Chapter 5Temperature and Heat

Another Kind of Energy

What is temperature?

Temperature is what we measure with a thermometer.

What is a thermometer?

A thermometer is any devise that has an observable and measurable property that changes in response to a change in the temperature of the device… Thermometric Property

How does a thermometer measure temperature?

The operation of a thermometer is based on the Zeroth Law of Thermodynamics

A thermometer can only measure its own temperature.

Zeroth Law of Thermodynamics

“If two objects initially at different temperatures are placed in thermal contact, their temperatures will change until they

are at the same equilibrium temperature”This condition is called thermal equilibrium.”

TH > TC

TH > Teq> TC

thermal equilibrium reached

TH TC

TH TC↑↓

TeqTeq

To measure the temperature of an object a thermometer is placed in thermal contact with the object. Once the thermometer and object have reached thermal equilibrium it can be assumed that the temperature of the thermometer is equal to the temperature of the object.

How do we measure the temperature of the thermometer?

It must be calibrated with systems whose temperatures are known or defined.

Two systems that are commonly used are:

1. A mixture of ice and water.

2. Boiling water

These systems are used because it has been observed that as long as ice and water are present together the temperature remains constant, and as long as water is boiling its temperature remains constant.

The temperature of a mixture of ice and water is defined to be:0 degrees Celsius, 0°C or 32 degrees Fahrenheit, 32°F.

The temperature of boiling water is defined to be:100 degrees Celsius, 100°C or 212 degrees Fahrenheit, 212°F.

Consider the calibration of a liquid-in-glass thermometer.

Liquid-in-Glass Thermometer

glass housing

capillary

liquid reservoir

The thermometric property is the height of the liquid in the capillary

As the temperature of the thermometer changes, the liquid in the reservoir expands or contracts causing the level of the liquid in the capillary to rise or fall.

Once the temperature of the thermometer becomes constant the level of the liquid will be constant.

What temperature corresponds to this level of liquid?

T =?

Calibration of a Liquid-in-Glass Thermometer

Insert the thermometer into a container holding a mixture of ice and water and wait for thermal equilibrium to be reached.

Height of liquid has

fallen.

0°C32°F

Place a “mark” on the thermometer where the liquid stopped moving and label with the defined temperature of ice/water (0°C or 32°F)

ThermalEquilibrium

reached

Insert the thermometer into a container holding boiling water and wait for thermal equilibrium to be reached.

Height of liquid has risen.

Source of heatTo keep water

boiling

0°C32°F

Place a “mark” on the thermometer where the liquid stopped moving and label with the defined temperature of boiling water (100°C or 212°F)

100°C212°F

ThermalEquilibrium

reached

0°C32°F

100°C212°F

Determine how the height of the liquid relates to the temperature.

Temperature, °C

Height, cm

The slope of the graph = ΔhΔT =constant

The space between the two marks can be divided into equally spaced divisions:

100 divisions for Celsius (each division = 1C°) or

180 divisions for Fahrenheit (each division = 1F°) .

Temperature Scales

Steam Point

Ice Point

Absolute Zero

Fahrenheit

-459°F

32°F

212°F

Celsius

-273°C

0°C

100°C

Kelvin

0 K

273 K

373 K

Temperature Conversions

Celsius to Fahrenheit TF =95 TC +32=1.8TC + 32

Fahrenheit to Celsius TC =59 TF −32( ) ≈.56 TF − 32( )

Celsius to Kelvin TK =TC +273

Kelvin to Celsius TC =TK −273

Example

Convert 77K (temperature of liquid nitrogen) to Fahrenheit.

TC =TK −273 =77−273 =−196°C

TF =1.8TC + 32 =1.8 −196( ) + 32 =

−352.8 + 32 = −320.8°F

What causes the temperatures of two objects placed in thermal contact to change?

TH TC

TH > TC

Something must move from the high temperature object to the low temperature object.

Is it matter or energy?

If it is matter the mass of the high temperature object would decrease while the mass of the low temperature object would increase.

This is not observed.

It must be energy flowing between the two objects that causes a change in their temperatures.

The energy flowing between the two objects must be on the microscopic level because we can not see it.

Energy Review

Kinetic energy, KE-the macroscopic energy an object has due to its motion, measured in Joules, J.

Gravitational potential energy energy, GPE-the macroscopic energy an object has due to its position , measured in Joules, J.

