The Second Law of Thermodynamics

Chapter 6

The Second Law

The second law of thermodynamics states that processes occur in a certain direction, not in just any direction.

Physical processes in nature proceed toward equilibrium spontaneously:

Water always flows downhill

Gases always expand from high pressure to low pressure

Heat always flows from high temperature to low temperature

We can reverse these processes

It requires the expenditure of workThe first law gives us no information

about the direction in which a process occurs – it only tells us that energy must balance

The second law tells us in what direction processes occur

Work Always Converts Directly and Completely to Heat, But not the ReverseWork Always Converts Directly and Completely to Heat, But not the Reverse

Work and Heat are not interchangeable forms of energy

We need a device to convert heat to work

Some Definitions

Heat ReservoirSourceSinkProvides heat energy, but does not

change temperature

Some Definitions

Thermodynamic CycleSystem returns to the initial conditionsThe initial state is the same as the final

state

Some Definitions

Heat Engine A heat engine is a thermodynamic system

operating in a thermodynamic cycle to which net heat is transferred and from which net work is delivered

This is the device that converts heat to work

A steam power plant is a heat engine

Some Definitions

Thermal Efficiency Index of performance of a deviceWhat you want over what you have to pay

for

input required

output desiredth

For a heat engine

in

outnetth Q

W ,

Sign Conventions

When we talk about engines, we generally dispense with our sign conventions

All the energy terms are positiveWe determine the direction of flow based

on the situation, and label carefully

inoutoutnet WWW ,

Cyclic heat engines operate between a high temperature source and a low temperature sink

For a cyclic heat engine

0,, UWQ outnetinnet

innetoutnet QW ,, outin QQ

in

outnet

Q

W ,in

outin

Q

QQ

in

out

Q

Q1

H

L

Q

Q1

Even the Most Efficient Heat Engines Reject Most Heat as Waste Heat

Even the Most Efficient Heat Engines Reject Most Heat as Waste Heat

4.0100

40thn

Steam power plants run at about 40% efficiency

A Heat-Engine Cycle Must Reject Some Heat to a Low-Temperature SinkA Heat-Engine Cycle Must Reject Some Heat to a Low-Temperature Sink

5-5

A heat-engine cycle cannot be completed without rejecting some heat to a low-temperature sink

Kelvin-Planck Statement of the Second Law

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

The Kelvin-Planck statement of the second law of thermodynamics states that no heat engine can produce a net amount of work while exchanging heat with a single reservoir only. In other words, the maximum possible efficiency is less than 100%.

Some Mechanical Devices accept work as input, and move heat from low to high temperaturesHeat PumpRefrigerators and Air

Conditioners

Heat always flows spontaneously from hot to cold

Heat pumps and refrigerators differ in their intended use. They work the same

net

LR W

QCOP

For a refrigerator or air conditioner

For a heat pump

net

HHP W

QCOP

COP

We use coefficient of performance (COP) instead of efficiency () for heat pumps and refrigerators

COP can be greater than 1 for refrigerators

It is always greater than 1 for heat pumps

COP Refrigerators

net

LR W

QCOP But what is Wnet

equal to?

LHnet QQW Substituting in…

LH

LR QQ

QCOP

1

1

LH QQ

Since QH is always greater than QL, COP can be greater than one, but only when QH /QL is less than 2

COP Heat Pumps

net

HHP W

QCOP But what is Wnet

equal to?

LHnet QQW Substituting in…

LH

HHP QQ

QCOP

HL QQ

1

1

Since QL is always less than QH, COP is always greater than 1

Clausius Statement of the Second Law

 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.

Energy from the surroundings in the form of work or heat has to be expended to force heat to flow from a low-temperature media to a high-temperature media. Thus, the COP of a refrigerator or heat pump must be less than infinity.

Perpetual Motion MachinesAny device that violates the first or second

law is called a perpetual motion machine

If it violates the first law, it is a perpetual motion machine of the first type (PMM1)

If it violates the second law, it is a perpetual motion machine of the second type (PMM2)

Perpetual Motion Machines are not possible

Reversible ProcessesHeat pumps, refrigerators and heat engines

all work best reversiblyReversible processes don’t have any losses

such as Friction Unrestrained expansion of gases Heat transfer through a finite temperature difference Mixing of two different substances Any deviation from a quasistatic process

Internally Reversible Process

 

The internally reversible process is a quasiequilibrium process, which once having taken place, can be reversed and in so doing leave no change in the system. This says nothing about what happens to the surroundings around the system.

Totally or Externally Reversible Process

The externally reversible process is a quasiequilibrium process, which once having taken place, can be reversed and in so doing leaves no change in the system or surroundings.

All real processes are irreversible!!

So why should we worry about reversible processes?

Reversible processes represent the best that we can do.

Carnot Cycle

Named for French engineer Nicolas Sadi Carnot (1769-1832)

One example of a reversible cycle

Nicolas Sadi Carnot

French Physicist Developed the

theory of heat engines

http://scienceworld.wolfram.com/biography/CarnotSadi.html

Carnot Cycle

Composed of four reversible processes 2 adiabatic expansion or compression 2 reversible isothermal heat transfer

Carnot Cycle Process 1-2 Reversible isothermal heat addition at high

temperature

Process 2-3 Reversible adiabatic expansion during which the system does work and the working fluid temperature changes from TH to TL

Process 3-4 Reversible isothermal heat exchange takes place while work of compression is done on the system.

Process 4-1 A reversible adiabatic compression process increases the working fluid temperature from TL to TH

Process 1-2 Reversible isothermal heat addition at high temperature, TH > TL to the working fluid in a piston-cylinder device which does some boundary work.

Pre

ssu

reSpecific Volume

1

QHTH=constan

t2

Process 2-3 Reversible adiabatic expansion during which the system does work as the working fluid temperature decreases from TH to TL.

Pre

ssu

reSpecific Volume

1

QHTH=constan

t2

3

Process 3-4 The system is brought in contact with a heat reservoir at TL < TH and a reversible isothermal heat exchange takes place while work of compression is done on the system.

Pre

ssure

Specific Volume

1

QHTH=constan

t2

34 QL

TL=constan

t

Process 4-1 A reversible adiabatic compression process increases the working fluid temperature from TL to TH

Pre

ssure

Specific Volume

1

QHTH=constan

t2

34 QL

TL=constan

t

Execution of the Carnot Cycle in a Closed SystemExecution of the Carnot Cycle in a Closed System

The Carnot cycle is a reversible heat engine

The area inside the figure represents the work

IsothermalIsothermal

Adiabatic Adiabatic

Reversed Carnot CycleA reversed Carnot Cycle is a refrigerator or a heat pump

Efficiency of a Carnot Engine

For a reversible cycle the amount of heat transferred is proportional to the temperature of the reservoir

H

Lrev Q

Q1

H

L

T

T1

Only true for the reversible case

COP of a Reversible Heat Pump and a Reversible Refrigerator

HLrevHP QQ

COP

1

1,

HL TT

1

1

1

1,

LH

revR QQCOP

1

1

LH TT

Only true for the reversible case

How do Reversible and Real Systems Compare?

The efficiency of a reversible heat engine, such as a Carnot engine, is always higher than a real engine

The COP of a reversible heat pump is always higher than a real heat pump

The COP of a reversible refrigerator is always higher than a real refrigerator

Carnot Principle

The thermal efficiency of all reversible heat engines operating between the same two reservoirs is the same

No heat engine is more efficient than a reversible heat engine

SummarySecond LawSummarySecond Law

•The second law of thermodynamics states that processes occur in a certain direction, not in any direction.

•A process will not occur unless it satisfies both the first and the second laws of thermodynamics. •Bodies that can absorb or reject finite amounts of heat isothermally are called thermal energy

reservoirs or heat reservoirs.

SummaryHeat EnginesSummaryHeat Engines

• Work can be converted to heat directly, but heat can be converted to work only by some devices called heat engines.

SummaryThermal EfficiencySummaryThermal Efficiency

• The thermal efficiency of a heat engine is defined as

where Wnet, is the net work output of the heat engine, QH is the amount of heat supplied to the engine, and QL is the amount of heat rejected by the engine.

SummaryRefrigerators and Heat PumpsSummaryRefrigerators and Heat Pumps

• Refrigerators and heat pumps are devices that absorb heat from low-temperature media and reject it to higher-temperature ones.

• The performance of a refrigerator or a heat pump is expressed in terms of the coefficient of performance.

SummaryKelvin-Plank StatementSummaryKelvin-Plank Statement• The Kelvin -Planck statement of the second law of thermodynamics

states that no heat engine can produce a net amount of work while exchanging heat with a single reservoir only.

SummaryClausius StatementSummaryClausius Statement

• The Clausius statement of the second law states that no device can transfer heat from a cooler body to a warmer one without leaving an effect on the surroundings.

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

SummaryReversible vs. IrreversibleSummaryReversible vs. Irreversible

• A process is said to be reversible if both the system and the surroundings can be restored to their original conditions.

• Any other process is irreversible.

SummaryIrreversibilities

Effects such as

• friction • non-quasi-equilibrium expansion or

compression• heat transfer through a finite temperature

difference

render a process irreversible and are called irreversibilities.

SummaryCarnot CycleSummaryCarnot Cycle

The Carnot cycle is a reversible cycle that is composed of four reversible processes, two isothermal and two adiabatic.

SummaryCarnot PrincipleSummaryCarnot Principle

•The Carnot principles state that the thermal efficiencies of all reversible heat engines operating between the same two reservoirs are the same, and that no heat engine is more efficient than a reversible one operating between the same two reservoirs.

SummaryThermodynamic Temperature ScaleSummaryThermodynamic Temperature Scale

• Based on heat transfer between a reversible device and the high- and low-temperature reservoirs.

• The QH/QL ratio can be replaced by TH/TL for reversible devices, where TH and TL are the absolute temperatures of the high- and low-temperature reservoirs, respectively.

SummaryEfficiency of a Carnot EngineSummaryEfficiency of a Carnot Engine

• A heat engine that operates on the reversible Carnot cycle is called a Carnot heat engine. The thermal efficiency of a Carnot heat engine, as well as all other reversible heat engines, is given by …

• This is the maximum efficiency a heat engine operating between two reservoirs at temperatures TH and TL can have.

SummaryCOP of reversible refrigerator and heat engine

SummaryCOP of reversible refrigerator and heat engine