Chapter 12

Temperature and Heat

Learning ObjectivesTemperature and heat Mechanical equivalent of heat

Students should understand the “mechanical equivalent of heat” so they can determine how much heat can be produced by the performance of a specified quantity of mechanical work.

Heat transfer and thermal expansionStudents should understand heat transfer and thermal expansion, so they can:

Calculate how the flow of heat through a slab of material is affected by changes in the thickness or area of the slab, or the temperature difference between the two faces of the slab.

Analyze what happens to the size and shape of an object when it is heated.

Analyze qualitatively the effects of conduction, radiation, and convection in thermal processes.

Table of Contents

1. Common Temperature Scales

2. The Kelvin Temperature Scale

3. Thermometers

4. Linear Thermal Expansion

5. Volume Thermal Expansion

6. Heat & Internal Energy

7. Heat & Temperature Change: Specific Heat Capacity

8. Heat and Phase Change: Latent Heat

9. Equilibrium between Phases of Matter (AP?)

10. Humidity (AP?)

Chapter 12:Temperature and Heat

Section 1:

Common Temperature Scales

Temperature A measure of the physical quantity of the thermal

energy held by an object A measure of the average internal kinetic energy of

the particles As the particles move faster, they have stronger

collisions. That energy exchanges rapidly Think of a bunch of kids in a “bounce house”

Temperature Scales First “Modern” Thermometer is thought to have been

created in 1654 Simply an unmarked tube of liquid that rose and fell

with different temperatures Late 1600’s Newton first put a scale on it

0 was the freezing point of water 12 was the human body temperature

The English were fascinated with 12 when it comes to measurement

12 inches=1 ft, 12 oz = 1 lb*, 12 pence = shilling, 12 units = 1 dozen, 12 dozen = 1 gross

Fahrenheit Scale Why 32o and 212o?

1701 Ole Rømer used a brine solution for freezing point (0)

Wanted 0o to be the coldest temperature at which water

could be a liquid

set boiling point of water as 60 on his scale

Daniel Fahrenheit modified Rømer’s scale in 1724

Used Mercury as liquid in device which increased range of

measurements

Used the temperature of the human body as 100 on scale

Adjusted the scale so the melting point and boiling point of

water were whole numbers, and difference was 180.

Celsius Scale First proposed by the Swedish Astronomer Anders Celsius in

1742 He set it up as 100o as the freezing point and 0o as boiling

point of distilled water at normal atmospheric pressure Swedish Botanist Carolus Linnaeus is among many scientist who

switched the direction of the scale around 1744 From 1744 until 1948, called the Centigrade scale Name changed to Celsius due to conflicts in translations with

measures of angles. (1 centigrade = 1/10,000 of a right angle) 1954 reformatted to directly match Kelvin Scale

Scale based on absolute zero and triple point of pure water Correctly written as degrees Celsius (capitalization is correct!) Zero is freezing, 10 is not. 20 is pleasant, 30 is hot.

Temperatures are reported in degreesCelsius or degrees Fahrenheit.

Temperatures changed, on theother hand, are reported in Celsius degrees or Fahrenheit degrees:

F 5

9C 1

Note: I haven’t seen this convention anywhereother than this textbook.I don’t think AP recognizes it!

“English” vs. SI Most scientist agree the SI system (yes that’s redundant) is a

superior system of measure Especially when is comes to conversions due to size

How many inches are in 2.67 miles? Some still argue about the Temperature scales.

Blame the French on this one Fahrenheit had ties to England, Celsius to France Lord Kelvin sealed the debate by “using” Celsius scale as

basis for his absolute scale But is it better? Habitable Earth fluctuates from 0 to 100 oF wouldn’t that fit

the SI’s power of 10 thing?

Example 1 Converting from a Fahrenheit to a Celsius Temperature

A healthy person has an oral temperature of 98.6oF. What would thisreading be on the Celsius scale?

F 6.66F32F98.6

degrees above ice point

C 0.37

F

C 1F 6.66

59

C0.37C 0.37C 0

ice point

Example 2 Converting from a Celsius to a Fahrenheit Temperature

A time and temperature sign on a bank indicates that the outdoor temperature is -20.0oC. Find the corresponding temperature onthe Fahrenheit scale.

