temperatures

00ooC = 273.16 K = 32C = 273.16 K = 32oo F F

• Steam point temperaturesSteam point temperatures

100100ooC = 373.16 K = 212C = 373.16 K = 212oo F F

C F

5

9T T T

Convert the following to equivalent temperatures Convert the following to equivalent temperatures on the Celsius and Kelvin scales: (a) the normal on the Celsius and Kelvin scales: (a) the normal human body temperature, human body temperature, 98.6°F98.6°F; (b) the air ; (b) the air temperature on a cold day, temperature on a cold day, –5.00°F–5.00°F..

Convert the following to equivalent temperatures Convert the following to equivalent temperatures on the Celsius and Kelvin scales: (a) the normal on the Celsius and Kelvin scales: (a) the normal human body temperature, human body temperature, 98.6°F98.6°F; (b) the air ; (b) the air temperature on a cold day, temperature on a cold day, –5.00°F–5.00°F..

(a) To convert from Fahrenheit to Celsius, we use:

5 532.0 98.6 32.0 37.0 C

9 9C FT T

and the Kelvin temperature is found as: 273 310 KCT T

(b)(b) 20.6 CCT

253 KT

The melting point of gold is The melting point of gold is 1 064°C1 064°C , and the , and the boiling point is boiling point is 2 660°C2 660°C. (a) Express these . (a) Express these temperatures in Kelvins. (b) Compute the temperatures in Kelvins. (b) Compute the difference between these temperatures in Celsius difference between these temperatures in Celsius degrees and Kelvins.degrees and Kelvins.

The melting point of gold is The melting point of gold is 1 064°C1 064°C , and the , and the boiling point is boiling point is 2 660°C2 660°C. (a) Express these . (a) Express these temperatures in Kelvins. (b) Compute the temperatures in Kelvins. (b) Compute the difference between these temperatures in Celsius difference between these temperatures in Celsius degrees and Kelvins.degrees and Kelvins.

1064 273 1337 KT (a)(a) melting pointmelting point

2660 273 2933 KT boiling pointboiling point

(b)(b) 1596 C 1596 KT

The differences are the same.The differences are the same.

Thermal ExpansionThermal Expansion

• Thermal expansion is the increase in the size of Thermal expansion is the increase in the size of an object with an increase in its temperaturean object with an increase in its temperature

• Thermal expansion is a consequence of the Thermal expansion is a consequence of the change in the average separation between the change in the average separation between the atoms in an objectatoms in an object

• If the expansion is small relative to the original If the expansion is small relative to the original dimensions of the object, the change in any dimensions of the object, the change in any dimension is, to a good approximation, dimension is, to a good approximation, proportional to the first power of the change in proportional to the first power of the change in temperaturetemperature

Linear ExpansionLinear Expansion

• Assume an object has an initial length Assume an object has an initial length LL

• That length increases by That length increases by LL as the as the temperature changes by temperature changes by TT

• We define the We define the coefficient of linear coefficient of linear expansionexpansion as as

• A convenient form is A convenient form is

LL = = LLi i TT

/ iL L

T

Linear ExpansionLinear Expansion

• This equation can also be written in terms This equation can also be written in terms of the initial and final conditions of the of the initial and final conditions of the object:object:

LLff – – LLii = = L Li i ((TTff – – TTii))

• The The coefficient of linear expansioncoefficient of linear expansion, , , , has units of has units of ((ooC)C)-1-1

Linear ExpansionLinear Expansion

• Some materials expand along one Some materials expand along one dimension, but contract along another as dimension, but contract along another as the temperature increasesthe temperature increases

• Since the linear dimensions change, it Since the linear dimensions change, it follows that the surface area and volume follows that the surface area and volume also change with a change in temperaturealso change with a change in temperature

Volume Expansion

• The change in volume is proportional to The change in volume is proportional to the original volume and to the change in the original volume and to the change in temperaturetemperature

VV = = VVii TT

is the is the coefficient of volume expansioncoefficient of volume expansion

For a solid, For a solid, 33This assumes the material is isotropic, the same in This assumes the material is isotropic, the same in all directionsall directions

For a liquid or gas, For a liquid or gas, is given in the table is given in the table

Area ExpansionArea Expansion

• The change in area is proportional to the The change in area is proportional to the original area and to the change in original area and to the change in temperature:temperature:

AA = 2 = 2AAi i TT

Thermal Expansion, Example• In many situations, joints In many situations, joints

are used to allow room are used to allow room for thermal expansion for thermal expansion

• The long, vertical joint is The long, vertical joint is filled with a soft material filled with a soft material that allows the wall to that allows the wall to expand and contract as expand and contract as the temperature of the the temperature of the bricks changesbricks changes

The New River Gorge bridge in West Virginia is a steel The New River Gorge bridge in West Virginia is a steel arch bridge arch bridge 518 m518 m in length. How much does the total in length. How much does the total length of the roadway decking change between length of the roadway decking change between temperature extremes of temperature extremes of –20.0°C–20.0°C and and 35.0°C35.0°C? The ? The result indicates the size of the expansion joints that must result indicates the size of the expansion joints that must be built into the structure.be built into the structure.