Total mechanical energy, E-the sum of an object’s kinetic and potential energies , measured in Joules, J.

Work, W-the process by which the total mechanical energy can be changed , measured in Joules, J.

Work,WChange in

Mechanical EnergyΔE

Change in Kinetic EnergyΔΚE

Change in Potential EnergyΔGPE

and/or

Work and the Related Changes in Macroscopic Energy

All macroscopic objects are composed of microscopic objects: atoms and molecules

These atoms and molecules are moving so they have a microscopic kinetic energy.

These atoms and molecules are subject to conservative forces (gravitational and electrical) so they have a microscopic potential energy.

Macroscopic Object

Atoms and Molecules

The sum of these microscopic kinetic and potential energies is called Thermal Energy, U.

When two objects with different temperatures are placed in thermal contact, thermal energy flows from the higher temperature object to the lower temperature object until thermal equilibrium is reached.

The thermal energy that flows between two objects because of a difference in temperature is called heat, Q.

Since heat is a form of energy it is measured in Joules, J.

For historical reasons another unit of thermal energy or heat is sometimes used: calorie, cal or kilocalorie, kcal.

Conversion Factor1kcal = 4186J

When work is done on or by an object there is a change in the object’s kinetic energy or its gravitational potential energy or both.

The change in kinetic energy is perceived as a change in object’s velocity.

The change in gravitational potential energy is perceived as a change in object’s position (height above the reference level).

When heat flows into or out of an object there is a change in the object’s thermal energy.

How is the change in the thermal energy of an object perceived?

A change in thermal energy is perceived as a change in the object’s temperature or phase (solid, liquid, or gas).

It has been observed that the change in temperature and the change in phase never occur at the same time.

When the temperature is changing the phase remains constant and when the phase is changing the temperature remains constant.

Heat, Q

Change in Thermal EnergyΔU

Change in PhaseΔ =0T

Change in TemperatureΔT Phase Constant

What variables determine the magnitude of the change in temperature?

Q QWaterWater

More heat results in a larger change in temperature: change in temperature is directly proportional to the amount of heat.

ΔT ∝Q

Water1kgQ

Water2kgQ

When the same quantity of heat flows into (or out of) a larger mass the change in temperature is less.The change in temperature is inversely proportional to the mass.

ΔT ∝ 1m

Water1kgQ Q

Alcohol1kg

When the same quantity of heat flows into (or out of) equal masses of different substances the change in temperature is different.The change in temperature depends on the specific heat, c of the substance.The specific heat of a substance is the amount of heat required to change the temperature of 1kg of the substance by 1C°.

Units : Jkg⋅C° or kcal

kg⋅C°

Alcohol1kg

calcohol

=0.6 kcalkg⋅C°

QQWater1kg

cwater

=1 kcalkg⋅C°

The substance with the higher specific heat experiences a smaller change in temperature. The change in temperature is inversely proportional to the specific heat.

ΔT ∝ 1c

What causes the temperatures of two objects placed in thermal contact to change?

TH TC

TH > TC

Something must move from the high temperature object to the low temperature object.

Is it matter or energy?

If it is matter the mass of the high temperature object would decrease while the mass of the low temperature object would increase.

This is not observed.

It must be energy flowing between the two objects that causes a change in their temperatures.

The energy flowing between the two objects must be on the microscopic level because we can not see it.

Energy Review

Kinetic energy, KE-the macroscopic energy an object has due to its motion, measured in Joules, J.

Gravitational potential energy energy, GPE-the macroscopic energy an object has due to its position , measured in Joules, J.

Total mechanical energy, E-the sum of an object’s kinetic and potential energies , measured in Joules, J.

Work, W-the process by which the total mechanical energy can be changed , measured in Joules, J.

Work,WChange in

Mechanical EnergyΔE

Change in Kinetic EnergyΔΚE

Change in Potential EnergyΔGPE

and/or

Work and the Related Changes in Macroscopic Energy

All macroscopic objects are composed of microscopic objects: atoms and molecules

These atoms and molecules are moving so they have a microscopic kinetic energy.

These atoms and molecules are subject to conservative forces (gravitational and electrical) so they have a microscopic potential energy.

Macroscopic Object

Atoms and Molecules

The sum of these microscopic kinetic and potential energies is called Thermal Energy, U.

When two objects with different temperatures are placed in thermal contact, thermal energy flows from the higher temperature object to the lower temperature object until thermal equilibrium is reached.