F 0.36

C 1

F C 0.20 5

9

degrees below ice point

F0.4F 0.36F 0.32

ice point

12.1.1. Three thermometers are used to measure the temperature inside a closed, insulated box. Thermometer A is calibrated in degrees Fahrenheit, thermometer B in degrees Celsius, and thermometer C in kelvin. When the thermometers reach thermal equilibrium with the interior of the box, B reads 40 C and C reads 233 K. Which one of the following statements is necessarily true?

a) Thermometer C should read 233 K.

b) Thermometer A must read –40 °F.

c) If the temperature of the interior of the box is increased until A reads 20 F, thermometer B will read 10 C.

d) Thermometer B should read 77 C.

e) If the temperature of the interior of the box is increased until C reads 293 K, thermometer A will read 36 F.

12.1.2. Unsatisfied with the Celsius and Fahrenheit temperature scales, you decide to create your own. On your temperature scale, the ice point is 77 M and the steam point is at 437 M, where “M” stands for “my scale.” What temperature on your scale corresponds to 68 F?

a) 154 M

b) 168 M

c) 140 M

d) 136 M

e) 149 M

Chapter 12:Temperature and Heat

Section 2:

The Kelvin Scale

An Absolute Scale Proposed by William Thomson, 1st Baron Kelvin in

1848 Does not use a “o” as it is an absolute scale

Double the number, double the energy The zero point is absolute zero

Temperature of zero internal energy Second point is now defined as triple point of water Celsius scale was slightly modified so that a change

of 1 oC is a change of 1 K. Similar scale developed by William Rankine in 1859

that was based on the Fahrenheit scale.

The Kelvin Temperature Scale

15.273 cTT

Kelvin temperature

A constant-volume gasthermometer.

absolute zero point = -273.15oC

12.2.1. Unsatisfied with the Celsius and Kelvin temperature scales, you decide to create your own. On your temperature scale, the ice point is 0.0 M and the steam point is at 366.1 M, where “M” stands for “my scale.” What temperature on your scale corresponds to 0 K?

a) 273.1 M

b) 500.0 M

c) 1000.0 M

d) 732.4 M

e) 633.9 M

Chapter 12:Temperature and Heat

Section 3:

Thermometers

Thermometers make use of the change in some physical property with temperature.A property that changes with temperature is called a thermometric property.

Thermometers

Thermometers Early thermometers used water, mercury and alcohol due to their

thermal expansion “Modern” devices often use other substances/properties

Bimetallic Coil thermometers (old A/C thermostats) Coiled metal expands and rotates a dial

Infrared Thermometers Measure the colors of light being produced

Thermocouples Joined metals produce an electric potential

Thermisters Electric Resistance depends on temperature

12.3.1. Which one of the following properties is not likely to be used as a temperature-sensitive property to construct a thermometer?

a) The volume of a liquid increases with increasing temperature.

b) A gas held within a constant volume container exhibits pressure changes with corresponding temperature changes.

c) The length of a metal rod changes linearly with temperature.

d) The mass of a solid decreases with increasing temperature.

e) The electrical resistance of a wire increases with increasing temperature.

Chapter 12:Temperature and Heat

Section 4:

Linear Thermal Expansion

Linear Thermal Expansion

Most objects expand as they rise in temperature

The particles are moving faster

The collisions have more energy

Net force of collisions is outward

Objects therefore tend to expand

oLL

Linear Thermal Expansion

TL

L

o

TkL

L

o

The length of an object changes when its temperature changes:

TLL o

coefficient of linear expansion

Common Unit for the Coefficient of Linear Expansion: 1C

C

1

LINEAR THERMAL EXPANSION OF A SOLID

Example 3 The Buckling of a Sidewalk

A concrete sidewalk is constructed betweentwo buildings on a day when the temperature is 25 oC. As the temperature rises to 38 oC, the slabs expand, but no space is provided forthermal expansion. Determine the distance yin part (b) of the drawing.

TLL o

22 m 00000.3m 00047.3 y

C 13m 0.3C101216 L m 00047.0

LLLL o

mmL 47000.000000.3 m 47000.3

m 053.0

The Bimetallic Strip

The Bimetallic Strip

Conceptual Example 5 The Expansion of Holes

The figure shows eight square tiles that are arranged to form a square patternwith a hold in the center. If the tiled are heated, what happens to the size of the hole?

The Expansion of Holes

A hole in a piece of solid material expands when heated and contracts whencooled, just as if it were filled with the material that surrounds it.

