Download JIF 314 Thermodynamics

JIF 314
Thermodynamics
Chapter 6
The second law of thermodynamics
Conversion of work into heat and vice
versa
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Consider a heat engine. A heat engine is one that
turns heat into work in a cyclic manner.
The heat engine interacts thermally with the
surroundings, which consists of a high-temperature
reservoir, HTR (at constant temperature TH), and a
low-temperature reservoir, LTR (at constant
temperature TH).
The heat engine system at initial state i absorbs heat
by the amount |QH| from HTR, turning part of this
heat into work |W|, and the balance of heat,
|QL| =|QH| -|W|,
is rejected into the LTR.
After the rejection of |QL|, the heat engine’s state will
resume to the initial state i.
Heat engine operating in a cycle
High-temperature reservoir at TH
|QH| is absorbed by system from HTR
state i
Intermediate
state m1
Intermediate
state m2
|QL| is rejected by system to LTR
Low-temperature reservoir at TL
|W| work is done by
system as an output
Thermal efficiency of a heat engine
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At the end of a complete cycle, dU =0 (since the
state of a heat engine returns to its initial one at
the conclusion of the cycle)
Thermal efficiency = work output/heat input

W
QH

QH  QL
QH
 1
QL
QH
due to first law
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Thermal efficiency will be 100% only if |QL|=0
Kelvin-Planck statement of the second
law
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“It is impossible to construct an engine that,
operating in a cycle, will produce no effect other
than the extraction of heat from a reservoir and the
performance of an equivalent amount of work”
In plain language, it means it is impossible to have a
machine that can convert totally all heat absorbed
from a HTR into work without rejecting any heat
back to the LTR.
The conversion of heat into work must associated
with at least certain minimal effect such a rejection
of heat into LTR.
Consequence of Kelvin-Planck statement
to heat engine
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Heat engine could never achieve 100%
efficiency since |QL| can never be zero.
Example of heat engines: The gasoline
engine
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6 processes, out of which 4 are ‘strokes’, 2 are heat
transfer processes.
Otto cycle describes an idealised gasoline engine
Referring to the Otto cycle, the states transition are in
the sequence …12  3  4  5 1…
The subsequent states are connected via
thermodynamic equations
51, 1  5, P0V=nRT1
12, adiabatic compression, T1V1g1T2V2g1
T
23, heat absorbed |QH|= T CV dT
34, adiabatic expansion, T3V2g1T4V1g1
T
41, heat rejected |QL|= T CV dT
4
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3
4
1
Figure 6-1
Thermal efficiency of Otto heat
engine
T1
  1
T2
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Real gasoline engine would have a much
less the efficiency of the idealised Otto
engine, which set the upper limit of the
thermal efficiency to any real gasoline engine
Air-standard idealised diesel engine
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In comparison to gasoline engine, the process 23 of
an air-standard diesel engine is an isobaric heat
absorption while the volume expands quasi-statically
23 is a horizontal line in Otto’s while it’s a vertical
line in Diesel’s.
For idealised Diesel Engine,


T
  1
 1
 ;r
g T  T 
g  r  1 T
1T4  T4 
1 rEg  1
1
E
3
2
E
2
V1

V3
Figure 6-2
The steam engine
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Figure 6-3(a), 6-3(b)
The steam engine
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Figure 6-3(a), 6-3(b)
Refrigerator
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The reverse of a heat engine is a refrigerator
– it absorbs heat |QL| from a LTR by pumping
work |W| into the system, and then ejects
heat of the amount |QH| to HTR.
For a refrigerator, |QL|+|W|=|QH|
A refrigerator is to extract as much heat |QL|
as possible from the LTR to a HTR with the
expenditure of as littler work |W| as possible.
Refrigerator operating in a cycle
High-temperature reservoir at TH
|QH| is rejected by system into HTR
Intermediate
state m1
Intermediate
state m2
State i
|QL| is absorbed by system from LTR
Low-temperature reservoir at TL
|W| work is done on
the system as an
input
Clausius statement of the second law
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“It is impossible to construct a refrigerator
that, operating in a cycle, will produce no
effect other than the transfer of heat from a
low-temperature reservoir to a higher
temperature reservoir”
Put in plain language: Heat does not flow
spontaneously from a LTR to a HTR. Work is
always necessary to transfer heat in such a
heat transfer process.
Equivalence of the Kelvin-Planck
statement and Clausis statements
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Using the language of logics, it can be shown
that both statements are equivalent, i.e. one
statement implies the other, and vice-versa.
Read page 156 yourself.
Definition of reversibility
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In practice, all natural process involve conversion of energy from
one form to another, W  Q U.
A reversible process is one that is performed in such a way that,
at the conclusion of the process, both the system and the local
surroundings may be restored to their initial states without
producing any changes in the rest of the universe.
A process that does not fulfilling these stringent requirements is
said to be irreversible.
Example: A system of gas expands and then contracts to its
original volume, without any change in the thermodynamic
coordinates of the gas system + the that of the rest of the
universe. Such would constitute an reversible process.
Question: Are natural processes reversible?
Most natural processes are not reversible
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Most representative natural processes are
not reversible
Most natural processes, particularly those
macroscopic processes, involves
performance of work into internal energy, a
process that can be categorised into two
classes, as followed:
Two large classes of processes involving
performance of work
1) Isothermal transformations of work done
through a system (which remains unchanged)
into internal energy of a reservoir. Heat flows
through the boundary of the system during such
processes. See Fig. 6.9.
2) Adiabatic transformation of work into internal
energy of a system. Heat does not flow through
the boundary of the system during such
processes. See Fig. 6.10.
2nd law of thermo infers non-reversibility
in processes involving transformation of
work into internal energy
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Both generic types of processes are not
reversible due to the second laws of
thermodynamics.
Read page. 159 Zemansky for the
arguments leading to such conclusion.
Dissipative effect
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In the processes mentioned previously, (i.e.
processes involves performance of work into internal
energy), the conversion of work into internal energy
is described as “work is ‘dissipated into internal
energy”.
Dissipative effects are necessary to transform work
into internal energy of a system. Without these
dissipative effects, no transformation of work into
internal energy is possible.
Example of dissipative effects: friction, viscosity,
inelasticity, electric resistance, magnetic hysteresis.
In most natural process, dissipative effect is always
present and it cannot be totally eliminated.
Dissipative effect (cont.)
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A generic natural process usually involve the conversion of forms of
energy.
In particular, the conversion of energy form from work into internal
energy, Wf = DU can only happen in the presence of an agent of
dissipation, e.g. friction or viscosity.
Say, consider a moving object with kinetic energy K is subjected to
frictional force, f. The force is responsible to dissipate the kinetic energy
of the object into internal energy.
The frictional force f, being an agent of conversion, converts the kinetic
energy into internal energy: DK  DU.
Should there be no friction, no conversion of kinetic energy into internal
energy is possible.
In the conversion of DK  DU, the amount of work done by the force f is
equal to the change of the kinetic energy of the object, i.e. DK   f  dr
DU is the increase of internal energy of the system + that of the
environment.
Due to the nature of all dissipative effect, it is not possible to convert all
K solely into the internal energy of the system (i.e. the moving object)
with no dissipation into ‘the rest of the universe’.
Once dissipated into ‘the rest of the universe’, the energy cannot be
recovered in practice for work-performing purpose.
In other words, dissipative effect always contribute to ‘wastage’ of useful
energy into some of form of internal energy that cannot be recovered.
All natural processes are non-reversible
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As a consequence of the pervasive presence of dissipative
effect in all natural processes, which necessarily involve
conversion of the form Wf  DU, exhibit irreversibility.
Such irreversibility due to the presence of dissipative effect
is called mechanical irreversibility.
As a conclusion, we revise the logic leading to mechanical
irreversibility:
Most representative natural processes involves conversion
of work into internal energy.
Dissipative effect is always present in such processes.
Hence, these processes exhibit mechanical irreversibility.
The statement of 2nd law on macroscopic processes is
closely related to the fact that dissipative effect can never
practically be totally eliminated from such processes.
Perpetual machine of the third kind
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Imagine an heat machine without any
‘dissipative effect’ of any sort.
Such an imaginary machine can convert all
energy into work without any work dissipated
into internal energy.
Such an imaginary perpetual machine that
has no friction is called ‘perpetual machine of
the third kind’.
Questions to arouse your curiosity
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What is perpetual machines of the first and
second kind?
What are the necessary conditions for
reversibility?
1) Thermodynamical equilibrium
AND
 2) No dissipative effects
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Both conditions must be satisfied if reversibility is to
be achieved.
It is not possible to satisfied these conditions
perfectly in practice
Hence, in nature all processes are irreversible