Behavior of Substance During A Process

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Behavior of Substance During A Process

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

Selection of Substance for A Happening..
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The substance contained by the system undergoes a
thermodynamic process/cycle
Recapitulation

• The potential of A Process/Cycle Depends on the
  substance used by (present in ) the system.

• How to begin the description of A Substance?
• Development of Equation of state
• Is it possible to develop a single EOS model for
  any substance?

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Pressure Temperature Diagram of A Pure Substance
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Pressure Temperature Diagram of A Pure Substance
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Pressure Temperature Diagram of A Pure Substance
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Pressure Temperature Diagram of A Pure Substance
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Pressure Temperature Diagram of A Pure Substance
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General Behaviour of Solids

• Incompressible Substance.
• Change in volume is infinitesimally small.
• Huge increase in temperature or pressure required
  for a finite change in volume/area/length.
• In an ideal (Hookean) solid, finite increase in
  pressure (stress) produces constant deformation
  (strain) at constant temperature.
• Thermal Expansion of Solids
• As the thermal energy in a solid increases, the
  mean separation of the atoms increases because
  the force curve is anharmonic.
• This causes the solid to expand.
• Linear, superficial and cubical Expansion
  coefficient.

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EOS for Solids

• The volume of A solid
• V f (p,T) p g (V,T)

Coefficient of volume or cubical expansion.
Bulk modulus
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Universal Equation of State for Solids
where
and
V0 is the volume of solid and B0 is bulk modulus
at reference pressure .
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Constants of EoS
Parameter Gold Nacl Xenon
B0 (1010 Pa) 16.6 2.35 0.302
?0(10-5 K-1) 4.25 12.0 60.0
(?B/?p)0 5.5 6.5 5.35 7.8
TR, K 300 298 60
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A common equation of state for Solid
Vm molar volume T temperature p pressure
C1, C2, C3, C4, C5 empirical constants The
empirical constants are all positive and specific
to each substance. For constant pressure
processes, this equation is often shortened to
Vmo molar volume at 00C A, B empirical
constants
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p-V-T Diagram of crystalline solid Phase
Pressure
Temperature
Volume
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Classification of Solids

• Crystal - Crystals are solids which are often
  very hard.
• The equations above are used for describing the
  physical properties of crystals.
• Glass - Glasses are generally very brittle.
• The equations above are useful for describing the
  physical behavior until the stress becomes too
  great and the material shatters.
• Elastomer - An elastomer is an amorphous solid
  which can be deformed with out breaking.
• The change in volume is generally negligible with
  deformation.
• However, the cross sectional area may change
  considerably.
• For changes in temperature and pressure,
  elastomers can be considered to be solids
  although much softer than other solids.

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Special Solids

• Superplastic - The unique ability of
  superplastics to stretch is a mechanical
  property.
• Physically, superplastics are treated as solids.
• Bose-Einstein Condensate - A Bose-Einstein
  condensate have just been released.
• It might be a solid or a very supercooled gas or
  one very large single atom.
• Refractory - Refractory materials behave
  physically as solids.

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Low Pressure Behavior of solids

• Direct vaporization of solids is known as
  sublimation
• Sublimation
•   solid   ?       vapor
• If the vapor pressure of the impurities in a
  solid are significantly lower than that of a
  solid sample, then sublimation can be used as a
  purification method.

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Sublimation Curves
Sublimation Point temperature at which Pvap
Psys.
Vapor pressure or equilibrium vapor pressure is
the pressure of a vapor in thermodynamic
equilibrium with its condensed phases in a closed
system.
Alloy
Elemental solid
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Sublimation of Ice
336 kJ/kg
2520 kJ/kg
psublimation
2856 kJ/kg
Sublimation of water occurs below 61.13Pa
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Sublimation Curve for Water
The triple point of water is 0.01oC, 611.3 Pa
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Triple Point

• The triple point of a substance is the
  temperature and pressure at which three phases of
  that substance coexist in thermodynamic
  equilibrium.
• For example, the triple point of mercury occurs
  at a temperature of 234.3156 K and a pressure of
  0.2 mPa.
• The single combination of pressure and
  temperature at which liquid water, solid ice, and
  water vapour can coexist in a stable equilibrium
  occurs at exactly 273.16 K (0.01 C) and a
  partial vapour pressure of 611.73 Pascals.
• Triple point of oxygen 54.3484K 152 Pa.
• Triple point of Nitrogen 63.151K 12520 Pa.

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Pressure Temperature Diagram of a Pure Substance
Substance Triple point K kPa
Oxygen 54 0.15
Nitrogen 63 12.53
Water 273.17 0.6113
Mercury 234 0.210-6
Copper 1376 0.000079
Silver 1234 0.01
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Melting Curve
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Properties of Liquids
The equation of state created by Peng and
Robinson has been found to be useful for liquids
p pressure a empirical constant Vm molar
volume R ideal gas constant b empirical
constant T temperature
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Liquid Vapour Equilibrium