Introduction to the second law of thermodynamics on board
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Introduction to the Second Law of Thermodynamics (on board). Heat engine. Thermal efficiency. A cyclic heat engine. : a simple steam power plant. Examples of heat engines. Refrigerators and heat pumps. Coefficient of performance. Heat pump is a device, which

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Introduction to the second law of thermodynamics on board

Introduction to the Second Law of Thermodynamics (on board)


Heat engine

Heat engine

Thermal

efficiency

A cyclic heat engine


Examples of heat engines

: a simple steam power plant

Examples of heat engines


Refrigerators and heat pumps

Refrigerators and heat pumps

Coefficient

of performance

Heat pump is a device, which

operating in a cycle, maintains a

body at a temperature higher than

the surroundings.

Refrigerator is a device, which

operating in a cycle, maintains a

body at a temperature lower than

the temperarature of its surroundings.


Example of a refrigerator

Example of a refrigerator

  • A vapor compression refrigeration system


Introduction to the second law of thermodynamics

Introduction to the Second Law of Thermodynamics


Introducing the second law

Introducing the second law

  • A process should satisfy the first law in order to occur.

  • However, satisfying first law alone does not guarantee that the process will take place.


Examples of impossible processes that do not violate first law

Examples of impossible processes that do not violate first law

  • One more:

  • A cup of coffee does not get hotter

  • in a cooler room by absorbing

  • heat from environment.

Transferring heat to a resistance will not generate

electrical energy

Transferring heat to this paddle-wheel device

will not cause the paddle-wheel to rotate and

raise the mass through the pulley.

Heat


Work was completely converted into heat in joule s experiment

Work was completely converted into heat in Joule’s experiment

Q=W


Some definitions on board discussion

Example of an heat engine: a simple steam power plant

Some definitions (on board/discussion)

  • Thermal energy reservoirs (source and sink)

  • Heat engines

  • Efficiency of a heat engine


Introducing the second law1

Introducing the second law

  • A process should satisfy the first law in order to occur.

  • However, satisfying first law alone does not guarantee that the process will take place.


Examples of impossible processes that do not violate first law1

Examples of impossible processes that do not violate first law

  • One more:

  • A cup of coffee does not get hotter

  • in a cooler room by absorbing

  • heat from environment.

Transferring heat to a resistance will not generate

electrical energy

Transferring heat to this paddle-wheel device

will not cause the paddle-wheel to rotate and

raise the mass through the pulley.

Heat


Statements of the second law

Statements of the second law

  • Two equivalent ways the second law can be stated are due to:

    • Kelvin and Planck (“The Kelvin-Planck statement”)

    • Clausius (“The Clausius statement”).

  • The direction in which processes actually occur can be judged by taking the help of these two statements.

  • Either of this statements can be used to detect impossible inventions and impossible processes.


Outline of our course of progression on second law

Outline of our course of progression on second law

  • DEDUCTION BASED ON either of the Kelvin-Planck and Clausiusstatements will give us the ability to

    C) state second law as an inequality involving engines/refrigerators in contact with more than one reservoirs

    B) Assign temperature values from a non-empirical perspective and

    find the most efficient refrigerators/engines

  • Following step 1, the property entropy will be defined to allow another more mathematical statement of the second law and another way to judge the actual direction of processes.


The kelvin planck statement of the second law

The Kelvin Planck Statement of the Second Law

  • It is impossible for any device that operates in a cycle to receive heat from a single reservoir and produce a net amount of work.

  • Equivalently:

    • “no heat engine can have a thermal efficiency of 100%”.

    • “For a power plant to operate, the working fluid must exchange heat with the environment as well as the furnace.”


A heat engine that violates the kelvin planck statement

A heat engine that violates the Kelvin Planck statement

You need more than one reservoir to convert heat to work by a cyclic engine (a cold reservoir, is needed to dump the heat which could not be converted to work).


Stating the kelvin planck statement analytically

Stating the Kelvin Planck statement analytically

  • The Kelvin-Planck statement do not forbid cyclic devices operating with a single reservoir, but insists that such a cyclic device should receive work.

  • So, according to the Kelvin Planck statement


Clausius statement of the second law of thermodynamics

Clausius statement of the second law of thermodynamics

  • It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower temperature body to a higher temperature body.

  • A refrigerator is not a self-acting device: energy (electrical work to the motor driving the compressor) has to be provided from the surroundings to run a refrigerator.


