chapter 1 and 2 _ heat and work
TRANSCRIPT
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CHEMICAL ENGINEERINGTHERMODYNAMICS
Course no: CHE C311 / F213
Dr. Srinivas Krishnaswamy
1st Semester 2012 – 2013
DEPT. OF CHEMICAL ENGG.
BITS – PILANI, K. K. BIRLA GOA CAMPUS
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Contents Reversibility and Irreversibility
What is quasi-equilibrium?
Understanding energy The concept of thermodynamic work
Evaluation of work for commonreversible processes
Work done in an irreversible process
Two inherently irreversible processes
Heat and its comparison with work
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Reversibility and
Irreversibility
A process is reversible if it can be completely reversed, i.e. when carried out in the opposite
direction the system follows the same
succession of states as it followed in theforward direction (very crude definition)
A process is reversible if after the processoccurs, the system can be restored to its
original state without any effect on itssurroundings
This effect occurs only when the driving forceis infinitesimally small
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Reversibility and
Irreversibility Note The 2nd definition involves the
surroundings
Important to understand that when a process
is reversible, interaction between system andsurroundings are equal and opposite indirection,i.e. both system and surroundingsare restored to initial conditions
A reversible process leaves no history of theprocess after it is reversed
No friction involved
The processes represent idealization and are
never realized in real life
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Reversibility and
Irreversibility A process which is not reversible is
irreversible
Irreversible processes have friction and arecarried out with finite driving forces
If a system in this case is restored to itsoriginal state, surroundings must be altered
Caused by friction, unrestrained expansion,mixing of substances, combustion, flow of electricity through a resistor, heat transfer over a finite temperature difference etc.
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Quasi-equilibrium
process
A process in which deviation fromequilibrium is infinitesimal
All states through which a system passes
during such a process can be considered asa succession of equilibrium states
Takes place very slowly with an infinitesimalchange in properties at each step
Path can be described for such a process
A quasi-equilibrium process without frictionis reversible
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Understanding Energy
Difficult to define in general, but isdefined as capacity of a body to dowork (causes an effect)
Exists in various forms and can be
converted from one form to another (partial or complete), but can never bedestroyed
Can be classified as energy intransition and energy in storage
SI units: Joules
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Understanding Energy
Energy transferred as a result of potentialdifference is energy is transition. Loss of identity as soon as soon as energy entersand leaves a system. E.g.: gradient of force,
temperature and potential result in transfer of mechanical work, heat and electricalenergy respectively
Stored energy possessed by a system as a
result of its position in a force field, itsmotion, its atomic or molecular structure etc.Examples are kinetic, rotational or vibrational energy, chemical or nuclear energy etc.
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The concept of
thermodynamic work By definition it is Force times
displacement, the latter measured in
the direction of the force from the pointof application
But then thermodynamics talk of
system and surroundings. Hence workneeds to be defined in thermodynamic
language
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The concept of
thermodynamic workWork is said to be done by a system if the soleeffect on the surroundings is reduced to
lifting of weight
Note The definition does not call for actualraising of a weight, but rather the possibility
of a weight being raised
Thermodynamic work is energy in transition
and is manifest at the system boundary onlyduring system-surrounding interaction.
Before the interaction work is present andafter the interaction no work exists
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The concept of
thermodynamic work
WORK
Work crosses
system boundary
in both cases
(green and red
boundaries)
Flow of electricity
across a system is
equivalent towork crossing the
system boundary
WORK
MOTOR
WORK
MOTOR
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The concept of
thermodynamic work Conventions important when solving
problems
In thermodynamics work done by a systemis positive and work done on a system isnegative
System and surroundings do equal, butopposite work
W system + W surroundings = 0
Net work done by a system is expressed as
W net = W out - W in
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Work done in a frictionless
quasi-equilibrium processInitial conditions
Gas at P , T and volumeV inside frictionless
piston and cylinder arrangement in thermalequilibrium
P exerts a force F . Under equilibrium, this is
balanced by a forcecaused by atmospheric
pressure and pistonweights (-F ) which
results in P ext
F
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Work done in a frictionless
quasi-equilibrium processRemove an infinitesimally
small weight. This willresult in reduction of pressure and slightexpansion will take
place.
