Energy Transport by Heat, Work and Mass.pdf - Yidnekachew

Thermodynamics I__________________________________________________________________ _
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Chapter 3
Energy Transport by Heat, Work and Mass
3.1 Energy of a System
Energy can be viewed as the ability to cause change.
Energy can exist in numerous forms such as thermal, mechanical, kinetic, potential, electric,
magnetic, chemical, and nuclear, and their sum constitutes the total energy E of a system. The
total energy of a system on a unit mass basis is denoted by e and is expressed as
E
e ( kJ / kg )
(3.1)
m
In thermodynamic analysis, energy can be group in to two forms:
Macroscopic
Microscopic
Microscopic forms of energy are those related to the molecular structure of a system and the
degree of the molecular activity, and they are independent of outside reference frames.
The sum of all the microscopic forms of energy is called the internal energy of a system and is
denoted by U.
Example:-
• Latent energy
• Chemical energy
• Nuclear energy
• Sensible energy
Internal energy
A system associated with the kinetic energies of the molecules is called the sensible
energy.
The internal energy associated with the phase of a system is called the latent energy.
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The internal energy associated with the atomic bonds in a molecule is called chemical
energy.
The tremendous amount of energy associated with the strong bonds within the nucleus of
the atom itself is called nuclear energy.
The total energy of a system, can be contained or stored in a system, and thus can be
viewed as the static forms of energy.
The forms of energy not stored in a system can be viewed as the dynamic forms of
energy.
The only two forms of energy interactions associated with a closed system are heat
transfer and work.
Macroscopic forms of energy are those a system possesses as a whole with respect to some
outside reference frame, such as kinetic and potential energies.
The energy that a system possesses as a result of its motion relative to some reference
frame is called kinetic energy (KE) and is expressed as
2
V
KE m
2
( kJ ) (3.2)
Per unit mass
2
V
ke ( kJ / kg ) (3.3)
2
The energy that a system possesses as a result of its elevation in a gravitational field is
called potential energy (PE) and is expressed as
Per unit mass
PE
pe
mgz ( kJ ) (3.4)
gz
( kJ ) (3.5)
The magnetic, electric, and surface tension effects are significant in some specialized cases only
and are usually ignored. In the absence of such effects, the total energy of a system consists of
the kinetic, potential, and internal energies and is expressed as
E U KE
PE
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E
U
V
m
2
2
mgz
(kJJ
)
(3.6)
Per unit mass
e uke
pe
Most closed systemss remain stationary during a processs and thus experience no
change in their
kinetic and potential energies.
e
u
2
V
gz
2
Closed systems whose velocity and elevation of the center of gravity remain constant during a
process are frequently referred to
as stationary systems. The change in the total energy ∆EE of a
stationary
system is identical to the change in
its internal
energy ∆U. .
3.2 Energy transport by heat and work
(kJJ
/ kg)
(3.7)
Energy can cross the boundary of a closed system in two
distinct forms: heat and
work.
Figure 3.1 Energy can cross the boundaries of a closed system in the
form of heat and work.
Energy
transportt by heat
Heat is defined as the form of energy that is transferred between two
systems (or
a system and its
surroundings) by virtue of a temperature difference.
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Figure 3.2 Heat transferr from hot surface to cold
surface
That is, an energy interaction is heat only if it takes place
because of
a temperature difference.
Then it follows that there cannot be any heat
transfer between two systems that are at the same
temperature.
A process during which there is no heat transfer is called an adiabatic process. The
adiabatic
comes from
the Greek word adiabatos, which means not to
be passed.
word
There are
two ways a process can be adiabatic: Either the system is well insulated so that only a
negligible amount of heat can
pass through the boundary, or
both the system and
the
surroundings are at the same temperature and thereforee there is no
driving force (temperature
difference) for heat transfer.
Figure 3.3 During an
adiabatic process, a system exchanges no heat with its surroundings.
As a form
of energy,
heat has energy units, kJ being the most common one. The amount of
heat
transferred during the process between two states (states 1 and 2) is denoted by Q 12 , or just Q.
