Chapter 9 Thermal Equilibrium · •Thermal Equilibrium •Thermal Expansion ... Transfer of...

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• Objectives

• Defining Temperature

• Thermal Equilibrium

• Thermal Expansion

• Measuring Temperature

Chapter 9 Section 1 Temperature and

Thermal Equilibrium

Section 1 Temperature and

Thermal Equilibrium Chapter 9

Objectives

• Relate temperature to the kinetic energy of atoms

and molecules.

• Describe the changes in the temperatures of two

objects reaching thermal equilibrium.

• Identify the various temperature scales, and convert

from one scale to another.

Chapter 9

Defining Temperature

• Temperature is a measure of the average kinetic

energy of the particles in a substance.

• Adding or removing energy usually changes

temperature.

• Internal energy is the energy of a substance due to

both the random motions of its particles and to the

potential energy that results from the distances and

alignments between the particles.


Thermal Equilibrium

Click below to watch the Visual Concept.

Visual Concepts

Visual Concept

Chapter 9

Forms of Internal Energy

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Chapter 9

Thermal Equilibrium

• Thermal equilibrium is the state in which two bodies

in physical contact with each other have identical

temperatures.

– By placing a thermometer in contact with an object and

waiting until the column of liquid in the thermometer stops

rising or falling, you can find the temperature of the object.

– The reason is that the thermometer is in thermal equilibrium

with the object.

• The temperature of any two objects in thermal

equilibrium always lies between their initial

temperatures.


Thermal Equilibrium


Visual Concept

Chapter 9

Thermal Equilibrium


Thermal Equilibrium

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Chapter 9

Thermal Expansion

• In general, if the temperature of a substance

increases, so does its volume. This phenomenon is

known as thermal expansion.

• Different substances undergo different amounts of

expansion for a given temperature change.

• The thermal expansion characteristics of a material

are indicated by a quantity called the coefficient of

volume expansion.

• Gases have the largest values for this coefficient.

Solids typically have the smallest values.


Thermal Equilibrium


Visual Concept

Chapter 9

Thermal Expansion


Thermal Equilibrium

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Chapter 9

Measuring Temperature

• The most common

thermometers use a glass tube

containing a thin column of

mercury, colored alcohol, or

colored mineral spirits.

• When the thermometer is

heated, the volume of the liquid

expands.

• The change in length of the

liquid column is proportional to

the temperature.


Thermal Equilibrium

Chapter 9

Measuring Temperature, continued

• When a thermometer is in thermal equilibrium with a mixture of water and ice at one atmosphere of pressure, the temperature is called the ice point or melting point of water. This is defined as zero degrees Celsius, or 0°C.

• When the thermometer is in thermal equilibrium with

a mixture of steam and water at one atmosphere of pressure, the temperature is called the steam point or boiling point of water. This is defined as 100°C.


Thermal Equilibrium

Chapter 9


• The temperature scales most widely used today are

the Fahrenheit, Celsius, and Kelvin scales.

• Celsius and Fahrenheit temperature measurements

can be converted to each other using this equation:


Thermal Equilibrium

9 32.0

5

9 Fahrenheit temperatu

re

Celsius temperature 32.05

F CT T

• The number 32.0 indicates the difference between

the ice point value in each scale: 0.0ºC and 32.0ºF.

Chapter 9



Thermal Equilibrium

• Temperature values in the Celsius and Fahrenheit

scales can have positive, negative, or zero values.

• But because the kinetic energy of the atoms in a

substance must be positive, the absolute

temperature that is proportional to that energy

should be positive also.

• A temperature scale with only positive values is

suggested by the graph on the next slide. This scale

is called the Kelvin scale.

Chapter 9



Thermal Equilibrium

• The graph suggests that if

the temperature could be

lowered to –273.15°C, the

pressure would be zero.

• This temperature is

designated in the Kelvin

scale as 0.00 K, where K

represents the

temperature unit called

the kelvin.

• Temperatures in the Kelvin scale are indicated by the

symbol T.

Chapter 9



Thermal Equilibrium

• A temperature difference of one degree is the same

on the Celsius and Kelvin scales. The two scales

differ only in the choice of zero point.

• Thus, the ice point (0.00°C) equals 273.15 K, and the

steam point (100.00°C) equals 373.15 K.

• The Celsius temperature can therefore be converted

to the Kelvin temperature by adding 273.15:

T TC 273.15

Kelvin temperature Celsius temperature 273.15

Chapter 9

Temperature Scales and Their Uses


Thermal Equilibrium

Preview

• Objectives

• Heat and Energy

• Thermal Conduction

• Conservation of Energy

• Sample Problem

Chapter 9 Section 2 Defining Heat

Section 2 Defining Heat Chapter 9

Objectives

• Explain heat as the energy transferred between

substances that are at different temperatures.

• Relate heat and temperature change on the

macroscopic level to particle motion on the

microscopic level.

• Apply the principle of energy conservation to

calculate changes in potential, kinetic, and internal

energy.


Heat and Energy

• Heat is the energy transferred between objects

because of a difference in their temperatures.

• From a macroscopic viewpoint, energy transferred as

heat tends to move from an object at higher

temperature to an object at lower temperature.

• The direction in which energy travels as heat can be

explained at the atomic level, as shown on the next

slide.

Chapter 9

Transfer of Particles’ Kinetic Energy as Heat

Section 2 Defining Heat

Energy is transferred as heat from the higher-energy particles to

the lower-energy particles, as shown on the left. The net energy

transferred is zero when thermal equilibrium is reached, as

shown on the right.


Visual Concept


Temperature and Heat

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Heat and Energy, continued

• The atoms of all objects are in continuous motion, so

all objects have some internal energy.

– Because temperature is a measure of that energy,

all objects have some temperature.

• Heat, on the other hand, is the energy transferred

from one object to another because of the

temperature difference between them.

– When there is no temperature difference

between a substance and its surroundings, no net

energy is transferred as heat.


Heat and Energy, continued

• Just as other forms of energy have a symbol that

identifies them (PE for potential energy, KE for kinetic

energy, U for internal energy, W for work), heat is

indicated by the symbol Q.

• Because heat, like work, is energy in transit, all heat

units can be converted to joules, the SI unit for

energy.

Chapter 9

Thermal Units and Their Values in Joules

Section 2 Defining Heat


Thermal Conduction

• The type of energy transfer that

is due to atoms transferring

vibrations to neighboring atoms

is called thermal conduction.

• The rate of thermal

conduction depends on the

substance.

• Two other mechanisms for

transferring energy as heat are

convection and

electromagnetic radiation.

When this burner is

turned on, the skillet’s

handle heats up

because of conduction.


Visual Concept


Convection, Conduction, and Radiation

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Conservation of Energy

• If changes in internal energy are taken into account

along with changes in mechanical energy, the total

energy is a universally conserved property.

• In other words, the sum of the changes in

potential, kinetic, and internal energy is equal to

zero.

CONSERVATION OF ENERGY

PE + KE + U = 0

the change in potential energy + the change in kinetic energy

+ the change in internal energy = 0


Visual Concepts

Visual Concept

Chapter 9


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Sample Problem


An arrangement similar to the one

used to demonstrate energy

conservation is shown in the figure.

A vessel contains water. Paddles

that are propelled by falling masses

turn in the water. This agitation

warms the water and increases its

internal energy. The temperature of

the water is then measured, giving

an indication of the water’s internal

energy increase.


Sample Problem, continued

Conservation of Energy, continued

If a total mass of 11.5 kg falls 1.3 m

and all of the mechanical energy is

converted to internal energy, by how

much will the internal energy of the

water increase? (Assume no energy

is transferred as heat out of the

vessel to the surroundings or from

the surroundings to the vessel’s

interior.)



1. Define

Given:

m = 11.5 kg

h = 1.3 m

g = 9.81 m/s2

Unknown:

U = ?



2. Plan

Choose an equation or situation: Use the conservation of energy, and solve for U.

PE + KE + U = 0

(PEf – PEi) + (KEf – KEi) + U = 0

U = –PEf + PEi – KEf + KEi

Tip: Don’t forget that a change in any quantity, indicated by the symbol ∆, equals the final value minus the initial value.



Because the masses begin at rest, KEi equals

zero. If we assume that KEf is small compared to

the loss of PE, we can set KEf equal to zero also.

KEf = 0 KEi = 0

Because all of the potential energy is assumed to

be converted to internal energy, PEi can be set

equal to mgh if PEf is set equal to zero.

PEi = mgh PEf = 0

Substitute each quantity into the equation for ∆U:

∆U = –PEf + PEi – KEf + KEi

∆U = 0 + mgh + 0 + 0 = mgh



4. Evaluate

The answer can be estimated using rounded

values. If m ≈ 10 kg and g ≈ 10 m/s2, then ∆U ≈

130 J, which is close to the actual value calculated.

3. Calculate

Substitute the values into the equation and

solve:

U = mgh

U = (11.5 kg)(9.81 m/s2)(1.3 m)

U = 1.5 102 J

Preview

• Objectives

• Specific Heat Capacity

• Calorimetry

• Sample Problem

• Latent Heat

Chapter 9 Section 3 Changes in

Temperature and Phase

Section 3 Changes in

Temperature and Phase Chapter 9

Objectives

• Perform calculations with specific heat capacity.

• Interpret the various sections of a heating curve.



Specific Heat Capacity

• The specific heat capacity of a substance is defined

as the energy required to change the temperature of 1

kg of that substance by 1°C.

• Every substance has a unique specific heat capacity.

• This value tells you how much the temperature of a

given mass of that substance will increase or

decrease, based on how much energy is added or

removed as heat.



Specific Heat Capacity, continued

• Specific heat capacity is expressed mathematically

as follows:

cp Q

mT

specific heat capacity = energy transferred as heat

mass change in temperature

• The subscript p indicates that the specific heat capacity is

measured at constant pressure.

• In this equation, T can be in degrees Celsius or in degrees

Kelvin.

Chapter 9

Specific Heat Capacities





Calorimetry

• Calorimetry is used

to determine specific

heat capacity.

• Calorimetry is an

experimental

procedure used to

measure the energy

transferred from one

substance to another

as heat.

A simple

calorimeter

allows the

specific

heat

capacity of a

substance to

be

determined.


Visual Concept



Calorimetry

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Calorimetry, continued

Because the specific heat capacity of water is well

known (cp,w= 4.186 kJ/kg•°C), the energy transferred as

heat between an object of unknown specific heat

capacity and a known quantity of water can be

measured.

energy absorbed by water = energy released by substance

Qw = –Qx

cp,wmw∆Tw = –cp,xmx∆Tx



Sample Problem

Calorimetry

A 0.050 kg metal bolt is heated to an unknown initial

temperature. It is then dropped into a calorimeter

containing 0.15 kg of water with an initial temperature

of 21.0°C. The bolt and the water then reach a final

temperature of 25.0°C. If the metal has a specific heat

capacity of 899 J/kg•°C, find the initial temperature of

the metal.




1. Define

Given: mm = 0.050 kg cp,m = 899 J/kg•°C

mw = 0.15 kg cp,w = 4186 J/kg•°C

Tw = 21.0°C Tf = 25.0°C

Unknown: Tm = ?

Diagram:




2. Plan

Choose an equation or situation: The energy absorbed by the

water equals the energy removed from the bolt.

Qw –Qm

cp,wmwTw –cp,mmmTm

cp,wmw (T f Tw ) –cp,mmm (T f Tm )

Rearrange the equation to isolate the unknown:

Tm cp,wmw(T f Tw )

cp,mmmT f




3. Calculate

Substitute the values into the equation and solve:

4. Evaluate

Tm is greater than Tf, as expected.

,

,

(4186 J/kg• C)(0.15 kg)(25.0 C 21.0 C)25.0 C

(899 J/kg C)(0.050 kg)

81 C

( )p w w f w

m f

p m m

m

m

c m T TT T

c m

T

T

Tip: Because Tw is less

than Tf, you know that Tm

must be greater than Tf.



Latent Heat

• When substances melt, freeze, boil, condense, or

sublime, the energy added or removed changes the

internal energy of the substance without changing the

substance’s temperature.

• These changes in matter are called phase changes.

• The energy per unit mass that is added or removed

during a phase change is called latent heat,

abbreviated as L.

Q = mL

energy transferred as heat during phase change = mass latent heat


Visual Concept



Latent Heat

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Latent Heat, continued

• During melting, the energy that is added to a

substance equals the difference between the total

potential energies for particles in the solid and the

liquid phases. This type of latent heat is called the

heat of fusion, abbreviated as Lf.

• During vaporization, the energy that is added to a

substance equals the difference in the potential

energy of attraction between the liquid particles and

between the gas particles. In this case, the latent

heat is called the heat of vaporization, abbreviated

as Lv.

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