The New River Gorge bridge in West Virginia is a steel The New River Gorge bridge in West Virginia is a steel arch bridge arch bridge 518 m518 m in length. How much does the total in length. How much does the total length of the roadway decking change between length of the roadway decking change between temperature extremes of temperature extremes of –20.0°C–20.0°C and and 35.0°C35.0°C? The ? The result indicates the size of the expansion joints that must result indicates the size of the expansion joints that must be built into the structure.be built into the structure.

5 11.10 10 C for steel

5 1518 m 1.10 10 C 35.0 C 20.0 C 0.313 mL

ΔΔL = L = ααLLiiΔΔTT

At At 20.0°C20.0°C, an aluminum ring has an inner diameter of , an aluminum ring has an inner diameter of 5.0000 cm5.0000 cm and a brass rod has a diameter of and a brass rod has a diameter of 5.0500 cm5.0500 cm. . (a) If only the ring is heated, what temperature must it (a) If only the ring is heated, what temperature must it reach so that it will just slip over the rod? (b) If both are reach so that it will just slip over the rod? (b) If both are heated together, what temperature mustheated together, what temperature must they both reach they both reach so that the ring just slips over the rod? Would this latter so that the ring just slips over the rod? Would this latter process work?process work?

At At 20.0°C20.0°C, an aluminum ring has an inner diameter of , an aluminum ring has an inner diameter of 5.000 cm5.000 cm and a brass rod has a diameter of and a brass rod has a diameter of 5.050 cm5.050 cm. (a) If only the . (a) If only the ring is heated, what temperature must it reach so that it will just ring is heated, what temperature must it reach so that it will just slip over the rod? (b) If both are heated together, what slip over the rod? (b) If both are heated together, what temperature musttemperature must they both reach so that the ring just slips over they both reach so that the ring just slips over the rod? Would this latter process work?the rod? Would this latter process work?

(a)(a) 1iL L T

6 15.050 cm 5.000 cm 1 24.0 10 C 20.0 CT 437 CT (b) (b) We must get We must get Al BrassL L for some for some T

, Al Al , Brass Brass

6 1 6 1

1 1

5.000 cm 1 24.0 10 C 5.050 cm 1 19.0 10 C

i iL T L T

T T

2080 CT aluminum melts at 660 Cbutbut

ααAlAl = 24.0 x 10 = 24.0 x 10-6-6 00CC-1-1

ααbrassbrass = 19.0 x 10 = 19.0 x 10-6-6 00CC-1-1

T = Ti + ΔT=21000C

Bimetallic StripBimetallic Strip

• Each substance has Each substance has its own characteristic its own characteristic average coefficient of average coefficient of expansionexpansion

• This can be made use This can be made use of in the device shown, of in the device shown, called a bimetallic stripcalled a bimetallic strip

• It can be used in a It can be used in a thermostatthermostat

Water’s Unusual BehaviorWater’s Unusual Behavior

• As the temperature As the temperature increases from increases from 00ooCC to to 44ooCC, water contracts, water contracts– Its density increasesIts density increases

• Above Above 44ooCC, water , water expands with expands with increasing temperatureincreasing temperature– Its density decreasesIts density decreases

• The maximum density The maximum density of water (of water (1.000 g/cm1.000 g/cm33) ) occurs at occurs at 44ooCC

An Ideal GasAn Ideal Gas

• For gases, the interatomic forces within the For gases, the interatomic forces within the gas are very weakgas are very weak– We can imagine these forces to be nonexistentWe can imagine these forces to be nonexistent

• Note that there is no equilibrium separation Note that there is no equilibrium separation for the atomsfor the atoms– Thus, no “standard” volume for gas at a given Thus, no “standard” volume for gas at a given

temperaturetemperature

Ideal GasIdeal Gas

• For a gas, the volume is entirely For a gas, the volume is entirely determined by the container holding the determined by the container holding the gasgas

• Equations involving gases will contain the Equations involving gases will contain the volume, volume, VV, as a variable, as a variable– This is instead of focusing on This is instead of focusing on VV

Gas: Equation of StateGas: Equation of State

• It is useful to know how the It is useful to know how the volumevolume, , pressurepressure, and , and temperaturetemperature of the gas of of the gas of mass mass m are related are related

• The equation that interrelates these The equation that interrelates these quantities is called the quantities is called the equation of stateequation of state– These are generally quite complicatedThese are generally quite complicated– If the gas is maintained at a low pressure, the If the gas is maintained at a low pressure, the

equation of state becomes much easierequation of state becomes much easier– This type of a low density gas is commonly This type of a low density gas is commonly

referred to as an referred to as an ideal gasideal gas

The MoleThe Mole

• The amount of gas in a given volume is The amount of gas in a given volume is conveniently expressed in terms of the conveniently expressed in terms of the number of number of moles.moles.

