ThermalPhysics

Temperature

and Heat

Phases of Matter

Four Phases of Matter:SolidLiquidGas

Plasma

Temperature is one thermodynamic variable that determines the phase.

Common Temperature Scales

Temperatures are reported in degreesCelsius or degrees Fahrenheit.

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

91 C F

5

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

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

FahrenheitAccording to a journal article Fahrenheit wrote in 1724, he based his scale on three reference points of temperature. The zero point is determined by placing the thermometer in brine: he used a mixture of ice, water, and ammonium chloride. The mixture automatically stabilizes its temperature at 0 °F. He then put a thermometer into the mixture and let the liquid in the thermometer descend to its lowest point. The second point is the 32 degree found by putting the thermometer in still water as ice is just forming on the surface. The third point, the 96 degree, was the level of the liquid in the thermometer when held in the mouth or under the armpit.

Later, work by other scientists observed that water boils about 180 degrees higher than the freezing point and decided to redefine the degree slightly to make it exactly 180 degrees higher. It is for this reason that normal body temperature is 98.6 on the revised scale (whereas it was 96 on Fahrenheit's original scale).

Daniel Fahrenheit1686 - 1736

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?

1. 154 M2. 168 M3. 140 M4. 136 M5. 149 M

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

KelvinTemperature Scale

15.273 cTT

William Thomson,1st Baron Kelvin (Lord Kelvin)

1824 - 1907

Temperatures have an extremely large range, both on Earth and throughout the Universe.

ThermometersThermometers make use of the change in some physical property with temperature. A property that changes with temperature is called a thermometric property. All thermometers require calibration.

Zeroth Law of Thermodynamics

If bodies A and B are each in thermal equilibrium with a third body C, then they are in thermal equilibrium with each other.

Translation: Every body has a property called temperature. When two bodies (one might be a thermometer) are found to be in thermal equilibrium, then their temperatures are the same. This may be used to determine the temperature of a third body (through calibration).

DEFINITION OF HEAT

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)

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.

OTHER UNITS

1 kcal = 4186 joules 1 cal = 4.186 joules1 BTU = 1055 J

Heat and Temperature Change: Specific Heat Capacity

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

TmcQ specific heatcapacity

Common Unit for SpecificHeat Capacity: J/(kg·Co)

1 kcal = 4186 J1 BTU = 1055 J

When you drink cold water, your body must expend metabolic energy to maintain normal body temperature of 37 oC by warming up the water in your stomach. Could drinking ice water substitute for exercise as a way to “burn calories?” Suppose you expend 430 kilocalories during a brisk one-hour walk. How many liters of ice water would you have to drink in order to use 430 kilocalories of metabolic energy? Note: the stomach can hold about one liter.

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 own temperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase?

TmcQ

C 5.3CkgJ3500kg 65

J100.8 5

mc

QT

Heat and Phase Change: Latent Heat

Saving Energy

1 2

69%

31%

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

A. turn up the burner to its fullest so the water vigorously boils, or

B. should you turn down the burner so the water barely boils?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Answer We need water at 100 oC for 10 minutes. Adding additional energy only produces

steam, which doesn’t help cook the spaghetti.

Keep the flame to just enough to boil and save energy and money.

A calorimeter consisting of a thin copper cup of mass 150 g containing 500 g of water is at a temperature of 20.0 oC. A 225-g sample of an unknown material at 508 oC is lowered into the bath, and the device is sealed. After a few minutes, the system reaches a constant temperature of 40.0 oC. Determine the specific heat of the unknown material. Ignore any losses due to the thermometer.

The heat transferred out of the sample (which is a negative number) equals the heat transferred into the water and the cup.

Cuu wQ Q Q

Cu Cu Cu

0.500 kg 4186 J 40 C 20 C 0.150 kg 390 J 40 C 20 C

0.225 kg 40 C 508 C

409 J/(kg C )

w w wu

u

m c T m c Tc

m T

Cu Cu Cuu u u w w wm c T m c T m c T

You find that you have let a 2.5 kg stainless steel barbeque grate become too hot for cooking. You Decide to cool the grate from 296 oC to 185 oC by spraying water onto the grate. The specific heat of steel = 445 J/kg - K. Calculate the mass of water at 20 oC you will need, assuming all the water evaporates to steam at 100 oC.

heat lost by plate = heat gained by water in raising its own temp + heat to transform water into steam

s s s w w w w vm c T m c T m L

Jkg C

5J Jkgkg C

2.5 kg 445 185 C 296 C

4186 100 C 20 C 22 6 10

0 048 kg or 48 g

.

.

s s s w w w w v w w w v

s s sw

w w v

m c T m c T m L m c T L

m c Tm

c T L

Heat = transfer of energy

From someplace hot to someplace cold Convection Conduction Radiation

ConvectionConvection is the process in which heat is carried from one placeto another by the bulk movement of a fluid.

Concepts in actionHot water baseboard heating units are mounted on the wall next to the floor. The cooling coil in a refrigerator is mounted near the top of the refrigerator. Each location is designed to maximize the production of convection currents.

Forced Convection

CONDUCTION

Conduction is the process whereby heat is transferred directly througha material, with any bulk motion of the material playing no role in the transfer.

One mechanism for conduction occurs when the atoms or moleculesin a hotter part of the material vibrate or move with greater energy thanthose in a cooler part. These vibrations have specific values and are called phonons.

By means of collisions, the more energetic molecules pass on some oftheir energy to their less energetic neighbors.

