Development of EoS for Vapours

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Development of EoS for Vapours Gases

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

Models for Highly Bountiful Phase....
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Behaviour of Vapour

• ? interatomic potential, Joules.
• r separation of molecules, nm (mean Free path).
• r? equivalent hard sphere radius of molecule
  (overlap of electron clouds).
• At high T, high p, collisions in the repulsive
  part of ? positive deviations from constancy.
• At low T, moderate p, collisions in the
  attractive portion of ? negative deviations
  from constancy.

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P v- T Relation

• The specific volume of A vapour
• v f (p,T)

• Greatest need for EoS of saturated and
  superheated steam.

• R and a are constants.
• The is called as Rankines Equation of state,
  1849.

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P v- T Relation

• The specific volume of A vapour
• v f (p,T)

• Callenders Characteristic Equation for saturated
  and superheated vapours.

• R and b are constants.
• c is a function of temperature and it is called
  as co-aggregation volume.

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Pressure Volume Diagram
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Van der Waals EOS

• One of the oldest but most extensively used of
  the EOS of non ideal gases
• Any EOS model must reproduce graphs such as that
  of the previous

• a, b are the Van der Waals constants for the
  particular gas
• for water a 0.5658 J-m3/mole2 b 3.049x10-5
  m3/mole,

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JO H A N N E S D . V A N D E R W A A L SThe
equation of state for gases and liquidsNobel
Lecture, December 12, 1910

• I intend to discuss in sequence
• (1) the broad outlines of my equation of state
  and how I arrived at it
• (2) what my attitude was and still is to that
  equation
• (3) how in the last four years I have sought to
  account for the discrepancies which remained
  between the experimental results and this
  equation
• (4) how I have also sought to explain the
  behaviour of binary and ternary mixtures by means
  of the equation of state.

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Van der Waals EOS

• a, b are the Van der Waals constants for the
  particular gas
• for water a 0.5658 J-m3/mole2 b 3.049x10-5
  m3/mole,

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Van der Waals Coefficients Van der Waals Coefficients Van der Waals Coefficients
Gas a (Pa m3) B (m3/mol)
Helium 3.46 x 10-3 23.71 x 10-6
Neon 2.12 x 10-2 17.10 x 10-6
Hydrogen 2.45 x 10-2 26.61 x 10-6
Carbon dioxide 3.96 x 10-1 42.69 x 10-6
Water vapor 5.47 x 10-1 30.52 x 10-6
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Van der Waals Isotherms
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Isotherms of Real Gases
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Improved Cubic Equations of State
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The constants a, b, c, Ao, Bo varies with
substance
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Compressibility Factor

• The deviation from ideal gas behaviour can also
  be expressed by compressibility factor, Z.
• The ratio of volume of real gas, Vreal to the
  ideal volume of that gas, Vperfect calculated by
  ideal gas equation is known as compressibility
  factor.

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• Compact description of non-ideality the
  compressibility factor,
• Z ? 1 as p ? 0 (ideality)
• Z lt 1 at low T, moderate p (point A)
• Z gt 1 at high p, high T (point B)

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Generalized Compressibility Chart
Reduced Temperature TR T/Tc
Reduced Pressure pR p/pc
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VdW EOS Compressibility

• a represents the attractive part of the
  potential with b 0, the VdW EOS gives a
  smaller v for the same T than the ideal gas
• b represents the repulsive portion of the
  potential with a 0, the VdW EOS gives a larger
  v for the same T than the ideal gas
• The VdW EOS is easily expressed in the forms
  p(T,v) or T(p,v).
• For the v(T,p) form, or, equivalently, Z(p,T)

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The ideal gas equation of state may be written
several ways.
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What More Happens at System Boundary during
Change of State
The Happenings Which are our Benefits!!!
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Global Wind Patterns The Simple Resource
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• The Ancient Green Method for Better Living
• Traditional Egyptian architecture in Ancient
  Egypt as demonstrated on the Pharonic house of
  Neb- Ammun, Egypt, 19th Dynasty, c.1300 BC.
• Persian ??????? bâdgir bâd "wind" gir
  "catcher
• Arabic ???? ?malqaf
• Eastern Arabia?????? barjeel

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An ancient Idea for Better LivingWindcatcher
(Bagdir)
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Evolution of Wind Turbines

• Wind is a clean, safe, renewable form of energy.
• Although the use of wind power in sailing vessels
  appeared in antiquity, the widespread use of wind
  power for grinding grain and pumping water was
  delayed until
• the 7th century in Persia,
• the 12th century in England, and
• the 15th century in Holland.
• 17th century, Leibniz proposed using windmills
  and waterwheels together to pump water from mines
  in the Harz Mountains.
• Dutch settlers brought Dutch mills to America in
  the 18th century.
• This led to the development of a multiblade wind
  turbine that was used to pump water for
  livestock.
• Wind turbines were used in Denmark in 1890 to
  generate electric power.
• Early in the 20th century American farms began to
  use wind turbines to drive electricity generators
  for charging storage batteries.

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The Modern Green Idea for Better Living Wind
Power
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What happens When there is a change in state?

• Any of these happenings is/are useful for
  engineering world?
• Does it consume any resource?
• How to recognize these Happenings?
• Thermal In-equilibrium
• Mechanical In-equilibrium
• Chemical In-equilibrium
• Any combinations of above.
• These are happenings or actions or path functions
  or interactions.
• Present only during a change of state.
• What action is work transfer?
• What action is Heat transfer?
• What action is Mass transfer?
• How to differentiate?

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Mechanical Work Tranfer

• Work is a mechanical concept given by the
  expression

• F is a force and s is a displacement
• Work is a scalar product
• Force components along the displacement vector
  only can do work
• Force components perpendicular to the
  displacement vector cannot do work.
• This relationship will be useful to find work
  required to raise a weight, to stretch a wire or
  to move a charged particle through a magnetic
  field.