The thermal energy that flows between two objects because of a difference in temperature is called heat, Q.

Since heat is a form of energy it is measured in Joules, J.

For historical reasons another unit of thermal energy or heat is sometimes used: calorie, cal or kilocalorie, kcal.

Conversion Factor1kcal = 4186J

When work is done on or by an object there is a change in the object’s kinetic energy or its gravitational potential energy or both.

The change in kinetic energy is perceived as a change in object’s velocity.

The change in gravitational potential energy is perceived as a change in object’s position (height above the reference level).

When heat flows into or out of an object there is a change in the object’s thermal energy.

How is the change in the thermal energy of an object perceived?

A change in thermal energy is perceived as a change in the object’s temperature or phase (solid, liquid, or gas).

It has been observed that the change in temperature and the change in phase never occur at the same time.

When the temperature is changing the phase remains constant and when the phase is changing the temperature remains constant.

Heat, Q

Change in Thermal EnergyΔU

Change in PhaseΔ =0T

Change in TemperatureΔT Phase Constant

or

What variables determine the magnitude of the change in temperature?

Q QWaterWater

More heat results in a larger change in temperature: change in temperature is directly proportional to the amount of heat.

ΔT ∝Q

Water1kgQ

Water2kgQ

When the same quantity of heat flows into (or out of) a larger mass the change in temperature is less.The change in temperature is inversely proportional to the mass.

ΔT ∝ 1m

Water1kgQ Q

Alcohol1kg

When the same quantity of heat flows into (or out of) equal masses of different substances the change in temperature is different.The change in temperature depends on the specific heat, c of the substance.The specific heat of a substance is the amount of heat required to change the temperature of 1kg of the substance by 1C°.

Units : Jkg⋅C° or kcal

kg⋅C°

Alcohol1kg

calcohol

=0.6 kcalkg⋅C°

QQWater1kg

cwater

=1 kcalkg⋅C°

The substance with the higher specific heat experiences a smaller change in temperature. The change in temperature is inversely proportional to the specific heat.

ΔT ∝ 1c

Combing All of the Proportions

ΔT ∝Q, 1m , 1

c ΔT = Qm⋅c

Q =mcΔT

Heat flow that results in a phase change can not be described by the equation above since during a phase change the temperature remains constant…ΔT=0.

It has been observed that phase changes can only occur at certain temperatures which depend on the particular substance.

Q Q

Temperature remains constant

Ice begins melting

Ice @ -20°C

-20°C

0°C

Ice @ 0°C

-20°C

0°C

0°C is the melting (or freezing) point of water.

As more heat is added the temperature will remain constant as more ice melts.

Once all of the ice has melted the addition of more heat will result in an increase in the temperature of the water.

Temperature increases

Water @ 0°C

-20°C

0°C

Q

100°C

Water @ 100°C

-20°C

0°C

100°C

Q

Temperature remains constant

Water begins boiling

100°C is the boiling point of water.

As more heat is added the temperature will remain constant as more water converts to steam.

Once all of the water has converted to steam the addition of more heat will result in an increase in the temperature of the steam.

Temperature increases

What determines how much ice melts or water converts to steam?

Q Ice @ 0°C

-20°C

0°C

Ice @ 0°C

-20°C

0°C

QMore heat results in a larger mass of ice melting. The mass of ice melted is directly proportional to the quantity of heat.

m ∝Q

Q 1kg ice @ 0°C

0°C

Q

When the same quantity of heat flows into (or out of) equal masses of the solid phase of different substances, each at its melting point, different masses will melt.

The mass that melts depends on the latent heat of fusion, Qf of the substance.

1kg solid alcohol @

-114°C

-114°C

The latent heat of fusion of a substance is the quantity of heat required to change 1kg of the solid phase of the substance, at its melting point, to 1kg of liquid at the same temperature.

Units :J

kgor kcal

kg

Q 1kg ice @ 0°C

0°C

Q 1kg solid alcohol @

-114°C

-114°C

Qf ,water =80 kcalkg

Qf ,alcohol =25 kcalkg

The substance with the greater heat of fusion experiences less melting. The mass melted is inversely proportional to the heat of fusion m ∝ 1

Qf

Combing All of the Proportions

m ∝Q, 1Qf

m = QQf

Q =mQf

There is a similar equation describing the phase change between liquid and gas.

