B

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I
II
A
B
III
(Path Function)
(VB-VA)I (VB-VA)II (VB-VA)III (state
Function)
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Between two states the change in a state variable
is always the same regardless of which path the
system travels.
Differential of a state function is called
EXACT DIFFERENTIAL
Differential of a path function is called
inexact differential.
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b
yb
II
ya
a
I
xa
xb
x
Path dependent hence inexact differential
Does not depend on path hence exact differential
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Simple test to see whether a differential is
exact(Eulers Criterion for exactness)
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Molar volume of an ideal gas
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State variables are also called state properties.
The state of a system is defined as the complete
set of all its properties which can change during
various specified processes.
When a system is at equilibrium, its state is
defined entirely by the state variables, and not
by the history of the system.
The properties of the system can be described by
an equation of state which specifies the
relationship between these variables.
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State Variables
P,T,V
Cut into half
P,T,V/2
P,T,V/2
P and T are intensive variables, V is an
extensive variable
The variables often form pairs such that their
product has the dimensions of energy (e.g.
pressure volume in a gas). The intensive
member plays the role of force and the extensive
the role of displacement.
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We can influence a system either by doing work
(e.g. compression), or thermally (e.g. heat with
a flame).
Work is done when an object is moved against an
opposing force.
The energy of the system is its capacity to do
work.
Heat is energy in transit due to temperature
difference.
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Work is transfer of energy that make use of
organized motion.
When a system does work, it stimulates orderly
motion in the surroundings.
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Heat is the transfer of energy that makes use of
unorganized molecular motion.
When energy is transferred to the surroundings as
heat, the transfer stimulates disordered motion
of the atoms in the surroundings.
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Joules experiment
Joule heated water by performing work on it, in
this case by rotating a paddle wheel.
adiabatic
He found that the temperature rise was dependent
only on the amount of work but independent of how
the work was performed (e.g. quickly or slowly,
large or small paddle wheel).
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Temperature rise means there is change in state.
The property of the system whose change is
calculated in this way is called internal energy.
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Same change in state (temperature rise) can be
achieved by allowing heat to flow in.
System in state 1
Heat reservoir
Heat conducting Wall
Heat reservoir
system
Heat reservoir
System in state 2
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Energy can be converted from one form to another,
but it cannot be created or destroyed.
Change in internal energy of a closed system is
equal to the energy that passes through its
boundary as heat or work.
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• The first law contains three essential features
  

• It is a statement of the principal of
  conservation of energy.
• It requires the existence of the internal energy
  function.
• It leads to the definition of heat as energy in
  transit.

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U is a function of the state variables and can
be written as
But Q and W are not functions of the state so we
cannot determine quantities like
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For an adiabatic system,
This means that work needed to change an
adiabatic system from one specified state to
another specified state is a state function. wad
is a state function.
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General expression for work
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• Free expansion
• pex0, w0

(b) Expansion against constant pressure (Expansion
of gas formed in a chemical reaction)
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h
P2,V2,T
P1,V1,T
P1
P2
V1
V2
P1
P2
V1
V2
P1
P2
V2
V1
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P1
P2
V2
V1
For infinite number of step
P1
P2
V2
V1
Infinite state expansion is called reversible
process.
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These infinite-step processes at constant
temperature are reversible because the energy
accumulated in the surroundings in the expansion
is exactly the amount required to compress the
gas back to the initial state.
P1
P2
V2
V1
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h
P2,V2,T
P1,V1,T
P1
P2
V1
V2
h
P1,V1,T
P2,V2,T
P2
P1
V2
V1
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Important points about reversible processes
They can be reversed at any point in the process
by making an infinitesimal change.

• A reversible expansion or compression requires
• A balancing of internal and external pressure.
• Time to reestablish equilibrium after each
  infinitesimal step.
• Absence of friction.

For the processes in the chemical industry, the
greater the irreversiblity, the greater is the
loss in capacity to do work. Every
irreversibility has its cost.
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Ways to approach reversibility
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Heat may be transferred nearly reversibly if the
temperature gradient across which it is
transferred is made very small.
Electrical charge may be transferred nearly
reversibly from a battery if a potentiometer is
used so that the difference in electric
potential is very small.
A liquid may be vaporized nearly reversibly if
the pressure of vapor is made only very slightly
less than the equilibrium vapor pressure.
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h
P2,V2,T
P1,V1,T
P1
P2(V2-V1)
P2
V1
V2
h
P2,V2,T
P1,V1,T
P1
-(P1(V2-V1))
P2
V1
V2
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h
P2,V2,T
P1,V1,T
P1
nRTln(P1/P2)
P2
V2
V1
h
P2,V2,T
P1,V1,T
P1
-nRTln(P1/P2)
P2
V2
V1
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The variables often form pairs such that their
product has the dimensions of energy). The
intensive member plays the role of force and the
extensive the role of displacement.
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Heat

• Heat is energy in transit due to temperature
  difference.
• Mechanical definition wad-w

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• If a quantity of heat is required to increase the
  temperature of a body by dT , the heat capacity C
  is defined to be

• Since heat is an inexact differential, depending
  upon the way in which energy changes occur, then
  it is clear that there cannot be a unique heat
  capacity for a system either.

• So the quantity of heat which flows in will
  depend upon the path of the transformation and
  there will be an infinite number of heat
  capacities.

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Of the infinite possible number, it is customary
to define two heat capacities. Heat capacity at
constant volume CV and heat capacity at constant
pressure Cp
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CV is called heat capacity at constant volume.
CV can be determined by burning a known mass of
substance that has known heat output. With CV
known, it is simple to interpret an observed
temperature rise as a release of heat
Specific heat is essentially a measure of how
thermally insensitive a substance is to the
addition of energy.
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Specific heat is essentially a measure of how
thermally insensitive a substance is to the
addition of energy.

• For solids and liquids cV and cp are very
  similar.

Aluminium 900 J Kg-1 C-1 Wood 1700 J Kg-1
C-1 Water 4186 J Kg-1 C-1

• The high specific heat of water is the reason
  that coastal regions have milder climates than
  inland regions at the same latitude.

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Important point about Internal energy
Internal energy is the total of the kinetic
energy of the constituent atoms or molecules due
to their motion (translational, rotational,
vibrational) and the potential energy associated
with intermolecular forces. It includes the
energy in all of the chemical bonds, and the
energy of the free, conduction electrons in
metals.
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Important point about Internal energy

• Internal energy does not include the
  translational or rotational kinetic energy of a
  body as a whole.
• It also does not include the relativistic
  mass-energy equivalent E  mc2.
• It excludes any potential energy a body may have
  because of its location in external gravitational
  or electrostatic field, although the potential
  energy it has in a field due to an induced
  electric or magnetic dipole moment does count.

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Most processes that occur in the laboratory, on
the surface of the earth, and in organisms do so
under a constant pressure of one atmosphere
Some of the energy supplied as heat to the
system is returned to the surrounding as
expansion work.
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Enthalpy is a state function. Enthalpy is an
extensive quantity. The change in enthalpy is
equal to the heat absorbed in a process at
constant pressure if the only work done is
reversible pressure-volume work.
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