Lecture Outlines Chapter 16 Physics, 3

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Lecture Outlines Chapter 16

Physics, 3 ^rd Edition

James S. Walker

Chapter 16

Temperature and Heat

Units of Chapter 16

• Temperature and the Zeroth Law of Thermodynamics

• Temperature Scales

• Thermal Expansion

• Heat and Mechanical Work

• Specific Heats

• Conduction, Convection, and Radiation

16-1 Temperature and the Zeroth Law of Thermodynamics

Definition of heat:

Heat is the energy transferred between objects because of a temperature difference.

Objects are in thermal contact if heat can flow between them.

When the transfer of heat between objects in

thermal contact ceases, they are in thermal

equilibrium.

16-1 Temperature and the Zeroth Law of Thermodynamics

The zeroth law of thermodynamics:

If object A is in thermal equilibrium with object B, and object C is also in thermal equilibrium with object B, then objects A and C will be in thermal equilibrium if brought into thermal contact.

That is, temperature is the only factor that

determines whether two objects in thermal

contact are in thermal equilibrium or not.

16-1 Temperature and the Zeroth Law of

Thermodynamics

16-2 Temperature Scales

The Celsius scale:

Water freezes at 0° Celsius.

Water boils at 100° Celsius.

The Fahrenheit scale:

Water freezes at 32° Fahrenheit .

Water boils at 212° Fahrenheit .

Converting between Celsius and Fahrenheit:

16-2 Temperature Scales

Converting between Fahrenheit and Celsius :

Example 16-1

Temperature Conversions

16-2 Temperature Scales

The pressure in a gas is proportional to its

temperature. The proportionality constant is

different for different gases, but they all reach

zero pressure at the same temperature, which

we call absolute zero:

Figure 16-2

A constant-volume gas thermometer

Example 16-2 It’s a Gas

Trycket vid 0,00° C är 80,0 kPa. Om gasen kan anses ideal, vad är

trycket vid 105° C? p(T) = kT med k = 80,0 kPa/273,15 K = 293 Pa/K

p = k(273,15 +105) = 111 kPa

16-2 Temperature Scales

The Kelvin scale is similar to the Celsius scale, except that the Kelvin scale has its zero at

absolute zero.

Conversion between a Celsius temperature and

a Kelvin temperature:

16-2 Temperature Scales

The three temperature scales compared:

16-3 Thermal Expansion

Most substances expand when heated; the change in length or volume is typically

proportional to the change in temperature.

The proportionality constant is called the

coefficient of linear expansion.

Conceptual Checkpoint 16–1a Compare Expansions

(Rätt överdrivna figurer för tydlighetens skull. Vad är en rimlig

temperaturdifferens som svarar mot figuren? (ΔT =1/3α = 20 kK för Cu!)

16-3 Thermal Expansion

Some typical coefficients of thermal expansion:

Exercise 16-2

La Tour Eiffel är 301 m högt, en sommardag då temperaturen är 22°C. Hur mycket minskar dess höjd om temperaturen sjunker till 0°C?

ΔT = - 22 K = (- 22°C) α = 12•10 ^-6 K ^-1 ger

ΔL = α L ₀ ΔT = - 0,079 m

16-3 Thermal Expansion

A bimetallic strip consists of two metals of

different coefficients of thermal expansion, A

and B in the figure. It will bend when heated or

cooled.

Figure 16-5

A bimetallic strip

16-3 Thermal Expansion

The expansion of an area of a flat substance is derived from the linear expansion in both

directions:

Holes expand as well:

16-3 Thermal Expansion

The change in volume of a solid is also derived from the linear expansion:

For liquids and gases, only the coefficient of

volume expansion is defined:

Area and Volume Expansions

A´= (L+ΔL) ² = (L + α L ΔT) ² A’ – A = ΔA ≈ 2 α A ΔT

V´= (L+ΔL) ³ = (L + α L ΔT) ³

V’ – V = ΔV ≈ 3 α V ΔT = β V ΔT

16-3 Thermal Expansion

Some typical coefficients of volume expansion:

Example 16-3 Oil Spill

En kopparbehållare (V = 150 cm

) fylls till bredden med olivolja och

värms därefter upp 25 grader. Hur mycket olja rinner då ut över kanten?

ΔV ≈ β V ΔT = 0,68 • 10

/K •150 cm

• 25 K = 2,55 cm

ΔV

≈ β V

ΔT = 3 •17•10

/K •150 cm

• 25 K = 0,19 cm

så den utrunna volymen olja blir ungefär 2,4 cm

16-3 Thermal Expansion

Water also expands when it is heated, except when it is close to freezing; it actually expands when cooling from 4° C to 0° C.

This is why ice floats and

frozen bottles burst.

16-4 Heat and Mechanical Work

Experimental work has shown that heat is another form of energy.

James Joule

(1818 -1889)

used a device

similar to this

one to measure

the mechanical

equivalent of

heat:

16-4 Heat and Mechanical Work

One kilocalorie (kcal) is defined as the amount of heat needed to raise the temperature of 1 kg of water from 14.5° C to 15.5° C.

