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Spring 2004 PHY 2053C: College Physics A

Today: Kinematic Theory of Gas

Ideal Gas Law PV=nRT Maxwell distribution Internal energy

Heat Heat: definition Specific Heat Thermal conductivity

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Motion, Forces, Energy, Heat, Waves Dr. David M. Lind Dr. Kun Yang Dr. David Van Winkle

L15—Ch13Ch14

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Temperature, Heat, & Thermodynamics:

IntroductionSo far we have looked at

properties of macroscopic objects. In order to study the subjects of

temperature, heat and thermodynamics, we need to understand what happens microscopically.

The correct understanding of these subjects depends on the knowledge of the micro-structure of matter and leads to the atomic theory of matter.

The building blocks of matter are the atoms of the chemical elements, molecules of the chemical compounds, and crystalline solids.

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Atomic Theory of MatterDemocritos: Matter can be divided

into very small units, which are indivisible: atoms.

All atoms of a given chemical element are identical. Z Protons Z Electrons (here 2)

N Neutrons add to atomic mass

Z is chemical element number (here 2=Helium) A = Z+N is mass number (here 4 =>4He) Atomic Mass ≈ (Z+N) * 1u (here 4u)

where 1u=1.66 x 10 -27kg “atomic mass unit”

Mole: definition

1 mole contains 1 NA= 6.022x1023 atoms.

“Avagadro’s number”

1 mole weighs A grams. (4g He = 1 mole)

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Question: Atoms A slightly irritated Taxi-Driver tells you that the

solution to all health problems lies in a certain powder (which you can mail-order) containing “activated micro-hydrogen”.

You reply:1) You ask him if his finances have improved since he is taking the powder2) You answer: There is only one type of hydrogen, all “hydrogen” atoms are of the same size and he might just as well drink clear water. 3) You ask him if he is talking about tritium (a radioactive isotope of hydrogen), in which case you call the CIA4) You tell him that you have had better experiences with fat-dissolving hydrocarbons (if you're over 21, that is).5) All of the above

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Brownian MotionAtomic Theory: Temperature is connected tounordered (random) motion of atoms and molecules.

Observation: (Thermal Equlibrium) Bring hot and cold objects in contact and they will eventually equalize their temperatures.

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Thermal ExpansionMost substances expand

with increasing Temp. The expansion is a result of

increased vibrational motion at the atomic level.

We write

, where α is a material constant.

typical values (around 20° C) Glass α= 9 x 10-6 (°C)-1

Aluminum α= 25 x 10-6 (°C)-

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Water α= 210 x 10-6 (°C)-1

L L0 1 T

L L0 T

expansion joint in roadway.

Eiffel Tower gains about 1/5th cm for each Celcius degree of temperature rise.

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Thermometers Most materials expand with higher Temperature

can be used to measure temperature (a) Liquid-in-glass thermometer:

as liquid in reservoir expands(by a few %), the level varies in narrow tube.

(b) bi-metallic strip-therm.two metals with different expansion properties bend with temperature

(c) Thermocouple (electric voltage function of temperature)

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Temperature ScalesTemperature was measured long before

people understood brownian motion.

Historic units are arbitrary:

Fahrenheit: lowest Temp. that winter = 0°F his body Temp.: = 100°F

(he had a fever!)

Celsius scale: (“centigrade”) water freezing temp. = 0°C (= 32°F) water boiling temp. = 100°C (= 212°F)

TC = 5/9(TF - 32°)

TF = (9/5TC) + 32°

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Absolute Temperature How cold can things get?

Both Celsius and Fahrenheit defined 0° to be some arbitrary point.

If we think about the analogy: temperature <=> random motion

zero temperature <=> NO random motion then there must be an absolute zero Temperature! This point is reached at -273°C (-459°F). There can never be anything colder than this.

Absolute Temperature: Kelvin scale Degrees Kelvin

= degrees Celsius above absolute zero

T(K) = T(°C) – 273

Lord Kelvin, born William Thompson

(1824-1907)

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Ideal Gas Law

PV n RT

Pressure*Volume = no.moles * R * Temp. R=8.315 J/(mol Kelvin) “universal gas constant” =0.0821 (L atm)/(mol K) absolute Temperature is used ! absolute Pressure is used !

What is an “ideal” gas T? -- well above liquefication point

We use: PV (=P1V1 = P2V2) = constant (if T and n constant)

“Boyle's law”

P/T (=P1/T1 = P2/T2) = constant (if V and n constant) “Gay-Lussac law”

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You have 1 mole of Hydrogen (atomic mass 2) and 1 mole of O2 (molecular mass 32), both at atmospheric pressure and room temperature.

1.) Oxygen occupies a larger volume 2.) They occupy the same volume 3.) Helium occupies a larger volume 4.) That depends on the density of the

surrounding gas.