The Expansion of Holes

Conceptual Example 7 Expanding Cylinders

Each cylinder is made from a different material. All three have the same temperature and theybarely fit inside each other.As the cylinders are heated to the same,but higher, temperature, cylinder C fallsoff, while cylinder A becomes tightly wedgedto cylinder B.Which cylinder is made from which material?

16

16

16

1029

1012

1019

C

C

C

oLead

oSteel

oBrass

12.4.1. An artist wishes to insert a gold pin into a hole in an iron sculpture and have it held permanently. The pin is slightly larger than the hole. The coefficient of linear thermal expansion of gold is slightly larger than that of iron. Consider the following options: (1) increase the temperature of the pin and the sculpture by the same amount, (2) decrease the temperature of the pin and the sculpture by the same amount, (3) increase the temperature of the pin and decrease the temperature of the sculpture, and (4) decrease the temperature of the pin and increase the temperature of the sculpture. Which of the choices would most likely accomplish the artist’s task?

a) 1

b) 2

c) 3

d) 4

e) 2 and 4

12.4.2. The length of an aluminum pendulum in a certain clock is 0.2480 m on a day when the temperature is 23.30 C. This length was chosen so that the period of the pendulum is exactly 1.000 s. The clock is then hung on a wall where the temperature is 5.00 C and set to the correct local time. Assuming the acceleration due to gravity is the same at both locations, by how much time is the clock incorrect after one day at this temperature?

a) 69.3 s

b) 115 s

c) 87.2 s

d) 31.0 s

e) 11.5 s

12.4.3. A rod of length L is heated so that its temperature increases by T. As a result, the length of the rod increases by L. The rod is then cut into two pieces, one of length L/3 and one of length 2L/3. What is the ratio of the change in length of the rod of length 2L/3 to L of the original rod when its temperature is increased by T?

a) 1/3

b) 2/3

c) 1

d) 3/2

e) 3

12.4.4. A square piece of metal has a hole drilled through its center. If the metal piece is uniformly heated, what is the effect on the hole?

a) The diameter of the hole will decrease, but remain open, as the temperature increases.

b) The diameter of the hole will increase as the temperature increases.

c) The diameter of the hole will not change, but the area of the square will increase as the temperature increases.

d) The diameter of the hole may either increase or decrease depending on the type of metal.

Chapter 12:Temperature and Heat

Section 5:

Volume Thermal Expansion

If the length expands, and Volume is L3,Then the volume must also expand

TVV o

coefficient of volume expansion

Common Unit for the Coefficient of Volume Expansion: 1C

C

1

Volume Thermal Expansion

Example 8 An Automobile Radiator

A small plastic container, called the coolant reservoir, catchesthe radiator fluid that overflows when an automobile enginebecomes hot. The radiator is made of copper and the coolant has an expansion coefficient of 4.0x10-4 (Co)-1. If the radiator is filled to its 15-quart capacitywhen the engine is cold (6oC),how much overflow will spill into the reservoir when the coolant reaches its operating temperature (92oC)?

quarts 53.0C 86quarts 15C1010.414

coolant V

quarts 066.0C 86quarts 15C105116

radiator V

quarts 0.46quarts 066.0quarts 53.0spill V

TVV o

Thermal Volume Expansion of Water

12.5.1. Which one of the following statements is the best explanation for the fact that metal pipes that carry water often burst during cold winter months?

a) Both the metal and the water expand, but the water expands to a greater extent.

b) Water contracts upon freezing while the metal expands at lower temperatures.

c) The metal contracts to a greater extent than the water.

d) The interior of the pipe contracts less than the outside of the pipe.

e) Water expands upon freezing while the metal contracts at lower temperatures.

12.5.2. Consider the four blocks made from the same material that are shown in the drawing. The sides have lengths of L, 2L, or 3L. Rank these blocks according to their expected increase, largest to smallest, in their volumes when their temperatures are increased by the same amount.

a) B > C > A > D

b) C > B > A > D

c) D > C > A > B

d) C > D > B > A

e) All would have the same increase in volume.

Chapter 12:Temperature and Heat

Section 6:

Heat & Internal Energy

Heat is energy that flows from a higher-temperature object to a lower-temperature object because of a difference in temperatures.

SI Unit of Heat: joule (J)

Definition of Heat

Think diffusion – If a bunch of particlesare randomly moving, their concentrationwill tend to spread out until it is even.

The heat that flows from hot to cold originates in the internal energy ofthe hot substance.