• One One molemole of any substance is that amount of of any substance is that amount of the substance that contains the substance that contains Avogadro’s Avogadro’s numbernumber of constituent particles of constituent particles– Avogadro’s number Avogadro’s number NNAA = 6.022 x 10 = 6.022 x 102323

– The constituent particles can be atoms or The constituent particles can be atoms or moleculesmolecules

MolesMoles

• The number of The number of molesmoles can be determined can be determined from the mass of the substance: from the mass of the substance: nn = = mm / /MM– MM is the molar mass of the substance is the molar mass of the substance– mm is the mass of the sample is the mass of the sample– nn is the number of moles is the number of moles

Gas LawsGas Laws

• When a gas is kept at a constant When a gas is kept at a constant temperature, its pressure is inversely temperature, its pressure is inversely proportional to its volume (proportional to its volume (Boyle’s lawBoyle’s law))

• When a gas is kept at a constant pressure, When a gas is kept at a constant pressure, its volume is directly proportional to its its volume is directly proportional to its temperature (temperature (Charles Charles andand Gay-Lussac’s Gay-Lussac’s lawlaw))

Ideal Gas LawIdeal Gas Law• The equation of state for an ideal gas combines and The equation of state for an ideal gas combines and

summarizes the other gas lawssummarizes the other gas laws

PV = RnTPV = RnT

• This is known as the This is known as the Ideal Gas LawIdeal Gas Law• RR is a constant, called the is a constant, called the Universal Gas ConstantUniversal Gas Constant

RR = 8.314 J/K = 8.314 J/K··mol = 0.08214 L ∙ atm/(mol ∙ K)mol = 0.08214 L ∙ atm/(mol ∙ K)

• From this, you can determine that the volume of From this, you can determine that the volume of 1 mole1 mole of any gas at atmospheric pressure and at of any gas at atmospheric pressure and at 00ooCC is is 22.4 L22.4 L

( 1 Liter = 1 x 10( 1 Liter = 1 x 1033cmcm33 = 1 x 10 = 1 x 10-3-3 m m33))

Ideal Gas LawIdeal Gas Law

• The The Ideal Gas LawIdeal Gas Law is often expressed in terms is often expressed in terms of the total number of molecules, of the total number of molecules, NN, present in , present in the samplethe sample

kkBB is Boltzmann’s constantis Boltzmann’s constant

kkBB = 1.38 x 10= 1.38 x 10-23-23 J/K J/K

• It is common to call It is common to call PP, , VV, and , and TT the the thermodynamic variablesthermodynamic variables of an ideal gas of an ideal gas

TNkRTnRTPV BNNA

Just Just 9.00 g9.00 g of water is placed in a of water is placed in a 2.00-L2.00-L pressure pressure cooker and heated to cooker and heated to 500°C500°C. What is the pressure . What is the pressure inside the container?inside the container?

Just Just 9.00 g9.00 g of water is placed in a of water is placed in a 2.00-L2.00-L pressure cooker pressure cooker and heated to and heated to 500°C500°C. What is the pressure inside the . What is the pressure inside the container?container?

3 3

9.00 g 8.314 J 773 K1.61 MPa 15.9 atm

18.0 g mol mol K 2.00 10 m

nRTP

V

molg

g

M

mn

/18

9

1atm = 1.013 x 105 Pa

atmatmPa

PaPaMPa 9.15

/10013.1

1061.11061.161.1

5

66

The density of gasoline is The density of gasoline is 730 kg/m730 kg/m33 at at 0°C0°C. Its average . Its average coefficient of volume expansion is coefficient of volume expansion is 9.60 9.60 10 10–4–4//CC. If . If 1.00 gal1.00 gal of gasoline occupies of gasoline occupies 0.00380 m0.00380 m33, how many extra kilograms , how many extra kilograms of gasoline would you get if you bought of gasoline would you get if you bought 10.0 gal10.0 gal of gasoline at of gasoline at 0°C0°C rather than at rather than at 20.0°C20.0°C from a pump that is not temperature from a pump that is not temperature compensated?compensated?

The density of gasoline is The density of gasoline is 730 kg/m730 kg/m33 at at 0°C0°C. Its average coefficient of . Its average coefficient of volume expansion is volume expansion is 9.60 9.60 10 10–4–4//CC. If . If 1.00 gal1.00 gal of gasoline occupies of gasoline occupies 0.00380 m0.00380 m33, how many extra kilograms of gasoline would you get if you , how many extra kilograms of gasoline would you get if you bought bought 10.0 gal10.0 gal of gasoline at of gasoline at 0°C0°C rather than at rather than at 20.0°C20.0°C from a pump that from a pump that is not temperature compensated?is not temperature compensated?

At At 0°C0°C, , 10.0 10.0 gallons of gasoline has mass,gallons of gasoline has mass, from :from : mV

3

3 0.00380 m730 kg m 10.0 gal 27.7 kg

1.00 galm V

The gasoline will expand in volume by:The gasoline will expand in volume by:

4 19.60 10 C 10.0 gal 20.0 C 0.0 C 0.192 galiV V T

At 20.0°C, At 20.0°C, 10.192 gal 27.7 kg10.0 gal

10.0 gal 27.7 kg 27.2 kg10.192 gal

27.7 kg 27.2 kg 0.523 kg The extra mass contained in The extra mass contained in 10.0 gallons at 0.0°C is:10.0 gallons at 0.0°C is: