Thermal Energy & Temperature

Thermal energy: the total potential and kinetic energy associated with the random motion and arrangement of the particles of a material.

When a material is hot, it has more thermal energy than when it is cold.

Temperature is the hotness or coldness of a material.

The quantity of thermal energy in a body affects its temperature.

The same quantity of thermal energy in different bodies does not give each the same temperature.

The ratio between temperature and thermal energy is different for different materials.

Temperature & Kinetic Energy

The temperature of a substance will increase if the average kinetic energy of its particles is increased.

If the average kinetic energy of particles decreases, so does the temperature of the substance.

Heat

Heat is thermal energy that is absorbed, given up, or transferred from one body to another.

Temperature is a measure of a body’s ability to give up heat to or absorb heat from another body.

The temperature of a body determines whether or not heat will be transferred to or from any nearby body.

Heat is a form of energy. Heat is thermal energy in motion. Heat is used when the transfer of thermal energy from

one body to another body at a different temperature is involved.

Temperature

Temperature is a physical quantity that is proportional to the average kinetic energy of translation of particles in matter.

To measure the temperature of a body, you place the thermometer in contact with the body.

If you want to know the temperature of a cup of hot coffee, you stick the thermometer in the coffee; as the two interact, the thermometer becomes hotter and the coffee cools off a little.

After the thermometer settles down to a steady value, you read the temperature. The system has reached a thermal equilibrium condition, in which the interaction between the thermometer and the coffee causes no further change in the system.

Temperature

Central concept of thermodynamics is temperature. Our “temperature sense” is often unreliable.

The same quantity of thermal energy in different bodies does not give each the same temperature.

On a cold winter day, an iron railing seems much colder to the touch than a wooden fence post, even though both are at the same temperature. This error in perception results because the iron removes energy from our fingers more quickly than the wood does.

Triple Point Temperature

Triple-point temperature: the single condition of temperature and pressure at which the solid, liquid, and vapor phases of a substance can coexist in stable equilibrium. Solid, liquid, and vapor phases in contact and

in equilibrium. Triple-point temperature of water is the SI

standard for defining temperature (0°C = 273.16 K).

Temperature Intervals

Originally, two fixed points were used to define the standard temperature interval. Steam point (100 C): the boiling point

of water at standard atmospheric pressure (1 atm or 760 mmHg).

Ice point (0 C): melting point of ice when in equilibrium with water saturated air at standard atmospheric pressure.

Kelvin, Celsius, & Fahrenheit Temperature Scales

Celsius to Kelvin: K = C + 273

Kelvin to Celsius: C = K – 273

Celsius to Fahrenheit: TF = (1.8·TC) + 32

Fahrenheit to Celsius: o

FC

5 (T 32 )T

9

Absolute zero of temperature (0 K):

The molecules of a substance at absolute zero have a minimum amount of kinetic energy, known as zero-point energy.

Molecular energy is at a minimum, but not zero.

Heat Units

Quantities of heat must be measured by the effects they produce. No instrument directly measures the

amount of thermal energy a body releases or absorbs.

Calorie (cal): quantity of heat required to raise the temperature of one gram of water one degree Celsius.

1 calorie = 4.186 Joules1 food calorie is 1000 kcal = 4186 J

Thermal Expansion of Solids

Solids expand when heated and contract when cooled (with a few exceptions). Heated solids increase or decrease in all

dimensions (length, width, and thickness). When a solid is heated, the increase in

thermal energy increases the average distance between the atoms and molecules of the solid and it expands.

Thermal Expansion of Solids

Thermal expansion can be explained on a molecular basis.

Picture the inter-atomic forces in a solid as springs, as shown in the picture on the right.

Each atom vibrates about its equilibrium position. When the temperature increases, the amplitude and associated energy of the vibration also increase.

Thermal Expansion of Solids

Thermal Expansion of Solids

When the amplitude of vibration increases, the average distance between molecules also increases. As the atoms get farther apart, every dimension increases, including the sizes of holes.

Thermal Expansion of Solids

Coefficient of Linear Expansion - Solid

Coefficient of Linear Expansion (): the change in length per unit of a solid when its temperature is changed one degree.

l = lf - li ; l = change in lengthl = original length; = coefficient of linear expansion

Tf = final temperature; Ti = initial temperature

new length = old length + l

Problem solving note: diameter is a length

if TTlΔTlΔl

Diameter = Diameter

For problems that involve the contraction or expansion of two metals with different coefficients of expansion , set:

22111 lΔTllΔTl

Coefficient of Area Expansion - Solid

Coefficient of Area Expansion: the change in area per unit area per degree change in temperature. The coefficient of area expansion for a solid is twice the coefficient of linear expansion.

new area = old area + A

if TTA2ΔTA2ΔA

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

Holes expand as well:

if TTA2ΔTA2ΔA

Coefficient of Volume Expansion - Solid

Coefficient of Volume Expansion: the change in volume per unit volume per degree change in temperature. The coefficient of volume expansion for a solid is three times the coefficient of linear expansion.

new volume = old volume + VCoefficient of volume expansion for a solid = 3·α

if TTV3ΔTV3ΔV

Thermal Expansion of Solid

If there is a hole in a solid body, the volume of the hole increases when the body expands, just as if the hole were a solid of the same material as the body. This remains true even if the hole becomes so large that the surrounding body is reduced to a thin shell. Thus the volume enclosed by a thin-walled flask or thermometer bulb increases just as would a solid body of glass of the same size.

Linear Expansion

Expansion and contraction of solids is considered in the design and construction of any structure that will undergo temperature changes.

Allowances must also be made not only for changes in size due to expansion and contraction, but also for the different rates of expansion and contraction of different materials.

Examples of Uses of Thermal Expansion

You can loosen a tight metal jar lid by holding it under a stream of hot water. Both the metal of the lid and the glass of the jar expand as the hot water adds energy to their atoms. With the added energy, the atoms can move a bit farther from each other than usual, against the inter-atomic forces that hold every solid together. However, because the atoms in the metal move farther apart than those in the glass, the lid expands more than the jar and is loosened.

Expansions slots are often placed in bridges to accommodate roadway expansion on hot days. This prevents buckling of the roadway. Driveways and sidewalks have expansion slots for the same reason.

Thermal Expansion of Liquids

Since liquids do not have a definite shape, but take the shape of their container, we are concerned only with their volume expansion.

Liquids have greater coefficients of volume expansion than solids.

V = change in volume; = coefficient of volume expansion; T = change in temperature

Tf = final temperature; Ti = initial temperature

new volume = old volume + V

if TTVΔTVΔV

Expansion of Liquid in a Solid Container

To determine the new volume of a liquid that is contained within a solid container, such as a flask, when both are heated:

V and T are the same for the flask and the liquid.

TΔVβTΔV3VV

VΔVΔVV

flaskoldnew

liquidflaskoldnew

Abnormal Expansion of Water

Increase the temperature of any common liquid and it will expand. Water at the temperature of melting ice, 0 C contracts when the temperature is increased.

As the water is heated and its temperature rises, it continues to contract until it reaches a temperature of 4C.

With further increase in temperature, the water then begins to expand and the expansion continues all the way to the boiling point, 100 C.

Abnormal Expansion of Water

Water has its maximum mass density, 1000 g/cm3, at 4 C. The same amount of water has its largest volume, and smallest density, in its solid form, ice. Which is why ice floats in water; ice is less dense than water.

Ice has a crystalline structure. The crystals of most solids are arranged in such a way that the solid state occupies a smaller volume than the liquid state.

Water molecules in this open structure occupy a greater volume than they do in the liquid state, consequently, ice is less dense than water.

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.

Abnormal Expansion of Water

Between 0 C and 4 C, the coefficient of expansion of water is negative.

When ice melts to water at 0 C, the water still contains groups of molecules bonded in the open crystal structure of ice.