Reduced gas pressure willbe balanced by reduced
weights which will beraised and work will bedone
W = F dz = (PA )dz = P dV
dz
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Work done in a frictionless
quasi-equilibrium processLet finite weights be removed
ensuring quasi-equilibrium
process 1- 2 in which volume
changes from V
1
to V
2During this change system and
surroundings are in
equilibrium
The net work done during the
expansion 1-2 is
1W 2 = W = P dV
Final state
after weights
are removed
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Work done in a frictionless
quasi-equilibrium process The integral represents the area under
the P – V diagram
Work done can be found by integrationprovided a relationship between P andV is known
This is displacement work and is valid
only for frictionless process This expression applies to any
compressible system of any arbitrary
shape
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Work done in a frictionless
quasi-equilibrium processSpecific work = Work per unit mass of the system
W = mw = P dV = m P d
The integral can be evaluated by graphical or numerical methods (if path known from
experimental data) or by curve fitting
experimental data to obtain a relationship
between P and V and then using directintegration
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Evaluating work for some
common processesCONSTANT PRESSURE PROCESS
P = CONSTANT
1W 2 = W = P dV = P dV
WORK DONE = P (V 2 – V 1)
V
P
1W 2
1 2
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Evaluating work for some
common processesCONSTANT VOLUME PROCESS
V = CONSTANT, dV = 0
WORK DONE = 0
1
V
P
2
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Evaluating work for some
common processesHYPERBOLIC PROCESS
PV = CONSTANT = P 1V 1 = P 2V 2
1W 2 = W = P 1V 1 (dV / V)
WORK DONE = P 1V 1 ln(V 2 / V 1) =
P 2V 2 ln(V 2 / V 1)
2
V
P
1W 2
1NOTE HYPERBOLIC
PROCESS BECOMES
ISOTHERMAL IF T IS
CONSTANT, PV = RT = C
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Evaluating work for some
common processesPOLYTROPIC PROCESS
PV n = P 1V 1n = P 2V 2
n = C
The index n is the polytropic index. It can beevaluated if P and V at initial and final states
are known, thus
n = ln (P 1 / P 2) / ln (V 2 / V 1)
The polytropic relation represents the mostconvenient curve fitting of actualexperimental data between P and V with thevalue of the index n evaluated with the help
of any two points on the curve
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Evaluating work for some
common processesFor integration purposes
P = C / V n = P 1V 1n / V n = P 2V 2
n / V n
1W 2 = W = C (dV / V n)
1W 2 = C (V 21 – n - V 1
1 – n ) / 1 – n
Substituting C = P 1V 1n = P 2V 2
n
1W 2 = (P 2V 2 - P 1V 1) / 1 –n
1W 2 = (P 1V 1 / 1 – n) [ (P 2 / P 1){(n – 1) / n}
– 1]
from V 2/V 1 =(P 1/P 2)1/n
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Evaluating work for some
common processes n, the polytropic index can have many
values. note that when n = 0, the
process is constant pressure (isobaric)and when n = , it is a process at
constant volume
Integration valid when n 1 For hyperbolic process n = 1
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Evaluating work for some
common processesIf the gas is ideal, then
P 1V 1 / T 1 = P 2V 2/T 2
A relationship between T –
P and V –
T canbe obtained thus
T 2 / T 1 = (P 2 / P 1)(n – 1 / n) = (V 1 / V 2)
(n – 1)
Putting P 2V
2= mRT
2and P
1V
1= mRT
1
1W 2 = m R (T2 - T1) / 1 – n
(Polytropic work for an ideal gas)
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Evaluating work for some
common processes A gas is contained in a cylinder fitted with a
piston loaded with a small number of
weights. The initial pressure of the gas is1.3 bar and the initial volume is 0.03 m3.
