Chapter 5
The Second Law of
Thermodynamics
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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
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Mohammad Suliman Abuhaiba, Ph.D., P.E.
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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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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
Inverse process would not take place
spontaneously, even though energy 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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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
Inverse process would not take place
spontaneously, even though energy could be
conserved
Mass would not return spontaneously to its
initial elevation while its internal energy or that
of its surroundings decreased.
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Introducing the 2nd Law Motivating the 2nd Law
Initial condition of a system can be restored,
but not in a spontaneous process.
Some auxiliary devices would be required.
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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
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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Introducing the 2nd Law Motivating the 2nd Law
Opportunities for Developing 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.
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Introducing the 2nd Law Motivating the 2nd Law
Opportunities for Developing Work
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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Introducing the 2nd Law Motivating the 2nd Law
Opportunities for Developing Work
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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Introducing the 2nd Law Motivating the 2nd Law
Opportunities for Developing Work
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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Introducing the 2nd Law Motivating the 2nd Law
Opportunities for Developing Work
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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Introducing the 2nd Law Motivating the 2nd Law
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.
Introducing the 2nd Law Statements of the 2nd Law
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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Introducing the 2nd Law Statements of the 2nd Law
KELVIN–PLANCK STATEMENT
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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Introducing the 2nd Law Statements of the 2nd Law
KELVIN–PLANCK STATEMENT
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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Introducing the 2nd Law Statements of the 2nd Law
KELVIN–PLANCK STATEMENT
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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Identifying irreversibility Irreversible Processes
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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Identifying irreversibility Irreversible Processes
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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Identifying irreversibility Irreversible Processes
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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Applying 2nd Law to Thermodynamic Cycles Power Cycles Interacting with Two Reservoirs
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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Applying 2nd Law to Thermodynamic Cycles 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 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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Applying 2nd Law to Thermodynamic Cycles Refrigeration and Heat Pump Cycles Interacting with Two Reservoirs
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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Applying 2nd Law to Thermodynamic Cycles Refrigeration and Heat Pump Cycles Interacting with Two Reservoirs
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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Maximum Performance Measures for Cycles
Operating Between Two Reservoirs Power Cycles
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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Maximum Performance Measures for Cycles
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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Maximum Performance Measures for Cycles
Operating Between Two Reservoirs Power Cycles
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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Maximum Performance Measures for Cycles
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
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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