It is not correct to say that a substancecontains heat. It contains internal energy.

Chapter 12:Temperature and Heat

Section 7:

Heat & Temperature Change: Specific Heat Capacity

Since Solids and Liquids tend to incompressible with a fixed volume,the ambient pressure is usually insignificant.

The heat that must be supplied or removed to change the temperature ofa substance is

TmCQ

specific heatcapacity

Common Unit for Specific Heat Capacity: J/(kg·oC)

Heat Changes in Solids and Liquids

Common Units for Heat 1 Cal = 1 kcal = 4186 joules

Example 9 A Hot Jogger

In a half-hour, a 65-kg jogger can generate 8.0x105J of heat. This heatis removed from the body by a variety of means, including the body’s owntemperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase?

TmCQ

mC

QT CkgJ3500kg 65

J100.8 5

C 5.3

Heat Changes in Gases

The value of the specific heat of a gas depends on

whether the pressure or volume is held constant.

This distinction is not important for solids.

This will be discussed in greater detail later in the

unit

If there is no heat loss to the surroundings,the heat lost by the hotter object equals theheat gained by the cooler ones.

Calorimetry

Example 12 Measuring the Specific Heat Capacity

The calorimeter is made of 0.15 kg of aluminumand contains 0.20 kg of water. Initially, thewater and cup have the same temperatureof 18.0oC. A 0.040 kg mass of unknown material is heated to a temperature of 97.0oC and then added to the water.

After thermal equilibrium is reached, thetemperature of the water, the cup, and the material is 22.0oC. Ignoring the small amountof heat gained by the thermometer, find the specific heat capacity of theunknown material.

unknownwaterAl TmCTmCTmC

CkgJ1300unknown C

unknown

waterAlunknown Tm

TmcTmcC

C 0.75kg 040.0

C 0.4kg 20.0CkgJ4186C 0.4kg 15.0CkgJ1000.9 2

unknown

C

12.7.1. A certain amount of heat Q is added to materials A, B, and C. The masses of these three materials are 0.04 kg, 0.01 kg, and 0.02 kg, respectively. The temperature of material A increases by 4.0 C while the temperature of the other two materials increases by only 3.0 C. Rank these three materials from the largest specific heat capacity to the smallest value.

a) A > B > C

b) C > B > A

c) B > A > C

d) B = C > A

e) A > B = C

12.7.2. A swimming pool has a width of 9.0 m and a length of 12.0 m. The depth of the water is 1.83 m. One morning, the temperature of the pool water was 15.0 C. The water then absorbed 2.00 109 J of heat from the Sun. What is the final temperature of the water? Assume no heat loss to the surroundings.

a) 16.9 C

b) 18.1 C

c) 17.4 C

d) 19.6 C

e) 20.2 C

12.7.3. Which of the following substances would be the most effective in cooling 0.300 kg of water at 98 C?

a) 0.100 kg of lead at 22 C

b) 0.100 kg of water at 22 C

c) 0.100 kg of glass at 22 C

d) 0.100 kg of aluminum at 22 C

e) 0.100 kg of copper at 22 C

12.7.4. Elena’s normal body temperature is 36.5 C. When she recently became ill, her body temperature increased to 38.0 C. What was the minimum amount of heat required for this increase in body temperature if her weight is 561 N?

a) 2.96 106 J

b) 3.50 103 J

c) 4.98 104 J

d) 3.00 105 J

e) 7.60 105 J

12.7.5. Four 1-kg cylinders are heated to 100 C and placed on top of a block of paraffin wax, which melts at 63 C. There is one cylinder made from lead, one of copper, one of aluminum, and one of iron. After a few minutes, it is observed that the cylinders have sunk into the paraffin to differing depths. Rank the depths of the cylinders from deepest to shallowest.

a) lead > iron > copper > aluminum

b) aluminum > copper > lead > iron

c) aluminum > iron > copper > lead

d) copper > aluminum > iron > lead

e) iron > copper > lead > aluminum

12.7.6. Why is water often used as a coolant in automobiles, other than the fact that it is abundant?

a) Water expands very little as it is heated.

b) The freezing temperature of water has a relatively large value.

c) The specific heat of water is relatively small and its temperature can be rapidly decreased.

d) The specific heat of water is relatively large and it can store a great deal of thermal energy.

e) Water does not easily change into a gas.