Through experiments such as Joule’s, it was

possible to find the mechanical equivalent:

16-4 Heat and Mechanical Work

Another unit of heat is the British thermal unit

(Btu). This is the energy required to heat 1 lb of

water from 63° F to 64° F.

Example 16-4

Stair Master

Example 16-4 Stair master

En person med massan 74,0 kg dricker en

milkshake (305 kcal). Hur många trappsteg à 20 cm måste han ta för att förbränna det energiintaget?

Q = 3,05 •10 ⁵ cal = (1 cal = 4,186 J) = 1276730 J För att ta ett steg åtgår energin

E = mgh = 74,0 kg•9,81 m/s ² •0,20 m = 145,188 J

Så antalet steg i trappan blir Q/E (= 8794) ≈ 8800

16-5 Specific Heats

The heat capacity of an object is the amount of heat added to it divided by its rise in temperature:

Q is positive if ΔT is positive; that is, if heat is added to a system.

Q is negative if ΔT is negative; that is, if heat is

removed from a system.

Exercise 16-3

Värmekapaciteten C för 1,00 kg vatten är 4186 J/K.

Vad blir temperaturändringen om värmet a) 505 J tillförs b) 1010 J bortförs?

Q = C•ΔT [= c•m•ΔT]

ΔT = + 505 J/4186 J/K = 0,121 K

ΔT = - 1010 J/4186 J/K = - 0,241 K

16-5 Specific Heats

The heat capacity of an object depends on its

mass. A quantity which is a property only of the

material is the specific heat:

16-5 Specific Heats

Here are some

specific heats of

various materials:

16-5 Specific Heats

A calorimeter is a lightweight, insulated flask containing water. When an object is put in, it and the water come to thermal equilibrium. If the mass of the flask can be ignored, and the insulation keeps any heat from escaping:

1. The final temperatures of the object and the water will be equal.

2. The total energy of the system is conserved.

This allows us to calculate the specific heat of

the object.

Active Example 16-2 Find the final Temperature

Vatten med massan 550 g och med en

begynnelsetemperatur på 32°C släpps ned i en aluminiumbehållare, som väger 210 g med

ursprungstemperaturen 15°C. Vad blir sluttemperaturen då man antar att inget värmeutbyte sker med omgivningen.

Q _behållare = c•m•ΔT = 900•0,210(T- 15°C ) Q _vatten = c•m•ΔT = 4186•0,550(T - 32°C)

om Q _behållare + Q _vatten = 0 fås T = 31°C (30,7°C)

Example 16-5

Cooling Off

Example 16-5 Cooling Off

Ett metallblock som väger 0,50 kg och med en begynnelsetemperatur på 54,5°C släpps ned i en behållare, som innehåller 1,1 kg vatten med

ursprungstemperaturen 20,0°C. Sluttemperaturen

blir 21,4°C då man bortser från behållarens inverkan och antar att inget värmeutbyte sker med

omgivningen. Beräkna metallens specifica värmekapacitet.

Q _block = c•m•ΔT = c•0,5(21,4 - 54,5)= - c•16,55•kg•K

Q _vatten = c•m•ΔT = 4186•1,1(21,4 -20,0)= 6446,44 J

c ≈ 390 J/(kg•K) (dvs Cu?) om Q _block + Q _vatten = 0

16-6 Conduction, Convection, and Radiation

Conduction (värmeledning), convection (konvektion) , and radiation (strålning) are three ways that heat can be exchanged.

Conduction is the flow of heat directly through

a physical material.

16-6 Conduction, Convection, and Radiation

Experimentally, it is found that the amount of heat Q that flows through a rod:

• increases proportionally to the cross- sectional area A

• increases proportionally to the temperature difference from one end to the other

• increases steadily with time

• decreases with the length of the rod

16-6 Conduction, Convection, and Radiation

Combining, we find:

The constant k is called the thermal

conductivity of the rod.

Conceptual checkpoint 16-3 The Feel of Tile

När vi vaknar på morgonen och kommer från

sovrummets matta till badrummets kakel, uppfattar

vi då kaklet som varmare, kallare eller ha samma

temperatur som mattan?

16-6 Conduction, Convection, and Radiation

Some typical thermal conductivities:

Substances with high thermal conductivities are good conductors of heat; those with low

thermal conductivities

are good insulators.

Example 16-6 What a Pane

Ett fönster (pane) har mått enligt figur. Hur mycket värme förloras genom rutan på en dag, om innertemperaturen är 21°C och

utetemperaturen är 0,0°C?

Example 16-6 What a Pane

Värmeflödet blir

Q _pane = k•A•ΔT•t/L =

= 0,84 W/(m•K)•(1 m) ² •21 K•24•3600 s/0,5•10 ^-2 m =

= 300 MWs = 300 MJ

Conceptual Checkpoint 16-4 Compare the Heat Flow

Sker värmeflödet i den vänstra uppställningen a) bättre b) sämre

c) med samma värmeflöde som i den högra?