A refrigerator that violates the clausius statement

A refrigerator that violates the Clausius statement


Equivalence of kelvin planck and clausius statements

Equivalence of Kelvin-Planck and Clausius statements

Violation of Clausius statementViolation of Kelvin-Planck statement

Violation of Kelvin-Planck statementViolation of Clausius statement


Violation of kp violation of clausius

Violation of KP  Violation of Clausius

TH

Q1

Q2

HE!+R

R

Q1

Q1

TC

The net heat exchange of the cyclic

device (HE+R) with the hot reservoir=Q2-Q

TH

Q

=Q1+W

=Q1+Q

W

W

HE!

TC


Violation of clausius violation of kp

Violation of Clausius  Violation of KP

HE+R!+TH

W

Q

Q

W

R!

HE

Q-Q1

Q

Q1

TC

TH

TC

KP statement requires the device in contact with the single reservoir (here at Tc)

to be a cyclic device. Because nothing happens to the TH reservoir (Qin=Qout=Q).

the combined device (HE+R!+TH)is a cyclic device.


Violation of clausius violation of kp alternative

Violation of Clausius  Violation of KP (Alternative)

TH

Q

Q

Q

and Q can be fed directly to H from R

W

W

HE+R!

HE

R!

Q-Q1

Q

Q1

TC

TC

TH can be eliminated


Equivalence of kelvin planck and clausius statements1

Equivalence of Kelvin-Planck and Clausius statements

Violation of Clausius statementViolation of Kelvin-Planck statement

Violation of Kelvin-Planck statementViolation of Clausius statement


Perpetual motion machines pmm

Perpetual motion machines (PMM)

Any device that violates the first or the second law of thermodynamics is called a perpetual motion machine.

Violates the First law: “perpetual machine of the first kind”: produces more energy than supplied.

Violates the Second law: “perpetual motion machine of the second kind”: Allows the efficiency of cyclic heat engines to equal 100%.


Example of a pmm1

Example of a PMM1

OK

Not OK! Produces net

energy output

without energy input.


Identifying pmm2 by kelvin planck clausius statement

Identifying PMM2 by Kelvin-Planck/Clausius statement

Not

OK!

Violates

KP

OK

  • A PMM2 according to Kelvin-Planck statement is a device that:

    • Operates in a cycle.

    • Accepts heat from a single reservoir (surroundings).

    • Develops a net work output.

  • Example: A power plant with no condenser


Identifying pmm2 by clausius statement

Identifying PMM2 by Clausius statement

tH

tC

  • A PMM2 according to Clausius statement is a device whose operation has the sole effect of transfer of

    heat from a low termperature to high temperature body.


How to make the most efficient heat engine

How to make the most efficient heat engine

Second law: no heat engine can have an efficiency of 100%.

So, what is the maximum efficiency?

It turns out (shown later) that maximum efficiency is realized when a heat engine runs on a cycle consisting of certain “idealized processes”.


Reversible process

Reversible process

vacuum

  • Reversible processes can be reversed leaving no trace on the surroundings.

  • If the original process and its reverse is combined into a cycle, after the cycle is executed,

    • both the system and surroundings will return to their original state.

    • If the surroundings can be considered as a single thermal energy reservoir, no net heat and work exchange between the system and surroundings occurs during this cycle.

  • Examples:

    • Pendulum swinging in vacuum (can be studied in mechanical co-orddinates alone)

    • Reversible work (slow or “quasiequilibrium expansion”)

    • Reversible heat transfer (on board)

    • Combinations thereof


Irreversible processes

Irreversible processes

Processes that are not reversible are irreversible.

After an irreversible process is executed, it is impossible to restore both the system and the surroundings to the original state.

All “natural” or “spontaneous” processes are irreversible.


Irreversibilities

Irreversibilities

  • Factors that render a process irreversible are irreversibilities.

  • Examples:

    • Friction

    • Unrestrained expansion, fast expansion/contraction

    • Heat transfer through a finite temperature difference

    • Electric current flow through a resistance

    • Inelastic deformation

    • Mixing of matter with different compositions/states

    • chemical reaction


Introduction to the second law of thermodynamics on board

Characteristics of reversible and irreversible processes

  • Irreversible process

  • In the intermediate stages the system is not in thermodynamic equilibrium.

  • Fast.

  • Driving forces (DT, DP etc. ) between the system and the surroundings and within parts of the system have finite magnitude.

  • Dissipative mechanisms are present.

Reversible process

  • Passes through a succession of thermodynamic equilibrium states.

  • Infinitely slow.

  • Driving forces (DT, DP etc.) between the system and the surroundings and within parts of the system are infinitesimal in magnitude.

  • Dissipative mechanisms (work done on the system incompletely converting to KE/PE change of the system) such as friction, Joule heating, inelastic deformation should be absent.


To show that heat transfer through a finite temperature difference is an irreversible process

To show that heat transfer through a finite temperature difference is an irreversible process

tH

tH

Q1-Q

Q1

W=Q1-Q

H

Q

W=Q1-Q

Q

Violation of Kelvin Planck

statement

tC

Note: Heat transfer through an infinitesimal temperature difference is a reversible

process.


Irreversible processes1

Irreversible processes

Processes that are not reversible are irreversible.

After an irreversible process is executed, it is impossible to restore both the system and the surroundings to the original state.

All “natural” or “spontaneous” processes are irreversible.


Irreversibilities1

Irreversibilities

Factors that render a process irreversible are irreversibilities.

Examples:

Friction

Unrestrained expansion, fast expansion/contraction

Heat transfer through a finite temperature difference

Electric current flow through a resistance

Inelastic deformation

Mixing of matter with different compositions/states

chemical reaction


Irreversibilities2

Irreversibilities

Factors that render a process irreversible are irreversibilities.

Examples:

Friction

Unrestrained expansion, fast expansion/contraction

Heat transfer through a finite temperature difference

Electric current flow through a resistance

Inelastic deformation

Mixing of matter with different compositions/states

chemical reaction


Introduction to the second law of thermodynamics on board

How to conduct a reversible process?

  • To conduct a process reversibly, at every stage of the there should be negligible “driving forces” from “property differentials between system and surroundings” such as DT, DP, D(composition), so that the system is “not driven” out of thermodynamic equilibrium.

  • Reversible processes are therefore very slow.

  • Example:

    • Reversible heat transfer (on board)

    • Reversible expansion/contraction (discussed with respect to quasi-equilibrium process)

The system stays infinitesimally close to thermodynamic equilibrium during a reversible process. In practice, a thermodynamic process can at most approach reversibility With DT0, DP0 etc.


Reversible expansion compression

Reversible expansion/compression

W=nw

One small weight is removed at a time and the gas expands from a a volume Vito a volume Vf (see also discussion on quasi-equilibrium process).

patm

p, V


Usefulness of reversible processes a demonstration

Usefulness of reversible processes: a demonstration

W=nw

Find work done by the system on surroundings when:

Process 1: One small weight is removed at a time and the gas expands from a volume Vito a volume Vf.

Process 2: All of the weights are removed at once from the

piston at t=0 (an irreversible process) expands from a volume Vito a volume Vf

patm

Here, in order to keep the end states same; both processes are

carried out isothermally.

pi , Vi

Note the careful choice of system boundary.

In this diagram,

p=patm is not the

pressure of the system.

Initial state: (pi=patm+W/A,Vi)

Final state: (pf=patm,Vf)

p=patm

p

p=patm

p

V

V


Internal and external irreversibilities

Internal and external irreversibilities

  • Internal irreversibility:

  • Irreversibility located within the system boundaries.

  • External irreversibility:

  • Irreversibility located outside the system boundary; usually in the part of surroundings immediately adjacent to the system boundary.

  • Internally reversible process:

  • An idealization of a process in which no internal irreversibilities are present.

  • (Totally) reversible process:

  • A process with no internal and external irreversibilities.

Another example:

Example: thermal energy reservoirs

undergo internally reversible processes

(add to definition)

Interpretation depends on choice of

system boundary.

Internally reversible process

proceed through a succession of

equilibrium states

=quasi-equilibrium process


Reversible and irreversible processes between two equilibrium states

Reversible and irreversible processes between two equilibrium states

p

Internally Reversible

v

The path of an irreversible process cannot be shown on

a property diagram, since intermediate states are not

equilibrium states. The dotted line (shape does not matter) is

just a convention to represent irreversible processes.


To show that a process is irreversible

To show that a process is irreversible

A process can be shown to be irreversible if it does not conform to the definition of a reversible process

Non-zero energy exchange with the surroundings is required to return the system to initial state.


Example of irreversibility due to lack of equilibrium unrestrained expansion of a gas

Example of irreversibility due to lack of equilibrium: unrestrained expansion of a gas

800 kPa

0 kPa

A

B

A membrane separates a gas in chamber A from vacuum

in chamber B. The membrane is ruptured and the gas expands

Into chamber B until pressure equilibrium is established. The

process is so fast and the container is insulated enough such

that negligible heat transfer takes place between

the gas and the surroundings during this process.

At the end of the unrestrained expansion process, the gas (system) has the same internal energy, as it had initially.


To show that unrestrained expansion is an irreversible process

To show that unrestrained expansion is an irreversible process

0 kPa

800 kPa

400 kPa

System (gas) has

been restored.

Qout

800 kPa

0 kPa

Converting Qout back completely to

work by a cyclic device

is impossible according to

second law; hence the surroundings

cannot be restored.

Vacuum pump

Win


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