chapter 5site.iugaza.edu.ps/.../2012/01/ch5-the-second-law-of-thermodyna… · 5.1 introducing the...

Chapter 5

The Second Law of

Thermodynamics

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Dr. Mohammad Abuhaiba, PE 1

Objectives of this chapter

Introduce 2nd law of

thermodynamics (SLT).

Corollaries of 2nd law are also

considered, including performance

limits for thermodynamic cycles.

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Dr. Mohammad Abuhaiba, PE

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5.1 Introducing the 2nd Law 5.1.1 Motivating the 2nd Law

Consider the three systems pictured in Fig. 5.1.

Fig. 5.1a: In conformity with the conservation of energy principle, the decrease

in internal energy of body would appear as an increase in internal energy of

surroundings.

The inverse process would not take place spontaneously, even though energy

could be conserved: The 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 the interconnecting valve were opened.

Eventually fluid motions would cease and all of air would be at same pressure as

the surroundings.


could be 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 the internal energy of the mass and its surroundings, in

accordance with the conservation of energy principle.

Eventually, mass also would come to the temperature of its much larger

surroundings.


could be conserved: The 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.

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

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.

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.

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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OPPORTUNITIES FOR DEVELOPING WORK

When an imbalance exists between two systems, there is an opportunity

for developing work that would be irrevocably lost if the systems were

allowed to come into equilibrium in an uncontrolled way.

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 preclude the realization of max value?

Devices would be subject to factors such as friction that would preclude

the attainment of the theoretical max work.

2nd law of thermodynamics provides means for determining theoretical

max and evaluating quantitatively factors that preclude attaining the max.

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SECOND LAW SUMMARY

2nd law & deductions are useful because they 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 preclude 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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5.1 Introducing the 2nd Law 5.1.2 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.

It is impossible to construct a refrigeration cycle that operates

without an input of work.

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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).

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.

At the conclusion of a cycle all properties have the

same values they had at the beginning.

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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1st and 2nd laws each impose constraints:

1st law: According to the cycle energy

balance

Although the cycle energy balance allows

the net work Wcycle to be positive or

negative, the 2nd law imposes a constraint

on its direction.

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A system undergoing a cycle while communicating

thermally with a single reservoir cannot deliver a net

amount of work to its surroundings. That is, the net

work of the cycle cannot be positive.

Analytical form of the Kelvin–Planck statement

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5.2 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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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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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.

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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Irreversibility of the process can be demonstrated using

Kelvin–Planck statement of 2nd law and the following

procedure:

1. Assume there is a way to return the system and

surroundings to their respective initial states.

2. It would be possible to devise a cycle that produces

work while no effect occurs other than a heat transfer

from a single reservoir. Since the existence of such a

cycle is denied by Kelvin–Planck statement, initial

assumption must be in error and it follows that the

process is irreversible.

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5.2 Identifying irreversibility REVERSIBLE PROCESSES

A process of a system is reversible if

the system and all parts of its

surroundings can be exactly restored

to their respective initial states after

the process has taken place.

The passage of a gas through a

properly designed nozzle or diffuser

is an example.

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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 5.3.1 Interpreting the Kelvin–Planck Statement

“

Applying 2nd Law to Thermodynamic Cycles 5.3.2 Power Cycles Interacting with Two Reservoirs

Thermal efficiency of cycle is

If value of QC were zero, the 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%.

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 must be less than 100%.

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Applying 2nd Law to Thermodynamic Cycles 5.3.2 Power Cycles Interacting with Two Reservoirs

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 5.3.3 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

Coefficient of performance of an irreversible

refrigeration cycle is always less than

coefficient of performance 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 coefficient of performance.

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Maximum Performance Measures for Cycles

Operating Between Two Reservoirs 5.5.1 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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Referring to segment a–b of the curve, where TH and h are relatively low,

h increases rapidly as TH increases, even a small increase in TH can have a large effect on efficiency.

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 5.5.2 Refrigeration and Heat Pump Cycles

Coefficient of performance of any system

undergoing a reversible refrigeration cycle while

operating between the two reservoirs

Coefficient of performance 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 coefficient of performance of refrigerator and compare with coefficient of performance 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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Home Work Assignment H15-1

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

Due Saturday 28/4/2012

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chapter 5site.iugaza.edu.ps/.../2012/01/ch5-the-second-law-of-thermodyna… · 5.1 introducing the...

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