The gas is now heated until the volume
increases to 0.1 m3. Calculate the work
done by the gas for the a constant pressure,constant temperature process and PV 1.3 = C
process
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Evaluating work for some
common processesCONSTANT PRESSURE PROCESS
(CAUSED BY MOVING PISTON AS GAS ISHEATED)
WORK DONE = P (V 2 – V 1) = 9.1 kJ
CONSTANT TEMPERATURE PROCESS(REMOVE WEIGHTS AT A RATE THAT
THE TEMPERATURE REMAINSCONSTANT WHILE HEAT IS ADDED TOTHE GAS)
WORK DONE = P 1V 1 ln(V 2 / V 1) = 4.695 kJ
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Evaluating work for some
common processesPOLYTROPIC PROCESS (ACHIEVED
BY REMOVING WEIGHTS AT A
RATE SUCH THAT P 1V 11.3
= P 2V 21.3
DESCRIBES P – V RELATIONSHIP
WORK DONE = (P 2V 2 - P 1V 1) / 1 – n = 3.933 kJ
STATE 1 –
2 CAN BE ACHIEVED THROUGHDIFFERENT ROUTES. WORK DONE IS
DIFFERENT FOR EACH PATH. WORK IS THUS
A PATH FUNCTION (REMEMBER QUASI-
EQUILIBRIUM)
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Evaluating work for some
common processes Work done in a process is not only a
function of the two end states, but italso depends on the path followed ingoing from one state to another
Work is a path function and an inexactdifferential
Thus 1W 2 = W W 2 –
W 1. Hencenever speak of work in state 1 or state2. There is only W in and W out which iswork in transition
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Work done in an
irreversible process Not all processes confirm to idealized
quasi-equilibrium conditions. Actual
process are inherently irreversible, i.e.surroundings are altered even whensystem returns to original state
A process maybe irreversible
essentially in two ways, i.e. non-equilibrium irreversible or due tofriction
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Work done in an
irreversible process In a non-equilibrium process, there is a finite
change. Path of the process is not known.Only end states are known
In a process where friction is present quasi-static conditions can exist, i.e.
P ext F / A = P
Local temperature changes due to frictionnear piston cylinder contacts.Thermodynamic equilibrium is thus absent.Work is dissipated as heat and cannot berecovered
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Work done in a non-
equilibrium process Actual case where finite weights are
removed. Only initial and final states
are known. The system andsurroundings are not in equilibrium at
each step
F
1
P ext =
P 1
2
P ext = P 2
V
P 1
21W 2
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Work done in a non-
equilibrium process P dV does not represent work
But some work has been done becausevolume has changed and this is finitechange, i.e. V
W = P ext V (work done in a non-equilibriumprocess)
Note pressure P ext here is external pressureand during the process never equal to P , thepressure of the gas.
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Work done in a process
with friction In this case P ext + F / A = P or P ext - F / A =
P is possible depending on whether expansion or compression takes place
For compression P ext > P and for expansion P ext < P (P is the gaspressure)
Thus in a process with frictionW = P extdV (P ext = P F / A)
Less work obtained during expansion andmore work required during compression
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Work done in an
irreversible processLost work = P dV - P extdV
It is seen that for a reversible process, for a
given change of state, work output duringexpansion is maximum and work input
during compression is minimum. In an
irreversible process during expansion work
output is less than maximum and duringcompression more than minimum
An irreversible process is always inferior
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Two inherently
irreversible process Free expansion where P dV is finite,
but work done is zero. Finite means
can be evaluated
Q = 0Fluid, state
2, P 2, V 2W = 0
Q = 0Fluid, state
1, P 1, V 1W = 0
Vacuum,
P ext = 0
P ext = 0
Not quasi-
equilibrium
P extdV = 0
No work done
during free
expansion
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Two inherently
irreversible process
MOTOR Paddle wheel
work
Volume does not
change and
friction not
involved
System boundary
does not move
A situation whereP dV is zero, but
work is still done
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The State Postulate
Simple system: A system which involves only
one work mode
State Postulate: The number of independent
intrinsic properties required to define thestate of a system is equal to one plus the
number of possible work modes
Thus for a simple system, the number of
independent intrinsic properties required is 2
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The concept of heat
In the case of paddle wheel work,temperature rises, i.e. a change of state occurs
The same state can be brought aboutif heat entered the system instead of work
Effect of heat on a system could besame as the effect of work
Heat is energy as work is and hasunits of work
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The concept of heat
Heat is thus defined as energy in
transition flowing by a virtue of a
temperature difference between twosystems or between a system and it s
surroundings
It manifests only at the system boundaryand cannot be contained
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The concept of heat
Sign convention of heat is just opposite to
that of work
Heat entering a system is positive (addedto) and leaving a system is negative
A process in which no heat transfer takes
place is an adiabatic process
In a closed system an application of work or
heat can cause a change of state
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The concept of heat
When heat is added to a pure substance it
is seen that either the phase changes with
temperature remaining constant (saturationstate) or temperature changes with
substance remaining in the same phase
In the former case it is called latent heat and
in the latter sensible heat Heat transfer by 3 modes: conduction,
convection or radiation
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Objective Assessment
Concept of reversibility andirreversibility
Concept of work
Estimating work for various processes
Concept of heat
There are two ways of meeting difficulties:you alter the difficulties or you alter yourself
meeting them. It is better than running away
from them.