Chapter 13-15

Thermal Physics and Thermodynamics

Chapter 13

Thermal Physics

Thermal Physics

• Thermal physics is the study of

▫ Temperature

▫ Heat

▫ How these affect matter

Thermal Physics, cont

• Concerned with the concepts of energy transfers between a system and its environment and the resulting temperature variations

• Historically, the development of thermodynamics paralleled the development of atomic theory

• Concerns itself with the physical and chemical transformations of matter in all of its forms: solid, liquid, and gas

Heat

• The process by which energy is exchanged between objects because of temperature differences is called heat

• Objects are in thermal contact if energy can be exchanged between them

• Thermal equilibrium exists when two objects in thermal contact with each other cease to exchange energy

Zeroth Law of Thermodynamics

• If objects A and B are separately in thermal equilibrium with a third object, C, then A and B are in thermal equilibrium with each other.

• Allows a definition of temperature

Temperature from the Zeroth Law

• Two objects in thermal equilibrium with each other are at the same temperature

• Temperature is the property that determines whether or not an object is in thermal equilibrium with other objects

Thermometers

• Used to measure the temperature of an object or a system

• Make use of physical properties that change with temperature

• Many physical properties can be used ▫ volume of a liquid

▫ length of a solid

▫ pressure of a gas held at constant volume

▫ volume of a gas held at constant pressure

▫ electric resistance of a conductor

▫ color of a very hot object

Thermometers, cont

• A mercury thermometer is an example of a common thermometer

• The level of the mercury rises due to thermal expansion

• Temperature can be defined by the height of the mercury column

Temperature Scales

• Thermometers can be calibrated by placing them in thermal contact with an environment that remains at constant temperature

▫ Environment could be mixture of ice and water in thermal equilibrium

▫ Also commonly used is water and steam in thermal equilibrium

Celsius Scale

• Temperature of an ice-water mixture is defined as 0º C ▫ This is the freezing point of water

• Temperature of a water-steam mixture is defined as 100º C ▫ This is the boiling point of water

• Distance between these points is divided into 100 segments or degrees

Gas Thermometer

• Temperature readings are nearly independent of the gas

• Pressure varies with temperature when maintaining a constant volume

Kelvin Scale

• When the pressure of a gas goes to zero, its temperature is –273.15º C

• This temperature is called absolute zero

• This is the zero point of the Kelvin scale ▫ –273.15º C = 0 K

• To convert: TC = TK – 273.15 ▫ The size of the degree in the Kelvin scale is the same as

the size of a Celsius degree

Pressure-Temperature Graph

• All gases extrapolate to the same temperature at zero pressure

• This temperature is absolute zero

Modern Definition of Kelvin Scale

• Defined in terms of two points ▫ Agreed upon by International Committee on Weights

and Measures in 1954

• First point is absolute zero

• Second point is the triple point of water ▫ Triple point is the single point where water can exist as

solid, liquid, and gas

▫ Single temperature and pressure

▫ Occurs at 0.01º C and P = 4.58 mm Hg

Modern Definition of Kelvin Scale, cont

• The temperature of the triple point on the Kelvin scale is 273.16 K

• Therefore, the current definition of of the Kelvin is defined as

1/273.16 of the temperature of the triple point of water

Some Kelvin

Temperatures

• Some representative Kelvin temperatures

• Note, this scale is logarithmic

• Absolute zero has never been reached

Fahrenheit Scales

• Most common scale used in the US

• Temperature of the freezing point is 32º

• Temperature of the boiling point is 212º

• 180 divisions between the points

Comparing Temperature Scales

Converting Among Temperature Scales

273.15

932

5

532

9

9

5

C K

F C

C F

F C

T T

T T

T T

T T

Thermal Expansion

• The thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or molecules

• At ordinary temperatures, molecules vibrate with a small amplitude

• As temperature increases, the amplitude increases ▫ This causes the overall object as a whole to expand

Linear Expansion

• For small changes in temperature

• , the coefficient of linear expansion, depends on the material ▫ See table 10.1 ▫ These are average coefficients, they can vary

somewhat with temperature

o o oL L T or L L T T

Applications of Thermal Expansion

– Bimetallic Strip

• Thermostats ▫ Use a bimetallic strip

▫ Two metals expand differently Since they have different coefficients of expansion

Area Expansion

• Two dimensions expand according to

▫ is the coefficient of area expansion

Volume Expansion

• Three dimensions expand

▫ For liquids, the coefficient of volume expansion is given in the table

3,solidsfor

TVV o

More Applications of Thermal

Expansion • Pyrex Glass

▫ Thermal stresses are smaller than for ordinary glass

• Sea levels

▫ Warming the oceans will increase the volume of the oceans

Unusual Behavior of Water

• As the temperature of water increases from 0ºC to 4 ºC, it contracts and its density increases

• Above 4 ºC, water exhibits the expected expansion with increasing temperature

• Maximum density of water is 1000 kg/m3 at 4 ºC

Ideal Gas

• A gas does not have a fixed volume or pressure

• In a container, the gas expands to fill the container

• Most gases at room temperature and pressure behave approximately as an ideal gas

Characteristics of an Ideal Gas

• Collection of atoms or molecules that move randomly

• Exert no long-range force on one another

• Each particle is individually point-like

▫ Occupying a negligible volume

Moles

• It’s convenient to express the amount of gas in a given volume in terms of the number of moles, n

• One mole is the amount of the substance that contains as many particles as there are atoms in 12 g of carbon-12

massmolar

massn

Avogadro’s Number

• The number of particles in a mole is called Avogadro’s Number

▫ NA=6.02 x 1023 particles / mole

▫ Defined so that 12 g of carbon contains NA atoms

• The mass of an individual atom can be calculated:

A

atomN

massmolarm

Avogadro’s Number and Masses

• The mass in grams of one Avogadro's number of an element is numerically the same as the mass of one atom of the element, expressed in atomic mass units, u

• Carbon has a mass of 12 u ▫ 12 g of carbon consists of NA atoms of carbon

• Holds for molecules, also

Ideal Gas Law

• PV = n R T

▫ R is the Universal Gas Constant

▫ R = 8.31 J / mole.K

▫ R = 0.0821 L. atm / mole.K

▫ Is the equation of state for an ideal gas

Ideal Gas Law, Alternative Version

• P V = N kB T

▫ kB is Boltzmann’s Constant

▫ kB = R / NA = 1.38 x 10-23 J/ K

▫ N is the total number of molecules

• n = N / NA

▫ n is the number of moles

▫ N is the number of molecules

Kinetic Theory of Gases – Assumptions

• The number of molecules in the gas is large and the average separation between them is large compared to their dimensions

• The molecules obey Newton’s laws of motion, but as a whole they move randomly

Kinetic Theory of Gases – Assumptions,

cont. • The molecules interact only by short-range

forces during elastic collisions • The molecules make elastic collisions with the

walls • The gas under consideration is a pure substance,

all the molecules are identical

Pressure of an Ideal Gas

•

Pressure, cont

• The pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of the molecule

• Pressure can be increased by ▫ Increasing the number of molecules per unit volume in

the container ▫ Increasing the average translational kinetic energy of

the molecules Increasing the temperature of the gas

Molecular Interpretation of

Temperature • Temperature is proportional to the average

kinetic energy of the molecules

• The total kinetic energy is proportional to the absolute temperature

Tk2

3mv

2

1B

2

nRT2

3KE total

Internal Energy

• In a monatomic gas, the KE is the only type of energy the molecules can have

• U is the internal energy of the gas • In a polyatomic gas, additional possibilities for

contributions to the internal energy are rotational and vibrational energy in the molecules

nRT2

3U

Speed of the Molecules

• Expressed as the root-mean-square (rms) speed

• At a given temperature, lighter molecules move faster, on average, than heavier ones ▫ Lighter molecules can more easily reach escape speed

from the earth

M

TR3

m

Tk3v B

rms

Some rms Speeds

Maxwell Distribution

• A system of gas at a given temperature will exhibit a variety of speeds

• Three speeds are of interest: ▫ Most probable ▫ Average ▫ rms

Maxwell Distribution, cont

• For every gas, vmp < vav < vrms

• As the temperature rises, these three speeds shift to the right

• The total area under the curve on the graph equals the total number of molecules

Chapter 14

Energy in Thermal Processes

Energy Transfer

• When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler increases

• The energy exchange ceases when the objects reach thermal equilibrium

• The concept of energy was broadened from just mechanical to include internal ▫ Made Conservation of Energy a universal law of nature

Heat Compared to

Internal Energy • Important to distinguish between them

▫ They are not interchangeable

• They mean very different things when used in physics

Internal Energy

• Internal Energy, U, is the energy associated with the microscopic components of the system ▫ Includes kinetic and potential energy associated with

the random translational, rotational and vibrational motion of the atoms or molecules

▫ Also includes any potential energy bonding the particles together

Heat

• Heat is the transfer of energy between a system and its environment because of a temperature difference between them ▫ The symbol Q is used to represent the amount of

energy transferred by heat between a system and its environment

Units of Heat • Calorie

▫ An historical unit, before the connection between thermodynamics and mechanics was recognized

▫ A calorie is the amount of energy necessary to raise the temperature of 1 g of water from 14.5° C to 15.5° C .

A Calorie (food calorie) is 1000 cal

Units of Heat, cont.

• US Customary Unit – BTU

• BTU stands for British Thermal Unit

▫ A BTU is the amount of energy necessary to raise the temperature of 1 lb of water from 63° F to 64° F

• 1 cal = 4.186 J

▫ This is called the Mechanical Equivalent of Heat

James Prescott Joule

• 1818 – 1889

• British physicist

• Conservation of Energy

• Relationship between heat and other forms of energy transfer

Specific Heat

• Every substance requires a unique amount of energy per unit mass to change the temperature of that substance by 1° C

• The specific heat, c, of a substance is a measure of this amount

Tm

Qc

Units of Specific Heat

• SI units

▫ J / kg °C

• Historical units

▫ cal / g °C

Heat and Specific Heat • Q = m c ΔT

• ΔT is always the final temperature minus the initial temperature

• When the temperature increases, ΔT and ΔQ are considered to be positive and energy flows into the system

• When the temperature decreases, ΔT and ΔQ are considered to be negative and energy flows out of the system

A Consequence of Different

Specific Heats

• Water has a high specific heat compared to land

• On a hot day, the air above the land warms faster

• The warmer air flows upward and cooler air moves toward the beach

Calorimeter

• One technique for determining the specific heat of a substance

• A calorimeter is a vessel that is a good insulator which allows a thermal equilibrium to be achieved between substances without any energy loss to the environment

Calorimetry

• Analysis performed using a calorimeter

• Conservation of energy applies to the isolated system

• The energy that leaves the warmer substance equals the energy that enters the water ▫ Qcold = -Qhot

▫ Negative sign keeps consistency in the sign convention of ΔT

Calorimetry with More Than Two

Materials • In some cases it may be difficult to determine

which materials gain heat and which materials lose heat

• You can start with Q = 0 ▫ Each Q = m c T

▫ Use Tf – Ti

▫ You don’t have to determine before using the equation which materials will gain or lose heat

Phase Changes

• A phase change occurs when the physical characteristics of the substance change from one form to another

• Common phases changes are ▫ Solid to liquid – melting

▫ Liquid to gas – boiling

• Phases changes involve a change in the internal energy, but no change in temperature

Latent Heat • During a phase change, the amount of heat is

given as ▫ Q = ±m L

• L is the latent heat of the substance ▫ Latent means hidden ▫ L depends on the substance and the nature of the

phase change

• Choose a positive sign if you are adding energy to the system and a negative sign if energy is being removed from the system

Latent Heat, cont.

• SI units of latent heat are J / kg

• Latent heat of fusion, Lf, is used for melting or freezing

• Latent heat of vaporization, Lv, is used for boiling or condensing

• Table 11.2 gives the latent heats for various substances

Graph of Ice to Steam

Warming Ice

• Start with one gram of ice at –30.0º C

• During A, the temperature of the ice changes from –30.0º C to 0º C

• Use Q = m c ΔT

• Will add 62.7 J of energy

Melting Ice

• Once at 0º C, the phase change (melting) starts

• The temperature stays the same although energy is still being added

• Use Q = m Lf

• Needs 333 J of energy

Warming Water

• Between 0º C and 100º C, the material is liquid and no phase changes take place

• Energy added increases the temperature

• Use Q = m c ΔT • 419 J of energy are

added

Boiling Water

• At 100º C, a phase change occurs (boiling)

• Temperature does not change

• Use Q = m Lv

• 2 260 J of energy are needed

Heating Steam

• After all the water is converted to steam, the steam will heat up

• No phase change occurs • The added energy goes to

increasing the temperature • Use Q = m c ΔT • To raise the temperature of the

steam to 120°, 40.2 J of energy are needed

Phase Diagram

Sublimation and Deposition

• Some substances will go directly from solid to gaseous phase

▫ Without passing through the liquid phase

• This process is called sublimation

▫ There will be a latent heat of sublimation associated with this phase change

• The reverse process of Sublimation is Deposition where a gas goes directly to a solid

Phase Diagrams 2

Problem Solving Strategies

• Make a table

▫ A column for each quantity

▫ A row for each phase and/or phase change

▫ Use a final column for the combination of quantities

• Use consistent units

Methods of Heat Transfer

• Need to know the rate at which energy is transferred

• Need to know the mechanisms responsible for the transfer

• Methods include ▫ Conduction ▫ Convection ▫ Radiation

Conduction

• The transfer can be viewed on an atomic scale ▫ It is an exchange of energy between microscopic

particles by collisions

▫ Less energetic particles gain energy during collisions with more energetic particles

• Rate of conduction depends upon the characteristics of the substance

Conduction example

• The molecules vibrate about their equilibrium positions

• Particles near the stove coil vibrate with larger amplitudes

• These collide with adjacent molecules and transfer some energy

• Eventually, the energy travels entirely through the pan and its handle

Conduction, equation

• The slab allows energy to transfer from the region of higher temperature to the region of lower temperature

h cT TQkA

t L

Conduction, equation explanation • A is the cross-sectional area • L = Δx is the thickness of the slab or the

length of a rod • P is in Watts when Q is in Joules and t is in

seconds • k is the thermal conductivity of the material

▫ See table 11.3 for some conductivities ▫ Good conductors have high k values and good

insulators have low k values

Home Insulation • Substances are rated by their R values

▫ R = L / k ▫ See table 11.4 for some R values

• For multiple layers, the total R value is the sum of the R values of each layer

• Wind increases the energy loss by conduction in a home

Conduction and Insulation with

Multiple Materials • Each portion will have a specific thickness and a

specific thermal conductivity

• The rate of conduction through each portion is equal

Multiple Materials, cont.

• The rate through the multiple materials will be

• TH and TC are the temperatures at the outer extremities of the compound material

h c h C

i ii

ii

T T T TQA A

Lt Rk

Convection

• Energy transferred by the movement of a substance

▫ When the movement results from differences in density, it is called natural convection

▫ When the movement is forced by a fan or a pump, it is called forced convection

Convection example

• Air directly above the flame is warmed and expands

• The density of the air decreases, and it rises

• The mass of air warms the hand as it moves by

Convection applications

• Boiling water

• Radiators

• Upwelling

• Cooling automobile engines

• Algal blooms in ponds and lakes

Convection Current Example

• The radiator warms the air in the lower region of the room

• The warm air is less dense, so it rises to the ceiling

• The denser, cooler air sinks

• A continuous air current pattern is set up as shown

Radiation

• Radiation does not require physical contact • All objects radiate energy continuously in the

form of electromagnetic waves due to thermal vibrations of the molecules

• Rate of radiation is given by Stefan’s Law

Radiation example

• The electromagnetic waves carry the energy from the fire to the hands

• No physical contact is necessary

• Cannot be accounted for by conduction or convection

Radiation equation

•

▫ The power is the rate of energy transfer, in Watts

▫ σ = 5.6696 x 10-8 W/m2.K4

▫ A is the surface area of the object

▫ e is a constant called the emissivity

e varies from 0 to 1

▫ T is the temperature in Kelvins

4= AeT

Energy Absorption and Emission by

Radiation • With its surroundings, the rate at which the

object at temperature T with surroundings at To radiates is

▫

▫ When an object is in equilibrium with its surroundings, it radiates and absorbs at the same rate

Its temperature will not change

4 4= net oAe T T

Ideal Absorbers

• An ideal absorber is defined as an object that absorbs all of the energy incident on it ▫ e = 1

• This type of object is called a black body • An ideal absorber is also an ideal radiator of

energy

Ideal Reflector

• An ideal reflector absorbs none of the energy incident on it

▫ e = 0

Applications of Radiation

• Clothing ▫ Black fabric acts as a good absorber ▫ White fabric is a better reflector

• Thermography ▫ The amount of energy radiated by an object can be

measured with a thermograph

• Body temperature ▫ Radiation thermometer measures the intensity of the

infrared radiation from the eardrum

Resisting Energy Transfer

• Dewar flask/thermos bottle

• Designed to minimize energy transfer to surroundings

• Space between walls is evacuated to minimize conduction and convection

• Silvered surface minimizes radiation

• Neck size is reduced

Chapter 15

The Laws of Thermodynamics

Law of Thermodynamics • Zeroth Law-If two thermodynamic systems are

each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

• 1st Law - Energy can be neither created nor destroyed. It can only change forms.

• 2nd Law- Entropy- Energy is lost to the surroundings. The universe increases in disorder over time.

• 3rd Law- It says that all processes cease as temperature approaches absolute zero

• Summed up as: You Can’t Win, You Can’t Break Even, and Can’t Quit the Game

First Law of Thermodynamics

• The First Law of Thermodynamics tells us that the internal energy of a system can be increased by ▫ Adding energy to the system ▫ Doing work on the system

• There are many processes through which these could be accomplished ▫ As long as energy is conserved

Second Law of Thermodynamics

• Constrains the First Law

• Establishes which processes actually occur

• Heat engines are an important application

Work in Thermodynamic Processes –

Assumptions • Dealing with a gas

• Assumed to be in thermodynamic equilibrium

▫ Every part of the gas is at the same temperature

▫ Every part of the gas is at the same pressure

• Ideal gas law applies

Work in a Gas Cylinder

• The gas is contained in a cylinder with a moveable piston

• The gas occupies a volume V and exerts pressure P on the walls of the cylinder and on the piston

Work in a Gas Cylinder, cont.

• A force is applied to slowly compress the gas ▫ The compression is slow

enough for all the system to remain essentially in thermal equilibrium

• W = - P ΔV ▫ This is the work done on

the gas

More about Work on a Gas Cylinder

• When the gas is compressed ▫ ΔV is negative

▫ The work done on the gas is positive

• When the gas is allowed to expand ▫ ΔV is positive

▫ The work done on the gas is negative

• When the volume remains constant ▫ No work is done on the gas

Notes about the Work Equation

• The pressure remains constant during the expansion or compression

▫ This is called an isobaric process

• If the pressure changes, the average pressure may be used to estimate the work done

PV Diagrams

• Used when the pressure and volume are known at each step of the process

• The work done on a gas that takes it from some initial state to some final state is the negative of the area under the curve on the PV diagram ▫ This is true whether or not the

pressure stays constant

PV Diagrams, cont.

• The curve on the diagram is called the path taken between the initial and final states

• The work done depends on the particular path ▫ Same initial and final states, but different amounts of work

are done

First Law of Thermodynamics

• Energy conservation law • Relates changes in internal energy to energy

transfers due to heat and work • Applicable to all types of processes • Provides a connection between microscopic and

macroscopic worlds

First Law, cont. • Energy transfers occur due to

▫ By doing work Requires a macroscopic displacement of an

object through the application of a force

▫ By heat Occurs through the random molecular collisions

• Both result in a change in the internal energy, U, of the system

First Law, Equation

• If a system undergoes a change from an initial state to a final state, then U = Uf – Ui = Q + W

▫ Q is the energy transferred to the system by heat

▫ W is the work done on the system

▫ U is the change in internal energy

First Law – Signs

• Signs of the terms in the equation ▫ Q Positive if energy is transferred to the system by heat

Negative if energy is transferred out of the system by heat

▫ W Positive if work is done on the system

Negative if work is done by the system

▫ U Positive if the temperature increases

Negative if the temperature decreases

Results of U

• Changes in the internal energy result in changes in the measurable macroscopic variables of the system

▫ These include

Pressure

Temperature

Volume

Notes About Work

• Positive work increases the internal energy of the system

• Negative work decreases the internal energy of the system

• This is consistent with the definition of mechanical work

Molar Specific Heat

• The molar specific heat at constant volume for an ideal gas

▫ Cv = 3/2 R

• The change in internal energy can be expressed as U = n Cv T

▫ For an ideal gas, this expression is always valid, even if not at a constant volume

Table 12-1, p.392

Molar Specific Heat, cont

• A gas with a large molar specific heat requires more energy for a given temperature change

• The value depends on the structure of the gas molecule

• The value also depends on the ways the molecule can store energy

Degrees of Freedom

• Each way a gas can store energy is called a degree of freedom

• Each degree of freedom contributes ½ R to the molar specific heat

• See table 12.1 for some Cvvalues

Types of Thermal Processes

• Isobaric ▫ Pressure stays constant ▫ Horizontal line on the PV diagram

• Isovolumetric ▫ Volume stays constant ▫ Vertical line on the PV diagram

• Isothermal ▫ Temperature stays the same

• Adiabatic ▫ No heat is exchanged with the surroundings

Table 12-2, p.399

Isolated System

• An isolated system does not interact with its surroundings

• No energy transfer takes place and no work is done

• Therefore, the internal energy of the isolated system remains constant

Cyclic Processes • A cyclic process is one in which the process

originates and ends at the same state

▫ Uf = Ui and Q = -W

• The net work done per cycle by the gas is equal to the area enclosed by the path representing the process on a PV diagram

Heat Engine

• A heat engine takes in energy by heat and partially converts it to other forms

• In general, a heat engine carries some working substance through a cyclic process

Heat Engine, cont.

• Energy is transferred from a source at a high temperature (Qh)

• Work is done by the engine (Weng)

• Energy is expelled to a source at a lower temperature (Qc)

Heat Engine, cont.

• Since it is a cyclical process, ΔU = 0 ▫ Its initial and final internal

energies are the same

• Therefore, Qnet = Weng • The work done by the

engine equals the net energy absorbed by the engine

• The work is equal to the area enclosed by the curve of the PV diagram

Thermal Efficiency of a Heat Engine

• Thermal efficiency is defined as the ratio of the work done by the engine to the energy absorbed at the higher temperature

• e = 1 (100% efficiency) only if Qc = 0 ▫ No energy expelled to cold reservoir

1eng h c c

h h h

W Q Q Q

Q Q Qe

Heat Pumps and Refrigerators • Heat engines can run in reverse

▫ Energy is injected

▫ Energy is extracted from the cold reservoir

▫ Energy is transferred to the hot reservoir

• This process means the heat engine is running as a heat pump ▫ A refrigerator is a common type of heat pump

▫ An air conditioner is another example of a heat pump

Heat Pump, cont

• The work is what you pay for

• The Qc is the desired benefit

• The coefficient of performance (COP) measures the performance of the heat pump running in cooling mode

Heat Pump, COP

• In cooling mode,

• The higher the number, the better

• A good refrigerator or air conditioner typically has a COP of 5 or 6

cQCOPW

Heat Pump, COP

• In heating mode,

• The heat pump warms the inside of the house by extracting heat from the colder outside air

• Typical values are greater than one

HQCOPW

Second Law of Thermodynamics • No heat engine operating in a cycle can

absorb energy from a reservoir and use it entirely for the performance of an equal amount of work ▫ Kelvin – Planck statement ▫ Means that Qc cannot equal 0 Some Qc must be expelled to the environment

▫ Means that e must be less than 100%

Summary of the First and Second Laws

• First Law

▫ We cannot get a greater amount of energy out of a cyclic process than we put in

• Second Law

▫ We can’t break even

Reversible and Irreversible Processes • A reversible process is one in which every state

along some path is an equilibrium state ▫ And one for which the system can be returned to its

initial state along the same path

• An irreversible process does not meet these requirements ▫ Most natural processes are irreversible

• Reversible process are an idealization, but some real processes are good approximations

Sadi Carnot

• 1796 – 1832 • French Engineer • Founder of the

science of thermodynamics

• First to recognize the relationship between work and heat

Carnot Engine

• A theoretical engine developed by Sadi Carnot • A heat engine operating in an ideal, reversible

cycle (now called a Carnot Cycle) between two reservoirs is the most efficient engine possible

• Carnot’s Theorem: No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs

Carnot Cycle

Carnot Cycle, A to B

• A to B is an isothermal expansion at temperature Th

• The gas is placed in contact with the high temperature reservoir

• The gas absorbs heat Qh • The gas does work WAB

in raising the piston

Carnot Cycle, B to C

• B to C is an adiabatic expansion

• The base of the cylinder is replaced by a thermally nonconducting wall

• No heat enters or leaves the system

• The temperature falls from Th to Tc

• The gas does work WBC

Carnot Cycle, C to D

• The gas is placed in contact with the cold temperature reservoir at temperature Tc

• C to D is an isothermal compression

• The gas expels energy QC

• Work WCD is done on the gas

Carnot Cycle, D to A

• D to A is an adiabatic compression

• The gas is again placed against a thermally nonconducting wall ▫ So no heat is exchanged with

the surroundings

• The temperature of the gas increases from TC to Th

• The work done on the gas is WCD

Carnot Cycle, PV Diagram

• The work done by the engine is shown by the area enclosed by the curve

• The net work is equal to Qh - Qc

Efficiency of a Carnot Engine • Carnot showed that the efficiency of the

engine depends on the temperatures of the reservoirs

• Temperatures must be in Kelvins

• All Carnot engines operating between the same two temperatures will have the same efficiency

h

Cc

T

T1e

Notes About Carnot Efficiency • Efficiency is 0 if Th = Tc • Efficiency is 100% only if Tc = 0 K

▫ Such reservoirs are not available

• The efficiency increases as Tc is lowered and as Th is raised

• In most practical cases, Tc is near room temperature, 300 K ▫ So generally Th is raised to increase efficiency

Real Engines Compared to Carnot

Engines • All real engines are less efficient than the Carnot

engine

▫ Real engines are irreversible because of friction

▫ Real engines are irreversible because they complete cycles in short amounts of time

Perpetual Motion Machines

• A perpetual motion machine would operate continuously without input of energy and without any net increase in entropy

• Perpetual motion machines of the first type would violate the First Law, giving out more energy than was put into the machine

• Perpetual motion machines of the second type would violate the Second Law, possibly by no exhaust

• Perpetual motion machines will never be invented

Heat Death of the Universe

• The entropy of the Universe always increases • The entropy of the Universe should ultimately

reach a maximum ▫ At this time, the Universe will be at a state of uniform

temperature and density ▫ This state of perfect disorder implies no energy will be

available for doing work

• This state is called the heat death of the Universe