Chapter 12:Temperature and Heat

Section 8:

Heat & Phase Change: Latent Heat

The 3 Basic Phases of Matter

During a phase change, the temperature of the mixture does not change (provided the system is in thermal equilibrium).

Heating Curve

Conceptual Example 13 Saving Energy

Suppose you are cooking spaghetti for dinner, and the instructionssay “boil pasta in water for 10 minutes.” To cook spaghetti in an openpot with the least amount of energy, should you turn up the burnerto its fullest so the water vigorously boils, or should you turn downthe burner so the water barely boils?

The heat that must be supplied or removed to change the phaseof a mass, m, of a substance is

mLQ

latent heat

SI Units of Latent Heat: J/kg

HEAT SUPPLIED OR REMOVED IN CHANGING THE PHASE OF A SUBSTANCE

Example 14 Ice-cold Lemonade

Ice at 0oC is placed in a Styrofoam cup containing 0.32 kg of lemonadeat 27oC. The specific heat capacity of lemonade is virtually the same asthat of water. After the ice and lemonade reach and equilibriumtemperature, some ice still remains. Assume that mass of the cup isso small that it absorbs a negligible amount of heat.

lemonade

bylost Heat

lemonade

iceby gainedHeat

iceTCmmL f

kgJ103.35

C0C27kg 32.0CkgJ41865

icem

f

lemonadeice L

TCmm

kg 11.0

12.8.1. Heat is added to a substance, but its temperature does not increase. Which one of the following statements provides the best explanation for this observation?

a) The substance has unusual thermal properties.

b) The substance must be cooler than its environment.

c) The substance must be a gas.

d) The substance must be an imperfect solid.

e) The substance undergoes a change of phase.

12.8.2. What is the final temperature when 2.50 105 J are added to 0.950 kg of ice at 0.0 C?

a) 0.0 C

b) 4.2 C

c) 15.7 C

d) 36.3 C

e) 62.8 C

12.8.3. By adding 25 kJ to solid material A, 4.0 kg will melt. By adding 50 kJ to solid material B, 6.0 kg will melt. Solid material C requires 30 kJ to melt 3.0 kg. Which of these materials, if any, has the largest value for the heat of fusion?

a) A

b) B

c) C

d) A = B

12.8.4. Consider the system shown in the drawing. A test tube containing water is inserted into boiling water. Will the water in the test tube eventually boil?

a) Yes, heat is continually transferred to the water inside the test tube and eventually it will boil?

b) Yes, the pressure above the water in the test tube will be reduced to less than atmospheric pressure and cause the water to boil.

c) No, heat will only be transferred until the water in the test tube is 100 C.

d) No, the temperature of the water in the test tube will never reach 100 C.

Chapter 12:Temperature and Heat

Section 9:

Equilibrium Between Phases of Matter

The pressure of vapor that coexists in equilibrium with the liquid iscalled the equilibrium vapor pressure of the liquid.

Equilibrium Between Phases

Only when the temperature and vapor pressure correspond to a pointon the curved line do the liquid and vapor phases coexist in equilibrium.

Conceptual Example 16 How to Boil Water That isCooling Down

Shortly after the flask is removed from the burner,the boiling stops. A cork is then placed in the neck of the flask to seal it. To restart the boiling, shouldyou pour hot or cold water over the neck of theflask?

As is the case for liquid/vapor equilibrium, a solid can be inequilibrium with its liquid phaseonly at specific conditions oftemperature and pressure.

All 3 Phases can be combined

Critical PointTC

Most SubstancesWater

Chapter 12:Temperature and Heat

Section 10:

Humidity

Air is a mixture of gases.

The total pressure is the sum of the partial pressures of the componentgases.

The partial pressure of water vapor depends on weather conditions. It can be as low as zero or as high as the vapor pressure of water at thegiven temperature.

100

re temperatuexistingat water of pressure vapor mEquilibriu

or water vapof pressure Partialhumidity relativePercent

To provide an indication of how much water vapor is in the air, weatherforecasters usually give the relative humidity:

Example 17 Relative Humidities

One day, the partial pressure of water vapor is 2.0x103 Pa. Using thevaporization curve, determine the relative humidity if the temperatureis 32oC.

100

re temperatuexistingat water of pressure vapor mEquilibriu

or water vapof pressure Partialhumidity relativePercent

%42100Pa 108.4

Pa 100.2humidity Relative

3

3

The temperature at which the relative humidity is 100% is called the dewpoint.