Miscellaneous Modes of Thermodynamic Work

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Miscellaneous Modes of Thermodynamic Work

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

More forms of work driving the Industry
Nature!!!
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Why cutting of a solid consumes power?
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Why cutting occurs at A Particular value of
stress?
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Who controls the Growth Shape Equilibrium Shape
of A Crystal
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Who decides the beauty of Table Cloth ???
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The Role of Surface Tension in Engineering

• When splitting a solid, the amount of energy
  required is 2sA, where 2A is the area created
  (one A on each side).
• This energy is less than that needed just to
  break the bonds, since there is atomic and
  electronic relaxation.
• The surface energy is always positive because the
  atoms are less bound at the surface.
• The surface tension can be defined as the
  reversible work of formation of a unit area of
  surface at constant T, V, m.
• The surface tension is the two-dimensional analog
  to the pressure.

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Surface Tension
On the surface there are atoms on one side only,
so there is a net inward cohesive force. This
creates a force on the surface that tries to
minimise its area. When considered as a force
rather than an energy, the force is called
"surface tension".
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Thermodynamic Definition of Surface Tension
The relative change in internal energy of a
control mass w.r.t. change in surface area at
constant temperature, volume.
Law of a Nature
The tendency to minimize surface energy is a
defining factor in the morphology and composition
of surfaces and interfaces. This Is important
for Solids Liquids.
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Values of Surface Tension for Selected Materials

Material g J/m2
Tungsten (solid) 2.9
Iron (solid) 2.2
Iron (liquid) 1.9
MgO 1.2
Mercury (liquid) 0.5
Water 0.07
Acetic acid 0.03
Nitrogen (liquid) 0.01
Helium (liquid) 0.0003
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Work Associated with the Stretching of a Liquid
Film
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Blood Vessels Blood Pressure

• For a cylinder of radius R and length  l such as
  a blood vessel, the wall supplies an inward force
  and the liquid supplies an outward pressure.
• Infinitesimal work to be done by blood on vessel

This work is stopped by surface tension of the
blood vessel material
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• There is a greater pressure difference for a
  smaller radius than a larger one. This inverse
  relationship is called Laplace's law.

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The Faradays Work An Amazing form of Work
Transfer

• Consider a conducting rod PQ moving at a steady
  speed V perpendicular to a field with a flux
  densityB.
• An electron (negative charge e) in the rod will
  experience a force ( Bev) that will push it
  towards the end P.

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Description of Work done by A Conductor

• The same is true for other electrons in the rod,
  so the end P will become negatively charged,
  leaving Q with a positive charge.
• As a result, an electric field E builds up until
  the force on electrons in the rod (unit length)
  due to this electric field ( Ee) balances the
  force due to the magnetic field

Force per unit charge on Rod of unit length
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For a rod of length L, define the EMF as
What happens when the EMF drives a current in an
external circuit? To do this, imagine that the
rod moves along a pair of parallel conductors
that are connected to an external circuit
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Electrical Loading of Conductor
The EMF will now cause a current to flow in the
external resistor R. This means that a similar
current flows through the rod itself giving a
magnetic force, BIL to the left.
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Quantification of the Faradays Work
L is now the separation of the two conductors
along which the rod PQ moves. An equal and
opposite force (to the right) is needed to keep
PQ moving at a steady speed.
In a time dt, the rod moves a distance dx
Vdt Infinitesimal Work done on the rod
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The Pairs of Work Transfers
Energy dissipated in R power x time EMF I
t Giving B I L V t EMF I t or,
as before, EMF B V L
http//tap.iop.org/fields/electromagnetism/414/pag
e_46948.html
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Generation of Shaft Work
Energy transmission with a rotating shaft is very
common in engineering practice.
A force F acting through a moment arm r generates
a torque T of
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Isothermal Process of Real Gases in a Control
Mass

• Van der Waals EOS

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Displacement Work done by Superheated Steam
During An Isothermal Process
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Spring Work