Kinematics and Dynamics of Point Particles and Extended Objects

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Kinematics and Dynamics ofPoint Particles and
Extended Objects

• We have completed this discussion for point
  particles.
• How do you treat extended systems of particles?

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Extended systems

• Rigid - even though extended, all particles move
  as a unit
• Non Rigid streamline - even though particles are
  not connected they seem to move as a unit
• Non Rigid random - cannot be described by looking
  at single particle motions. Just impossible!

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Extended non-rigid systems gases and liquids

• Listing individual speeds, forces, and positions
  is impossible for even small parts of real
  systems.
• Consider the standard volume of air at
  standard room temperature. There are about 1024
  particles in such a system which occupies about
  a cubic meter. How long would it take for a fast
  computer to one calculation on each particle?

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Description of extended non-rigid bodies

• What parameters are used to describe such
  systems?
• Pressure
• Volume
• Temperature
• Average energy

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Initial description of extended non-rigid
systems

• Empirical relationship between pressure volume
  and temperature with no reference to particle
  kinematics.
• PV NkT - Ideal Gas Law
• N of molecules
• k constant
• Heat - amount of caloric entering or leaving a
  body - 1 calorie heat necessary to raise the
  temperature of 1 gm of water 1 degree C.

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Connection between Temperature and the
microscopic nature of matter

• Temperature and molecular motion are related!
• Specifically
• average kinetic energy per particle is related
  to temperature if one looks microscopically at
  pressure and momentum of individual particles.
• lt(1/2)mv2gt (3/2)PV/N (3/2)kT
• How is the average measured if you cant
  measure all the particles in a sample?

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Heat

• In the microscopic view, heat is simply the total
  energy content of a sample - Q is the symbol for
  heat.
• Q (3/2)NkT
• where N is the total number of particles in the
  system
• the joule and calorie are related
• 1 cal 4.184 joules

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States of Matter

• Solid
• Liquid
• Gas

• requires 330 joules/gm added to ice to get
  liquid water
• requires 2260 joules/gm added to liquid to get
  steam(gas)
• note! The numbers are different for every
  substance

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Specific Heat Capacity - c

• If different substances take up the same amount
  of heat they all should reach the same
  temperature.
• They dont! Can you think of some examples?
• A description of this is
• c (1/ m)?Q/ ?T
• c is a measured number for each substance in
  order to categorize the substance.
• m is the mass of the substance

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Examples of Specific Heat Capacity

• Water - 1 cal/gmK
• Copper - .1cal/gmK
• Why are they different? How can you put energy
  into a system and not change the temperature?
• We must look to the microscopic description of
  matter and carefully analyze the temperature
  measurement process.

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Specific Heat Capacity Explained

• From the detailed microscopic investigation of
  matter we find
• the act of measuring temperature changes
  temperature
• specific heat capacity can be predicted if one
  knows the number of ways a system can move. (or
  can absorb energy)

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Heat Transfer

• conduction
• convection
• radiation

• Energy imparted by direct contact - collision
• energetic particles move from one place to
  another
• light-this is like convection but no medium
  needed. Light is different!