Another mechanism is free electrons within a metal conduct heat.

Materials that conduct heat well are called thermal conductors, and thosethat conduct heat poorly are called thermal insulators.

Conduction

The amount of heat Q that is conducted through the bar depends on a number of factors:

1. The time during which conduction takes place.2. The temperature difference between the ends of the bar.3. The cross sectional area of the bar.4. The length of the bar.

The heat Q conducted during a time t through a bar of lengthL and cross-sectional area A is kA T t

QL

SI Units of Thermal Conductivity: J/(s·m·Co)

Thermal Conductivity

What thickness of concrete, with a thermal conductivity of 1.1 J/(smK) will conduct heat at the same rate as 0.25 m of air, which has a thermal conductivity of 0.0256 J/(smK), if all other conditions are the same?

kA T t Q kA TQ

L t L

concrete air

concrete air

concrete air

concrete air

Jconcrete s m K

concrete air Jair s m K

1 1 0 25 m = 11 m

0 0256

..

.

k A T k A T

L L

k k

L L

kL L

k

InsulationMaterials with dead air spaces are usually excellent thermal insulators.

Example: Thermal ConductionOne wall of a house consists of plywood backed by insulation. The thermal conductivities ofthe insulation and plywood are, respectively, 0.030 and 0.080 J/(s·m·Co), and the area of the wall is 35 m2.

Find the amount of heat conducted through the wall in one hour.

Example: Thermal Conduction

insulation plywoodQ Q Q

But first we must solve for the interface temperature.

insulation plywood

kA T t kA T t

L L

m 019.0

C0.4CmsJ080.0

m 076.0

C0.25CmsJ030.0 tTAtTA

C8.5 T

Example: Thermal Conduction

2

insulation

5

0.030J s m C 35 m 25.0 C 5.8 C 3600 s

0.076 m

9.5 10 J

Q

Three building materials, plasterboard, brick, and wood, are sandwiched together as the drawing illustrates. The temperatures at the inside and outside surfaces are 27 °C and 0 °C, respectively. Each material has the same thickness and cross-sectional area. Find the temperature (a) at the plasterboard–brick interface and (b) at the brick–wood interface.

The rate of heat transfer is the same for all three materials so

Let Ti be the inside temperature, T1 be the temperature at the plasterboard-brick interface, T2 be the temperature at the brick-wood interface, and To be the outside temperature.

p

b

w

0 30 J/ s m C

0 60 J/ s m C

0 10 J/ s m C

.

.

.

k

k

k

1

0 30 J/ s m C 0 10 J/ s m C1 27 C

0 60 J/ s m C 0 60 J/ s m C

0 10 J/ s m C0 C

0 60 J/ s m C

0 10 J/ s m C 0 30 J/ s m C1 1

0 60 J/ s m C 0 60 J/ s m C

. .

. .

.

.

. .

. .

T

1

21 C

p

b

w

0 30 J/ s m C

0 60 J/ s m C

0 10 J/ s m C

.

.

.

k

k

k

2

0 30 J/ s m C 0 60 J/ s m C 21 C 0 30 J/ s m C 27 C

0 60 J/ s m C 0 60 J/ s m C

18 C

. . .

. .T

RadiationRadiation is the process in whichenergy is transferred by means ofelectromagnetic waves.

A material that is a good absorber is also a good emitter.

A material that absorbs completelyis called a perfect blackbody.

Black Robe Mystery

Scientists checked into the matter by having a man stand in the hot desert sun first in a white robe and then in a black one. They found that the black robe absorbed 2.5 times more solar radiation and was 11 oF (6 oC) hotter than the white one.

The skin temperature was the same in either robe, but the man felt cooler in the black one.

The extra warm air trapped by the black color experiences a buoyancy force equal

to the weight of the cool air it displaces. The warm air rises up and out of the robe

top. This, in turn, creates a breeze as cooler air is drawn in at the bottom. The

breeze evaporates sweat, cooling the robe wearer, and moves the sweat-laden air out

the robe top.

The loose-fitting burnoose is a solar air-conditioning system.

Why do Bedouins wear black robes?

Blackbody Radiation

The maximum of the intensity shifts to shorter wavelengths as the black-body temperature increases.

THE STEFAN-BOLTZMANN LAW OF RADIATION

The radiant energy Q, emitted in a time t by an object that has aKelvin temperature T, a surface area A, and an emissivity e, is given by

4Q e T At The emissivity e is a dimensionless number between zero and one. It is the ratio of what an object radiates to what the object would radiate ifit were a perfect emitter. 8 2 45 67 10 J s m K.

Stefan-Boltzmann constant

4Qe T A

tRate of Heat Transfer

A cube, 10 cm on a side, of rough steel is heated in a furnace to a temperature of 400.0 oC. If its total emissivity is 0.97, determine the rate at which it radiates energy from each face.

4

4 28 2 40 97 5 67 10 J (s m K ) 400 273 K 0 10 m113 J/s = 113 W. . .

Qe T A

t

Example: RadiationThe supergiant star Betelgeuse has a

surface temperature ofabout 2900 K and emits a power of

approximately 4 x1030 W.

Assuming that Betelgeuse is a perfect emitter and spherical,

find its radius.

4 2(4 )Q e T r t

4Q e T At24 r

30

44 8 2 4

11

4 10 W

4 4 1 5.67 10 J s m K 2900 K

3 10 m

Q tr

e T

A thermos bottle minimizes heattransfer via conduction, convection, and radiation.

Application: Thermos Bottle