Microscopic Energy

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Microscopic Energy

• P M V Subbarao
• Professor
• Mechanical Engineering Department

A Thermodynamic Property of Substances..
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Hydro Electric Plant The Work Done by A Falling
Water Ligament
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Microscopic Energy

• This energy is defined as the energy associated
  with the random, disordered motion of molecules
  and due to intermolecular forces.
• It is separated in scale from the macroscopic
  ordered energy associated with moving or
  stationary objects
• It refers to the invisible form of energy at
  atomic and molecular scales.
• Popularly known as Internal Energy, U.

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Internal (Microscopic) Energy Ideal Gas

• Internal energy involves energy at the
  microscopic scale.
• Potential and Kinetic energies of individual
  molecules/atoms.
• But the potential energy is associated with
  intermolecular forces which are presumed to be
  zero in an ideal gas.
• Therefore the internal energy of an ideal gas is
  entirely kinetic energy.

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Internal (Microscopic) Energy Monatomic Ideal
Gas

• For an ideal monatomic gas, this is just the
  translational kinetic energy of the linear motion
  of the "hard sphere" type atoms.

For a monatomic ideal gas this change in internal
energy is given by
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Internal (Microscopic) Energy Diatomic Ideal
Gas

• For polyatomic gases there is rotational and
  vibrational kinetic energy as well.

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Internal (Microscopic) Energy Polyatomic Ideal
Gas
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Internal (Microscopic) Energy Other Substances

• Then in real gases, liquids and solids there is
  potential energy associated with the
  intermolecular attractive forces.

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Increase of Internal Energy
Supply enough heat to each of these systems till
the there is 1?C increase in temperature.
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Internal Energy and Temperature
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Internal Energy of an Ideal Gas

• Internal energy in general includes both kinetic
  energy and potential energy associated with the
  molecular motion.
• But the potential energy is associated with
  intermolecular forces which are presumed to be
  zero in an ideal gas.
• Therefore the internal energy of an ideal gas is
  entirely kinetic energy.
• For a monoatomic ideal gas this change in
  internal energy is given by

• If rotation and vibrational kinetic energies are
  involved (polyatomic molecules) then

f Number of degrees of freedom of a molecule
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Means to Measure Energy

• Macroscopic Energy Easy to measure.
• Microscopic Energy Needs a detailed experiment.
• Identify methods to measure economically.

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Measurement of Change in Internal Energy

• First law for A control mass

Constant Volume Heating
1Q2 U2 U1

• Consider a homogeneous phase of a substance with
  constant composition.
• Define Specific Heat The amount of heat required
  per unit mass/mole to raise the temperature by
  one degree.
• No change in other forms of energy, except
  internal energy.

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Constant Volume Specific Heat

• The molar specific heat at constant volume is
  defined by

• For a monatomic ideal gas,

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CV Specific Heats of Ideal Gases
Experimental results
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Polytropic Process of A Control Mass

• Polytropic process of a control mass

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Measurement of Changes during Constant Pressure
Process

• Constant pressure heating of a control mass

Constant Pressure Heating
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Changes during Constant Pressure Process

• Infinitesimal constant pressure heating process
  by a control mass

The quantity pV is also having a behaviour of
property ! This is called flow energy, flow work
or internal work. However, the significance of
this property is not felt in a Control Mass.
Constant Pressure Heating
Another way of representing this effect is to
combine U and PV. Let this be H.
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The issue of Increasing unit Temperature of A
Pure Substance
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Flow Work or Flow Energy

• Unlike control mass, control volumes involve mass
  flow across their boundaries.
• The substance inside a control volume will be at
  some pressure, temperature..
• The fluid entering the control volume is pushing
  itself against the pressure of the control
  volume.
• Some work transfer is involved in pushing this
  mass into the control volume.
• This is an internal work.
• This is called flow work or flow energy.

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Visualization of Flow Work

• F pA will be a driving force responsible for the
  pushing of the fluid into the CV.
• This force will perform a work transfer of F.L to
  push the fluid.
• Therefore, the flow work F L p A L p
  V
• This can exists even when there is a fluid pushed
  out of the CV.

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Flow work

• It is interesting to note that unlike other work
  quantities, the flow work is expressed in terms
  of state variables.
• This is also a state variable, point function and
  hence a thermodynamic property.
• This is also called flow energy, convected energy
  or transport energy.
• The total energy of non flowing fluid E m(u
  ½V2 gz)
• The total energy of flowing fluid Q m(u pv
  ½V2 gz).
• This total energy is also called as Methalpy.
• The term u pv is called as specific Enthalpy, h.

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Energy transport by Moving fluid

• Amount of energy transport by a moving fluid of
  mass m
• Q m? m ( h ½V2 gz )
• Rate of Energy Transport

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Internal Energy Enthalpy of Wet Mixtures

• x is the dryness fraction.
• U (1-x) Uf x Ug
• Specific Internal energy Internal energy per
  unit mass u
• u (1-x) uf x ug
• Specific enthalpy
• h (1-x) hf x hg

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