Chapter 5site.iugaza.edu.ps/.../12/CH5-The-Second-Law-of-Thermodynamics.pdf · Chapter 5 The Second Law of Thermodynamics 2/1/2015 9:55 PM 1 Mohammad Suliman Abuhaiba, Ph.D., P.E.

Chapter 5

The Second Law of

Thermodynamics

2/1/2015 9:55 PM

Mohammad Suliman Abuhaiba, Ph.D., P.E. 1

Home Work Assignment H15-1

18, 23, 29, 33, 35, 42, 46

Due Monday 2/2/2015

2/1/2015 9:55 PM

Mohammad Suliman Abuhaiba, Ph.D., P.E.

2

Objectives of this chapter

Introduce:

2nd law of thermodynamics (SLT).

Corollaries of 2nd

Performance limits for thermodynamic

cycles

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Introducing the 2nd Law Motivating the 2nd Law

Consider three systems (Fig. 5.1)

Fig. 5.1a: In conformity with conservation of

energy principle, decrease in internal energy of

body would appear as an increase in internal

energy of surroundings.

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Introducing the 2nd Law Motivating the 2nd Law Inverse process would not take place

spontaneously, even though energy could be

conserved

Internal energy of surroundings would not

decrease spontaneously while body warmed from

T0 to its initial temperature.

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System b: Air held at a high pressure pi in a

closed tank would flow spontaneously to lower

pressure surroundings at p0 if valve is opened.

Eventually fluid motions would cease and all of air

would be at same pressure as the surroundings.

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Inverse process would not take place


conserved

Air would not flow spontaneously from

surroundings at p0 into the tank, returning

pressure to its initial value.

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System c: A mass suspended by a cable at elevation zi

would fall when released.

When it comes to rest, potential energy of mass in its

initial condition would appear as an increase in internal

energy of the mass and its surroundings

Eventually, mass also would come to the temperature of

its much larger surroundings.

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Inverse process would not take place


conserved

Mass would not return spontaneously to its

initial elevation while its internal energy or that

of its surroundings decreased.

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Initial condition of a system can be restored,

but not in a spontaneous process.

Some auxiliary devices would be required.

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By such auxiliary means:

object could be reheated to its initial temperature

air could be returned to tank and restored to its

initial pressure

mass could be lifted to its initial height

In each case, a fuel or electrical input normally

would be required for the auxiliary devices to

function.

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Not every process consistent with the

principle of energy conservation can

occur.

Generally, an energy balance alone:

neither enables the preferred direction to be

predicted

nor permits processes that can occur to be

distinguished from those that cannot.

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When left to themselves, systems tend to

undergo spontaneous changes until a

condition of equilibrium is achieved, both

internally and with their surroundings.

In some cases equilibrium is reached quickly

in others it is achieved slowly

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Whether process is rapid or slow, it must of

course satisfy conservation of energy

However, that alone would be insufficient for

determining the final equilibrium state.

Another general principle is required. Second

law.

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Opportunities for Developing Work

Fig. 5.1a: Instead of permitting the body to cool

spontaneously with no other result, energy could

be delivered by heat transfer to a system

undergoing a power cycle that would develop a

net amount of work.

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Fig. 5.1b: instead of permitting the air to expand

aimlessly into the lower-pressure surroundings,

the stream could be passed through a turbine and

work could be developed.

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Fig. 5.1c: instead of permitting the mass to fall in

an uncontrolled way, it could be lowered gradually

while turning a wheel, lifting another mass.

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When an imbalance exists between two

systems, there is an opportunity for developing

work that would be lost if the systems were

allowed to come into equilibrium in an

uncontrolled way.

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Recognizing this possibility for work, we can

pose two questions:

1. What is the theoretical max value for work that could

be obtained?

2. What are the factors that would impede the

realization of max value?

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Devices would be subject to factors such as

friction that would impede the attainment of

the theoretical max work.

2nd law of thermodynamics provides means for

determining theoretical max

evaluating quantitatively factors that impede

attaining the max

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2nd law & deductions provide means for:

1. predicting direction of processes

2. establishing conditions for equilibrium

3. determining best theoretical performance of cycles, engines, and other

devices.

4. evaluating quantitatively factors that impede attainment of best

theoretical performance level.

5. defining a temperature scale independent of properties of any

thermometric substance.

6. developing means for evaluating properties such as u and h in terms of

properties that are more readily obtained experimentally.

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Introducing the 2nd Law Statements of the 2nd Law

CLAUSIUS STATEMENT

It is impossible for any system to operate in

such a way that the sole result would be an

energy transfer by heat from a cooler to a

hotter body.

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It is impossible to construct

a refrigeration cycle that

operates without an input of

work.


KELVIN–PLANCK STATEMENT

A thermal reservoir: a special kind of system that

always remains at constant temperature even though

energy is added or removed by heat transfer.

earth’s atmosphere

large bodies of water (lakes, oceans)

large block of copper

system consisting of two phases (although the ratio of the

masses of the two phases changes as the system is heated or

cooled at constant pressure, the temperature remains constant

as long as both phases coexist).

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Extensive properties of a thermal reservoir

such as internal energy can change in

interactions with other systems even though

the reservoir temperature remains constant.

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A thermodynamic cycle: a sequence of

processes that begins and ends at the same

state.

Over the cycle the system experiences no net

change of state.

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It is impossible for any system to operate

in a thermodynamic cycle and deliver a

net amount of energy by work to its

surroundings while receiving energy by

heat transfer from a single thermal

reservoir.

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Identifying irreversibility Irreversible Processes

An irreversible process: system and all

parts of its surroundings cannot be

exactly restored to their respective initial

states after the process has occurred.

A reversible process: both system and

surroundings can be returned to their

initial states.

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A system that has undergone an irreversible process is not necessarily precluded from being restored to its initial state.

While the system restored to its initial state, it would not be possible also to return the surroundings to the state they were in initially.

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From Clausius statement of 2nd law, any process involving a spontaneous heat transfer from a hotter body to a cooler body is irreversible.

Friction, electrical resistance, hysteresis, and inelastic deformation are examples of effects whose presence during a process renders it irreversible.

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5.2 Identifying irreversibility Irreversible Processes

Irreversibilities can be divided into two

classes:

1. Internal irreversibilities: occur within the

system.

2. External irreversibilities: occur within the

surroundings.

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5.2 Identifying irreversibility Irreversible Processes

Consider two bodies at different temperatures

that are able to communicate thermally.

With a finite temperature difference between

them, a spontaneous heat transfer would take

place and, this would be a source of

irreversibility.

The importance of this irreversibility would

diminish as the temperature difference

approaches zero.

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5.2 Identifying irreversibility IRREVERSIBLE PROCESSES

The transfer of a finite amount of energy by

heat between bodies whose temperatures

differ only slightly would require a

considerable amount of time, a larger heat

transfer surface area, or both.

To eliminate this source of irreversibility,

therefore, would require an infinite amount

of time and/or an infinite surface area.

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Internally Reversible Processes

An internally reversible process: one in which there are

no irreversibilities within the system.

At every intermediate state of an internally reversible

process of a closed system, all intensive properties are

uniform throughout each phase present.

Temperature, pressure, specific volume, and other intensive

properties do not vary with position.

Internally reversible process consists of a series of

equilibrium states: It is a quasiequilibrium process.

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Applying 2nd Law to Thermodynamic Cycles Power Cycles Interacting with Two Reservoirs

Thermal efficiency of cycle is

If value of QC were zero,

system would withdraw

energy QH from hot reservoir

and produce an equal

amount of work, while

undergoing a cycle. Thermal

efficiency of such a cycle

would be 100%.

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This method of operation

would violate Kelvin–Planck

statement and thus is not

allowed.

For any system executing a

power cycle while operating

between two reservoirs, only

a portion of QH can be

obtained as work, and the

remainder, QC, must be

discharged by heat transfer

to the cold reservoir.

Thermal efficiency < 100%

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CARNOT COROLLARIES

1. Thermal efficiency of an irreversible power

cycle is always less than thermal efficiency

of a reversible power cycle when each

operates between same two thermal

reservoirs.

2. All reversible power cycles operating

between same two thermal reservoirs have

same thermal efficiency.

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Applying 2nd Law to Thermodynamic Cycles Refrigeration and Heat Pump Cycles Interacting with Two Reservoirs

Coefficient of performance

of a refrigeration cycle

Coefficient of performance

for a heat pump cycle is

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As Wcycle tends to zero, coefficients of

performance approach infinity.

If Wcycle were identically zero, system would

withdraw energy QC from the cold reservoir

and deliver energy QC to the hot reservoir,

while undergoing a cycle.

This method of operation would violate

Clausius statement of 2nd law and thus is not

allowed.

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Corollaries for Refrigeration & Heat Pump Cycles

COP of an irreversible refrigeration cycle is

always less than COP of a reversible

refrigeration cycle when each operates

between same two thermal reservoirs.

All reversible refrigeration cycles operating

between same two thermal reservoirs have

same COP.

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Maximum Performance Measures for Cycles

Operating Between Two Reservoirs Power Cycles

Thermal efficiency of a system

undergoing a reversible power

cycle while operating between

thermal reservoirs at

temperatures TH and TC.

Carnot efficiency increases as TH

increases and/or TC decreases.

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Possibility of increasing thermal

efficiency by reducing TC below

that of the environment is not

practical,

For maintaining TC lower than

ambient temperature would

require a refrigerator that

would have to be supplied work

to operate.

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Operating Between Two Reservoirs 5.5.1 Power Cycles

Referring to segment a–b of

the curve, where TH and h

are relatively low,

h increases rapidly as TH

increases,

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Thermal efficiencies of

actual cycles increase as

average temperature at

which energy is added by

heat transfer increases

and/or average temperature

at which energy is

discharged by heat transfer

is reduced.

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Operating Between Two Reservoirs Refrigeration and Heat Pump Cycles

COP of any system undergoing a reversible

refrigeration cycle while operating between

the two reservoirs

COP of any system undergoing a reversible

heat pump cycle while operating between

the two reservoirs

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EXAMPLE 5.1

Evaluating a Power Cycle Performance Claim

An inventor claims to have developed a power cycle

capable of delivering a net work output of 410 kJ for an

energy input by heat transfer of 1000 kJ. The system

undergoing the cycle receives the heat transfer from hot

gases at a temperature of 500 K and discharges energy by

heat transfer to the atmosphere at 300 K. Evaluate this

claim.

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EXAMPLE 5.2

Evaluating Refrigerator Performance

By steadily circulating a refrigerant at

low temperature through passages in

the walls of freezer compartment, a

refrigerator maintains freezer

compartment at -5°C when air

surrounding refrigerator is at 22°C.

The rate of heat transfer from freezer

compartment to refrigerant is 8000

kJ/h and power input required to

operate the refrigerator is 3200 kJ/h.

Determine COP of refrigerator and

compare with COP of a reversible

refrigeration cycle operating between

reservoirs at the same two

temperatures.

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EXAMPLE 5.3 Evaluating Heat Pump Performance

A dwelling requires 5×105 kJ per day to maintain

its temperature at 22°C when the outside

temperature is 10°C. If an electric heat pump is

used to supply this energy, determine the

minimum theoretical work input for one day of

operation, in kJ.

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Carnot Cycle

a reversible power

cycle operating

between two thermal

reservoirs.

The system is a gas

in a piston cylinder

assembly.

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Carnot Cycle

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Carnot Cycle

Area under adiabatic process line 1–2 = work

done per unit of mass to compress the gas.

Areas under process lines 2–3 and 3–4 =

work done per unit of mass by the gas as it

expands in these processes.

Area under process line 4–1 = work done per

unit of mass to compress the gas.

The enclosed area on p–v diagram = net work

developed by the cycle per unit of mass.

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Carnot Cycle

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Chapter 5site.iugaza.edu.ps/.../12/CH5-The-Second-Law-of-Thermodynamics.pdf · Chapter 5 The Second Law of Thermodynamics 2/1/2015 9:55 PM 1 Mohammad Suliman Abuhaiba, Ph.D., P.E.

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