Heat transfer per unit mass of a system is denoted q and is determined from
Q
q ( kJ / kg)
(3.8)
m
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Sometimes it is desirable to know the rate of heat transfer (the amount of heat transferred per
unit time) instead of the total heat transferred over some time interval.
Figure 3.4 The relationships among q, Q, and Q .
The heat transfer rate is denoted , where the overdot stands for the time derivative, or “per unit
time.” The heat transfer rate has the unit kJ/s, which is equivalent to kW. When varies with
time, the amount of heat transfer during a process is determined by integrating over the time
interval of the process:
Q
t
2
t1
Qdt
( kJ ) (3.9)
When remains constant during a process, this relation reduces to
Where: t t2 t1
Q Q t
( kJ ) (3.10)
Heat is transferred by three mechanisms: conduction, convection, and radiation. Conduction is
the transfer of energy from the more energetic particles of a substance to the adjacent less
energetic ones as a result of interaction between particles. Convection is the transfer of energy
between a solid surface and the adjacent fluid that is in motion, and it involves the combined
effects of conduction and fluid motion. Radiation is the transfer of energy due to the emission of
electromagnetic waves (or photons).
Energy Transport by Work
Work, like heat, is an energy interaction between a system and its surroundings. As mentioned
earlier, energy can cross the boundary of a closed system in the form of heat or work. Therefore,
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If the energy crossing the boundary of a closed system is not heat, it must be work. Work is the
energy transfer associated with force acting through a distance.
Example:-
• A rising piston
• A rotating shaft
Work is also a form of energy transferred like heat and, therefore, has energy units such as kJ.
The work done during a process between states 1 and 2 is denoted by W 12 , or simply W. The
work done per unit mass of a system is denoted by w and is expressed as
W
w ( kJ / kg )
(3.11)
m
The work done per unit time is called power and is denoted by . The unit of power
is kJ/s, or kW.
Heat and work are energy transfer mechanisms between a system and its surroundings, and there
are many similarities between them:
Both are recognized at the boundaries of a system as they cross the boundaries. That is,
both heat and work are boundary phenomena.
Systems possess energy, but not heat or work.
Both are associated with a process, not a state. Unlike properties, heat or work has no
meaning at a state.
Both are path functions (i.e., their magnitudes depend on the path followed during a
process as well as the end states).
Sign convention for energy transported by heat and work
Heat and work are directional quantities, and thus the complete description of a heat or work
interaction requires the specification of both the magnitude and direction. One way of doing that
is to adopt a sign convention. The generally accepted formal sign convention for heat and work
interactions is as follows: heat transfer to a system and work done by a system are positive; heat
transfer from a system and work done on a system are negative. Another way is to use the
subscripts in and out to indicate direction
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Figure 3.5 Specifying the directions of heat and work.
Q in > 0 Heat transfer to a system (positive)
Q out < 0 Heat transfer from a system (negative)
Figure 3.6 Process from
stage 1 to 2 Figure 3.7 Process from stage 1 to 2
W >
W <
0 work done by the system (positive) Figure 3.6
0 work done on the system (negative) Figure 3.7
Path functions have
inexact differentials designated by
the symbol . Therefore, a differential
amount of heat or work is represented by
Q or W, respectively, instead
of dQ or
dW.
Properties, however, are point functions (i.e., they depend on the state only, and not on how a
system reaches that state), and they have exact differentials designated by the symbol d.
A small change in volume, for example, is represented by dv, and the
total volume change during
a processs between states 1 and 2 is
2
1 dv
v
v
v
2 1
(3.12)
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Figure 3.8 Properties are point functions; but heat and work are path functions
The total
work done during process 1–2, however, is
1
2
W
W (not
W)
12
(3.13)
That is, the total work is obtained by following the process path
and adding
the differential
amounts of work (W) done along the way. The integral of W is not W 2 - W 1 (i.e., the work at
state 2 minus work at state 1), which is meaningless since work is not a property
and systems do
not possess work at a state.