Example 16-7

Parallel Rods

Example 16-7 Parallel Rods

Två stavar, 0,525 m långa, den ena av bly, den andra av koppar, är förbundna mellan två metallplattor som håll vid temperaturerna 2,00 och 106 °C respektive.

Stavarna är kvadratiska med kantlängden 1,50 cm.

Hur stort värmeflöde sker genom stavarna på 1,00 s?

Inget värmeutbyte sker med omgivningen.

Q _Pb = k•A•ΔT•t/L= 34,3 W/(m•K)•(0,015 m) ² •104 K • 1s/0,525 m = 1,53 J

Q _Cu = k•A•ΔT•t/L = 395 W/(m•K)•(0,015 m) ² •104 K•

1s/0,525 m = 17,6 J

Q = 1,53 J + 17,6 J = 19,1 J

16-6 Conduction, Convection, and Radiation

Convection is the flow of fluid due to a difference in temperatures, such as

warm air rising. The fluid

“carries” the heat with it as it moves.

konvektion =

värmetransport i ett

medium (gas eller vätska)

Figure 16-10

Countercurrent heat exchange in the human arm

16-6 Conduction, Convection, and Radiation

All objects give off energy in the form of

radiation, as electromagnetic waves – infrared, visible light, ultraviolet – which, unlike

conduction and convection, can transport heat through a vacuum (dvs inget medium behövs).

Objects that are hot enough will glow – first

red, then yellow, white, and blue. Objects at

body temperature radiate in the infrared, and

can be seen with night vision binoculars.

16-6 Conduction, Convection, and Radiation

The amount of energy radiated by an object due to its temperature is proportional to its surface area and also to the fourth (!) power of its

temperature.

It also depends on the emissivity, which is a

number between 0 and 1 that indicates how

effective a radiator the object is; a perfect

radiator would have an emissivity of 1.

16-6 Conduction, Convection, and Radiation

This behavior is contained in the Stefan- Boltzmann law:

Here, e is the emissivity, and σ is the Stefan-

Boltzmann constant:

Exercise 16-4

Beräkna den utstrålade effekten från en sfär med radien 5,00 cm och temperaturen 355 K. Anta att emissiviten = 1.

P = ε•σ•A•T ⁴ =

= 5,67•10 ^-8 W/(m ² •K ⁴ )•4π(0,05 m) ² •(355 K) ⁴ = 28,3 W

Example 16-8

Human Polar Bears

Example 16-8 Human Polar Bears

Beräkna den utstrålade effekten från en ”polar bear” som har arean 1,15 m ² och yttemperaturen 303 K när han

befinner sig i omklädningsrummet (där temperaturen är 293 K) och när han står ute (där temperaturen är 273 K).

Anta att emissiviten = 0,9 (observera att detta värde också anger måttet för absorptionen!)

P = ε•σ•A•(T ⁴ - T _in ⁴ ) = 0,9•5,67•10 ^-8 W/(m ² •K ⁴ )•1,15 m ² •(303 K) ⁴ - 0,9•5,67•10 ^-8 W/(m ² •K ⁴ )•1,15 m ² •(293 K) ⁴ =

= 494,6 W – 432,5 W = 62,1 W

P = ε•σ•A•(T ⁴ – T _ut ⁴ ) = 494,6 W - 0,9•5,67•10 ^-8 W/(m ² •K ⁴ )•1,15

m ² •(273 K) ⁴ = 494,6 W – 326,0 W ≈ 169 W

Figure 16-12 The Thermos bottle (p.538) (med en utmärkt reflektor,

ε ≈ 0 och därför en dålig “strålare”) invented by Sir James Dewar

(1842-1923) skotsk fysiker och kemist.

Summary of Chapter 16

• Heat is the energy transferred between objects due to a temperature difference.

• Objects are in thermal contact if heat can flow between them.

• Objects that are in thermal contact without any flow of heat are in thermal equilibrium.

• Thermodynamics is the study of physical processes that involve heat.

• If objects A and B are both in thermal

equilibrium with C, they are in thermal

equilibrium with each other.

Summary of Chapter 16

• Temperature determines whether two objects will be in thermal equilibrium.

• Celsius scale: water freezes at 0° C, boils at 100° C

• The lowest attainable temperature is absolute zero.

• Kelvin: absolute zero is 0 K; water freezes at

273.15 K and boils at 373.15 K

Summary of Chapter 16

• Temperature scale conversions:

• Most substances expand when heated.

• Linear expansion:

• Volume expansion:

• Water contracts when heated from 0° C to

4° C.

Summary of Chapter 16

• Heat is a form of energy:

• Heat capacity of an object:

• Specific heat is heat capacity per unit mass:

• Energy is conserved in heat flow.

Summary of Chapter 16

• Conduction: heat exchange from one part of a material to a cooler part, with no bulk motion of the material.

• Heat exchanged in time t:

• Convection is heat exchange due to the bulk motion of an unevenly heated fluid.

• Radiation is heat exchange due to

electromagnetic radiation.

Summary of Chapter 16

• Radiated power as a function of temperature:

• Stefan-Boltzmann constant: