The Laws of Thermodynamics

The Zeroth Law of Thermodynamics

“If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.”

This allows the design & the use of Thermometers!

The First Law of ThermodynamicsQ = ∆Ē + W

For Infinitesimal, Quasi-Static Processes

đQ = dĒ + đW

Total Energy is Conserved

Heat absorbed by the system

Work done by the systemChange in the system’s

internal energy

“Energy can neither be created nor destroyed. It can only be changed from one form to another.”

Rudolf Clausius, 1850

(courtesy F. Remer)

• The 1st Law of Thermodynamics is

Conservation of Total Energy!!!! • It says nothing about

The Direction of Energy Transfer!

(courtesy F. Remer)

The Second Law of Thermodynamics “The entropy of an isolated system increases in any

irreversible process and is unaltered in any reversible process.”

• This is sometimes called

The Principle of Increasing Entropy S 0• This gives the Preferred (natural)

Direction of Energy Transfer• This determines whether a process can occur or not.

Change in entropy of the system

Historical Comments• Much early thermodynamics development was driven by practical considerations.• For example, building heat engines & refrigerators.

• So, the original statements of the

Second Law of Thermodynamicsmay seem different than that just mentioned.

Various Statements of the Second Law1. “No series of processes is possible whose sole

result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work.” That is

There are no perfect engines!2. “It will arouse changes while the heat transfers

from a low temperature object to a high temperature object.”

Rudolf Clausius’statement of the Second Law.

Strange sounding?

3. “It will arouse other changes while the heat from the single thermal source is taken out and is totally changed into work.”

4. “It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir.”

Lord Kelvin’s (William Thompson’s) statement of the Second Law.

The Kelvin-Planck statement of the Second Law.

Heat Engine A system that can convert some of the random molecular energy of heat flow into macroscopic mechanical energy.

QH HEAT absorbed by a Heat Engine from a

hot body

-W WORK performed by a Heat Engine on the surroundings

-QC HEAT emitted by Heat Engine to a cold body

The Second Law Applied to Heat Engines

Efficiency= (W/QH) = [(QH - QC)/QH]

A “Heat Engine” That Violates the Second Law

Heat Reservoir

Heat q

Cyclic Machine

Work Output=q

Refrigerator A system that can do macroscopic work to extract heat from a cold body and exhaust it to a hot body, thus cooling the cold

body further. A system that operates like a Heat Engine in reverse.

QC HEAT extracted by a Refrigerator from a cold body

W WORK performed by a Refrigerator on the surroundings

-QH HEAT emitted by a Refrigerator to a hot body

The 2nd Law of ThermodynamicsClausius’ statement for Refrigerators

• “It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object.”

There are no perfect Refrigerators!• This statement about refrigerators also applies to air

conditioners and heat pumps which use the same principles.

The Second Law Applied to Refrigerators

Efficiency= (QC/W) = [(QC)/(QH - QC)]

The 2nd Law of Thermodynamics can be used to classify

Thermodynamic Processes into 3 Types:

1. Natural Processes (or Irreversible Processes,

or Spontaneous Processes)

2. Impossible Processes

3. Reversible Processes

We’ll discuss each more thoroughly with examples soon.

(courtesy F. Remer)

The Third Law of Thermodynamics

“It is impossible to reach a temperature of absolute zero.”

On the Kelvin Temperature Scale,

T = 0 K is often referred to as

“Absolute Zero”

“The entropy of a true equilibrium state of a system at T = 0 K is zero.”

(Strictly speaking, this is true only if the quantum mechanical ground state is non-degenerate. If it is degenerate,

the entropy at T = 0 K is a small constant, not 0!)

This is Equivalent to:“It is impossible to reduce the temperature of a

system to T = 0 K using a finite number of processes.”

Another Statement of The Third Law of Thermodynamics

Some Popular Versions of The Laws of Thermodynamics

1st Law: You can’t win.

2nd Law: You can’t break even.

3rd Law: There’s no point in trying.

Version 1

Zeroth Law: You must play the game.

First Law: You can't win the game.

Second Law: You can't break even in the game.

Third Law: You can't quit the game.

Version 2

Zeroth Law: You must play the game.

First Law: You can't win the game, you can only break even.

Second Law: You can only break even at absolute zero.

Third Law: You can't reach absolute zero.

Other Popular Versions of The Laws of Thermodynamics

Version 3

Zeroth Law: You must play the game.

First Law: You can't win the game.

Second Law: You can't break even except on a very cold day.

Third Law: It never gets that cold!

Version 4

Zeroth Law: There is a game.

First Law: You can't win the game.

Second Law: You must lose the game.

Third Law: You can't quit the game.

“Murphy's Law of Thermodynamics”

Things get worse under pressure!!

From Statistical Arguments we’ve seen that a Quantitative Definition of

Entropy is S kBln()

kB Boltzmann’s constant = (E) Number of

microstates at a given energy

Spontaneous Processes & EntropySpontaneous Processes

Processes that can proceed with no outside intervention

Entropy• In qualitative terms, Entropy can be

viewed as a measure of the randomness or disorder of the atoms & molecules in a system.

2nd Law of ThermodynamicsTotal Entropy always increases in a

spontaneous process!

So, Microscopic Disorder also increases in a

spontaneous process!

Spontaneous ProcessesSpontaneous Processes

Processes that can proceed with no outside intervention.

• Example in the figure: Due to the

2nd Law of Thermodynamicsthe gas in container B will spontaneously

effuse into container A. But, once the gas is in both containers,

it will notspontaneously effuse back into container B.

Processes that are spontaneous in one direction are not

spontaneous in the reverse direction.

Example in the figure: Due to the

2nd Law of Thermodynamicsthe shiny nail in the top figure will, over a long time, rust & eventually look as in the bottom figure. But, if the nail is rusty,

it will not spontaneously become shiny again!!

The 2nd Law of Thermodynamics

• Processes that are spontaneous at one temperature may be non-spontaneous at other temperatures.

• Example in the figure:

For T > 0C ice will melt spontaneously.

For T < 0C, the reverse process is spontaneous.

Irreversible Processes

Irreversible Processes Processes that cannot be undone by exactly reversing the process.

All Spontaneous Processes are Irreversible.

All Real processes are Irreversible.

1. Due to frictional effects, mechanical work changes into heat automatically.

2. Gas inflates toward vacuum.

3. Heat transfers from a high temperature object to a low temperature object.

4. Two solutions of different concentrations are put together and mixed uniformly.

Note!!The 2nd Law of Thermodynamics says that the opposite processes of these cannot proceed automatically. In order to take a system back to it’s initial state, external work must be done on it.

Examples of Spontaneous, Irreversible Processes

Spontaneous Processes (changes): Once the process begins, it proceeds automatically without the need to do work on the system.

• The opposite of every Spontaneous Process is a

Non-Spontaneous Processthat can only proceed if external work is done on the system.

Reversible Processes• In a

Reversible Process,the system undergoes changes such that the system plus it’s surroundings can be put back in their original states by exactly reversing the process.

• In a

Reversible Process,changes proceed in infinitesimally small steps, so that the system is infinitesimally close to equilibrium at every step. This is obviously an idealization & can never happen in a real system!

Another Statement of the 2nd Law of Thermodynamics

“The entropy of the universe does not change for Reversible Processes” and also:

“The entropy of the universe increases for Spontaneous Processes” “You can’t break even”.

For Reversible (ideal) Processes:

For Irreversible (real, spontaneous) Processes:

Still Another Statement of the 2nd Law of Thermodynamics

“In any spontaneous process, there is always an increase in the entropy of the

universe.”

The Total Entropy S of the Universe has the property that, for any process,

∆S ≥ 0.

Free Expansion of a Gas• The container on the right is filled with gas. The

container on the left is vacuum. The valve between them is closed. Now, imagine that the valve is opened.

ValveClosedVacuumVacuum GasGas

(courtesy F. Remer)

More Examples of Spontaneous Processes

ValveOpen GasGas

The Entropy Increases!!!!

After some time, there is a new

EquilibriumGasGas

(courtesy F. Remer)

Free Expansion of a Gas• After the valve is opened, for some time, it is no longer an

equilibrium situation. The 2nd Law says the molecules on the right will flow to the left. After a sufficient time, a new equilibrium is reached & the molecules are uniformly distributed between the 2 containers.

Thermal Conduction• A hot object (red) is brought into thermal contact with a

colder object (blue). The 2nd Law says that heat đQ will flow from the hot object to the colder object.

Hot ColdđQ

(courtesy F. Remer)

Warm

(courtesy F. Remer)

• After the 2 objects are brought into thermal contact, for some time, by the 2nd Law, heat đQ flows from the hot object to the colder object. During that time, it is no longer an equilibrium situation. After a sufficient time, a new equilibrium is reached & the 2 objects are at the same temperature.

After some time, there is a new

Equilibrium

The Entropy Increases!!!!

(courtesy F. Remer)

Just before hitting the ground,

E = KE = (½)mv2

Mechanical Energy E is conserved!

Mechanical Energy to Internal Energy Conversion• Consider a ball of mass m. It’s Mechanical Energy is defined as

E = KE + PE. KE = Kinetic Energy, PE = Potential Energy.

• For conservative forces, E is conserved (a constant).

• Drop the ball from rest at a height h above the ground.

h

Initially, E = PE =

mgh

Conservation of Mechanical Energy

tells us that mgh =

(½)mv2

(courtesy F. Remer)

• At the bottom of it’s fall, the ball collides with the ground & bounces upward. If it has an Elastic Collision with the ground, by

definition, right after it has started up, its mechanical & kinetic energies would be the same as just before it hit:

E = (½)mv2 = mgh• In reality, the Collision will be Inelastic. So, the initial upward kinetic energy, KE', will be less than KE just

before it hit.

Just before hitting the ground,

KE = (½)mv2.

The collision is Inelastic, so right after it bounces,

its kinetic energy is

KE' < KE.

Where did the lost KE go? It is converted to heat, which changes the internal energy Ē of the ball. As a result, the ball heats up!!

(courtesy F. Remer)

The ball’s collision with the ground is inelastic, so it loses some kinetic energy: KE' < KE. The lost kinetic energy is converted to heat, which changes the ball’s internal energy Ē.

So, the ball gets warmer!! In Ch. 4, we’ll show that, for an infinitesimal, quasi-static process in which an object heats up, changing its temperature by an amount dT, it’s internal energy change is dĒ = mcVdT

m ≡ ball’s mass & cV ≡ specific heat at constant volume

KE = (½)mv2 KE' < KE

The change in the ball’s internal energy is

dĒ = mcVdT

Multiple Bounces of the ball Multiple Inelastic Collisions with the ground.

When it finally comes to rest after several bounces,it may be MUCH warmer than when it was dropped!

The ball loses more KE on each bounce & it eventually stops on the ground. Thus, after sufficient time, it tends towards Equilibrium

The more bounces the ball has, the warmer it gets!

(courtesy F. Remer)

The Ball’s Entropy Increases!!!!

Brief Discussion of

“Impossible Processes” • Processes which are

allowed by the 1st Law of Thermodynamics

but which Cannot Occur Naturallybecause they would violate the 2nd Law of Thermodynamics.

• Any process which would take a system from an equilibrium state to a non-equilibrium state without work being done on the system would violate the 2nd Law of Thermodynamics & thus would be an Impossible Process!

(courtesy F. Remer)

Examples of Impossible Processes• Example 1: “Free Compression” of a Gas!

ValveOpen GasGasGas

(courtesy F. Remer)

Initially, the valve is open & gas molecules are uniformly distributed in the 2 containers.

Vacuum ValveOpen

Gas

After some time, all gas molecules are gathered in the right container & the left container is empty.

The Entropy Decreases!!

Thermal Conduction

Warm

(courtesy F. Remer)

Initially, an object is warm.

After some time, the left side is hot & the right side is cold .

Hot Cold

The Entropy Decreases!!

(courtesy F. Remer)

Conversion of Internal Energy to Mechanical Energy

Initially, a ball is on the ground

& is hot.

Hot

After some time, the ball begins to move upward with kinetic energy KE = (½) mv2 & it cools down!

Warm

The Entropy Decreases!!

Impossible Processes

Cannot occur without the input of work

đW

(courtesy F. Remer)

• In such a process, the System’s Entropy Decreases, but the Total Entropy of the System + Environment Increases

đW

Decrease in Entropy

Increase in Entropy

Environment

(courtesy F. Remer)