As the temperature increases the open crystal fragments begin to collapse and the molecules move closer together.

The effect of the collapsing crystal structure predominates over the increase in the molecular speed of the molecules and the density increases.

Above 4 C, the effect of increasing molecular speed exceeds the effect of collapsing crystal structures and volume increases.

Examples of Uses of Thermal Expansion

Examples of Uses of Thermal Expansion

Dental materials used for fillings must be matched in their thermal expansion properties to those of tooth enamel, otherwise consuming hot drinks or cold ice cream would be painful.

In aircraft manufacturing, rivets and other fasteners are often cooled using dry ice before insertion and then allowed to expand to a tight fit.

Anti-scalding device (shown in figure):

Linear Expansion Example

The supersonic airliner Concorde is 62.1 m long when sitting on the ground on a 20° C day. It is made primarily of aluminum. In flight at twice the speed of sound, friction with the air warms the Concorde’s skin and causes the aircraft to lengthen by 25 cm. The passenger cabin is on wheels and the airplane expands around the passengers. What is the temperature of Concorde’s skin in flight?

What we know: l = 62.1 m Ti = 20° C l = 25 cm = 0.25 m Al = 23.8 x 10-6/° C

Linear Expansion Example

C77.1457T

C20C77.1437T

C20TC77.1437

C20TC/m10x7388.1

m25.0

C20TC/m10x7388.1m25.0

C20Tm1.62C/10x8.23m25.0

TTll

of

of

fo

fo4

fo4

fo6

if

o

o

o

o

o

Volume Expansion Example

A farmer milks a cow into a 20 L steel milk pail. The milk comes out of the cow at 37° C. If the pail is initially full and also at 37° C, how much empty space will there be when the milk and the pail cool to 3° C? milk = 2 x 10-4/ ° C; steel = 1.2 x 10-5/ ° C

Volume change for steel pail: V = 3··V·T

L02448.0V

C37C3L20C/10x2.13V ooo5

Volume Expansion Example

Volume change for milk: V = ·V·T

The change in volume between the milk and the pail represents the amount of empty space in the pail at the 3° C:

V = 0.136 L – 0.02448 L = 0.11152 L

L136.0V

C37C3L20C/10x2V ooo4

Diameter = DiameterFinal Temperature Example

A steel tube has an outside diameter of 3 cm at room temperature (20° C). A brass tube has an inside diameter of 2.997 cm at 20° C. To what temperature must the ends of the tubes be heated if the steel tube is to be inserted into the brass tube? steel = 1.1 x 10-5/° C; brass = 1.9 x 10-5/° C

5 5

5 5

5 5

3 1.1 10 / 3 2.997 1.9 10 / 2.997

3 3.3 10 / 2.997 5.6943 10 /

3 2.997 5.6943 10 / 3.3 10 /

0.003 2.3943

steel brasssteel brass

o o

o o

o o

l l T l l T

cm x C cm T cm x C cm T

cm x cm C T cm x cm C T

cm cm x cm C T x cm C T

cm

5

5

10 /

0.003125.3

2.3943 10 /

125.3 20 145.3

o

of io

o o oi

x cm C T

cmT C T T T

x cm C

Tf T T C C C

A Word About Temperature Conversions

The Celsius degree and the Kelvin degree are equal; 1 ºC = 1 K, therefore, for temperature changes expressed as an increase or decrease in ºC or K, the units are interchangeable. Ex. … for a temperature increase of 20 ºC …; T

= 20 ºC = 20 K The Celsius and the Fahrenheit degree are NOT

equal; 1 ºC = 1.8 ºF, therefore, for temperature changes expressed as an increase or decrease in ºC or ºF, you must convert between units.

A Word About Temperature Conversions

Ex. … for a temperature increase of 20 ºF …;

Ex. … for a temperature increase of 20 ºC …;

oo

o

1 CT =20 ºF 11.11 C

1.8 F

oo

o

1.8 FT =20 ºC 36 F

1 C