Question

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Kinetic Gas Theory

Atoms/Molecules bounce off the walls: The pressure exerted by a gas

comes from the rate at which atoms/molecules bounce per surface area timestheir average momentum

Many, many atoms are in the air around you you “feel” no bouncing, but constant pressure.

Temperature is related to average kin. energy

PV n RT

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Kinetic Gas TheoryTemperature: unordered (random) motion of atoms.

definition: “average kinetic energy of one atom/molecule” ~

temperature

where kB =1.38 x 10-23 J/K

The atoms/molecules have a wide range of

different speeds.(called the Maxwell distribution)

Notice: this is dependent both on atomic/molecular

mass and on temperature.

KE 12

mv2 32

kBT

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example: Speed of Molecules speed of air-molecules around you.

for air (O2) at 24 °C = 297 K,

KE 12

m v2 32

k BT

KE32

1.38 10 23JK

297K

= 6.14 10 21J12 mv

2 12 mv rms

2

m O2 32 1.67 10 27kg 5.3 10 26kg

=>vrms2 KEm O2

481 ms

214 mph

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Ideal Gases: Temperature, Heat, and Internal Energy

Let's first look at gas of single atoms (He, Ar, Kr ..)

Here: the kinetic energy is the only energy an atom can have

where kB =1.38 x 10-23 J/K

The total internal energy U in this case is: the number of atoms times kinetic energy per atom

Heat transferred increases internal Energy

U32N k BT

32n RT

KE 12

mv2 32

kBT

Q U

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Questions Question

A 100-g piece of steel (A) is at 200°C (473 K) and a 200-g piece of steel (B) is at 100°C (373 K).

Which one has higher average KE per atom?1) A

2) B

3) same Question

Which object has the higher internal energy?1) A

2) B

3) same

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example: Heat capacity of Helium

How much heat is required to raise the temperature of 1 kg of Helium by 1 °C?

For the single-atom gas Helium:

How many moles is 1kg? (Mass number 4: 4g He is one mole) 250 moles!

Q32

250 mol 8.315J

K mol1 K 3118J

Q U32n R T

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Internal Energy: Molecular Gases

Different materials have different forms of internal energy: (“degrees of freedom”)

In addition to linear KE, Molecules may have rotational KE Molecules may have elastic Potential E.

The more degrees of freedom, the higher the specific heat capacity!

U N KE rot.KE P.E

= 32 kBT 2

2 kBT 12 kBT

=energy forms

number of dimensions x 12 kBT

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Real Gases, Condensation:Water and Vapor

Raise Pressure, lower Temp=> condensation. (gas to liquid) gas and liquid co-exist (vapor)

until all is converted.

p1VT

V

P=F/A

T=high

T=low

pV n RT

P

V

P

T(°C)

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Heat Originally, heat was thought to be a separate quantity, connected to Temperature.

Heat is energy. Mechanical energy can become heat through friction.

symbol: Q

unit: 1 J = “1 Joule”

unit: 1 cal = Heat required to raise 1g of Water: Temp +1 C°

(1 kcal = 1 Cal)

James Prescott Joule (1818-1889):

showed that you can raise temperature by mechanical work

Q

KE

mgh

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Specific HeatDifferent materials require different amount of Q to change their temperature! The difference is called:

Specific Heat c:the amount of Heat required to raise the temperature of 1 kg of given material by 1 °C.

positive Q “heats up”, negative Q “cools down”

Several examples: cWater= 4186 J/(K kg) cGlass= 840 J/(K kg)

cIron = 450 J/(K kg) cProtein = 1700 J/(K kg)

cAluminumn = 900 J/(K kg) clead = 128 J/(K kg)

cQT m

cQT m

Q cm T

demo: “melting races”Al, Fe, Pb

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Heat will flow from higher to lower temperature. Heat is transfer of energy, and energy is conserved,

so: Q2 = -Q1

+Q will raise T2, while -Q will lower T1 => until T1=T2 and Heat stops flowing.

Heat is the change of the internal energy U !

Heat and Temperature

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Heat and Temperature:Thermal conductivity

The rate of heat flow is proportional to the thermal conductivity of the materials. Q/t = kA (T1-T2)/l

several examples: kcopper= 380 J/(s m °C) kice= 2 J/(s m °C)

kAluminum = 200 J/(s m °C) kGlass= 0.84 J/(s m °C)

ksteel = 40 J/(s m °C) kstyrofoam= 0.010 J/(s m °C)

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Question

A 100-g piece of steel (A) is at 200°C and a 200-g piece of steel (B) is at 100°C.

Which object gains internal energy when the two are in contact?

● 1) A● 2) B● 3) none

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Stay tuned...

Friday: CAPA10/Recitation Monday: Chapter 14 (cont.):

More CalorimetryLatent Heat Heat Exchange

Wednesday: Mini-Exam#5 (chapters 9, 13)