3.3 Boundary
work
The work associated
with a moving boundary is called boundary
work. The expansionn and
compression work is often called moving boundary work or simply boundary work.
Example:- piston–cylinder
device.
Figure 3.9 The work associated with a moving boundary is called boundary work.
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In this section, we analyze the moving boundary work for a quasiequilibrium process, a process
during which the system remains
nearly in equilibrium at all times. A quasi-equilibrium process,
Boundary
work is done by the steam on the piston is calculated from
figure 3.10.
Figure 3.10 The area under the process curve on a P-V
diagram represents the boundary work.
Wb
W b
1
2
Fd
2
Wb
W b
s
1 PdV
F
Ads PdV
A
(3.14)
(3.15)
(3.16)
This integral can be
evaluated
during the process.
only if we
know the functional relationship between P and v
P= f (V) is simply the equation of the process path on a P-V diagram. The differential area dA is
equal to PdV. The total area A under the
process curve 1–2 is
obtained by adding these
differential areas:
Area
A
A comparison of this equation with the above ( Wb
1
2
dA
1
2
PdV
( 3.17)
2
1
PdV ), reveals that the
area under the
process curve on a P-v diagram is equal,
in magnitude, to the work done during a quasi-
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equilibrium expansion or compression process of a closed system. (On the
represents the boundary work done per unit mass.)
P-v diagram, it
Some typical process
Wb
Boundary work at constant volume process
1
2
PdV
(3.18)
Figure 3.11 Schematic and P-V
diagram for constant pressure process
If the volume is held constant, =0 and the boundary work equation becomes
W
Boundary work at constant pressure
b
1
2
PdV
0
(3.19)
Figure 3.12
Schematic and P-v diagram for constant pressure
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If the pressure is held constant the boundary
work equation becomes.
Wb
1
2
PdV P dV
PV (
V (3.20)
Boundary work at constant temperature (Isothermal)
1
2
2
1 )
Figure 3.13 Schematic and P-V diagram
for a polytropic process.
If the temperature of
an ideal gas
system held
constant, then the equation of state
provides the
pressure volume relation.
mRT
P
V
(3.21)
The boundary work is:
2
Wb
PdV But
1
mRT
P
V
(3.22)
Wb
1
2
mRT dV
V
(3.23)
Let
mRT
C
PV
W C
b
1
2
dv
V
(3.24)
V
Wb
Cln V
2
1
(3.25)
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Substitute the
value of C
Wb
Wb
V2
mRTln PV
1 1ln V
V V
PV
1 1ln ln
V 2
V1
1
2
1
(3.25)
(3.26)
Polytropic Process
During actual expansion and compression processes of gases, pressure and volume are often
related by
PV n = C. where n and C are constants
Wb
1
2
PdV
but
PV n = C
2
n
W b
CV dV
1
V
C
n1 n
1
2
V
1
n
1
PV PV
1
n
2 2 1 1
(3.27)
Since C PV
n
PV
For an ideal gas (PVV = mRT), this equation can also be written as
n
1 1 2 2
Wb
mR( T2 T1)
1
n
n 1
(3.28)
For the special case of n = 1the system is isothermal process and the boundary work becomes
W
b
1
2
PdV
1
2
CV
n
2
dV
PV ln V V 1
(3.29)
Spring Work
When the
length of the spring changes by a differential amount dx under the influence of a force
F, the work done is
Figure 3.14 Elongation of a spring under the influence of a force.
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But
F kx
W spri ing
1
2
Fdx
(3.30)
W
spring
1
k (
2
x
2 x 2
) 2 1
(3.31)
3.4 Energy transferred
by Masss
Mass flow
into and out of a system changes the energy content of the system. When mass enters
a control
volume, the energy of
the control
volume increase because the entering mass carries
some energy with it. Likewise when some mass leaves the control volume, the energy contained
within the control volume decreases becausee some leaving mass takeout some energy within
it.
Figure 3.14 The energy content of a control volume can be changed by mass flow
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