Q =mQv

solid ⇔ liquid

liquid ⇔ gasQv is the latent heat of vaporization, the quantity of heat required to change 1kg of the liquid phase of the substance, at its boiling point, to 1kg of gas at the same temperature.

Units :J

kgor kcal

kg

Heat, Q

Change in Thermal EnergyΔU

Change in PhaseΔ =0T

Change in TemperatureΔT Phase Constant

Q =mcΔT

Q =mQf solid⇔ liquid

Q =mQv liquid⇔ gas

Summary of Thermodynamic Properties and RelationshipsI) Phase Change Temperatures- °C, K, °F

A) Melting / Freezing Point, Tf

B) Boiling Point, Tb

II) Specific Heat - Jkg⋅C° ,

kcalkg⋅C°

A) Solid Phase, csolid

B) Liquid Phase, cliquid

C) Gas (vapor) Phase, cgas

1. cp , constant pressure

2. cv , constant volume

III) Latent Heat - Jkg , kcal

kg

A) Latent Heat of Fusion, Qf

B) Latent Heat of Vaporization, Qv

IV) Thermodynamic Relationships

A) Change in Temperature, Q = mcΔT

B) Change in Phase (solid ⇔ ),liquid Q=mQf

C) Change in Phase (liquid⇔ ),gas Q=mQv

Example: Water

Tf = 0°C, 273K, 32°F

Tb = 100°C, 373K, 212°F

cice =2093 Jkg⋅C° , 0.5

kcalkg⋅C°

cwater =4186 Jkg⋅C° , 1.0

kcalkg⋅C°

cp,steam =2020 Jkg⋅C° , 0.483

kcalkg⋅C°

cv,steam =1520 Jkg⋅C° , 0.363

kcalkg⋅C°

Qf =3.34×105 Jkg , 80.0kcalkg

Qv =2.26 ×106 Jkg , 540.0kcalkg

Graphical Representation of Heat Flow, Temperature Change, and Phase Change

Heat Flow Q, kcal

Heat flow w/ Temperature Change

Heat flow w/ Phase Change

Melting Point

Tf

Tb

Boiling Point

Initial Temperature

Tinitial

FinalTemperature

Tfinal

Step #1 Raise the temperature to the melting point

Step #2 Melt all of the solid

Step #3 Raise temperature of liquid to boiling point

Step #4 Convert the liquid to gas

Step #5 Raise the temperature of the gas to the final temperature

Graphical Representation of Heat Flow, Temperature Change, and Phase Change In Converting 2kg of ice @ -20°C to steam @ 120°C

Heat Flow Q, kcal

Tf = 0°C

Tb = 100°C

Tinitial = -20°C

Tfinal = 120°C

ice @ -20°C

Step #1 Raise temperature of the ice to the melting point.

ice @ 0°C

Q1 =mciceΔTice

Step #2 Melt all of the ice

water @ 0°CQ2 =mQf

Step #3 Raise the temperature of the water to the boiling point

water @ 100°C

Q3 =mcwaterΔTwaterStep #4 Convert all of the water to steam

steam @ 100°C

Q4 =mQv

Step #5 Raise temperature of steam to final temperature, 120°C

steam @ 120°C

Q5 =mcsteamΔTsteam

Calculation of Total Heat Required

Step #1

Q1 =mciceΔTice= 2kg( ) 0.5 kcalkg⋅C°

⎛ ⎝ ⎜ ⎞

⎠ ⎟ 20C°( ) =

20kcalStep #2

Q2 =mQf = 2kg( ) 80 kcalkg

⎛ ⎝ ⎜ ⎞

⎠ ⎟=160kcal

Step #3Q3 =mcwaterΔTwater= 2kg( ) 1.0 kcal

kg⋅C° ⎛ ⎝ ⎜ ⎞

⎠ ⎟ 100C°( ) =

200kcalStep #4

Q4 =mQv = 2kg( ) 540 kcalkg

⎛ ⎝ ⎜ ⎞

⎠ ⎟=1080kcal

Step #5Q5 =mcsteamΔTsteam=

2kg( ) 0.483 kcalkg⋅C°

⎛ ⎝ ⎜ ⎞

⎠ ⎟ 20C°( ) =19.32kcal

20kcal 160kcal 200kcal 1080kcal 19.32kcal

Total Heat Required

+ +++

= 1479.32 kcal

1479.32 kcal ×4186J1kcal = 6.2×106 J