THERMAL PROCESSES

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THERMAL PROCESSES

• When a thermal variable changes there is a
  thermal process occurring.
• Reservoir does not change during a
  thermal process.
• P V diagram Tconstant isothermal
• P T diagram Vconstant isochoric
• V T diagram Pconstant isobaric
• Any diagram ?Econstant adiabatic

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THERMAL PROCESSES

• Real Gases deviate from the ideal gas law
• The P vs T, P vs V and V vs T diagrams for real
  gases must also incorporate phase changes. These
  are called phase diagrams and the boundary across
  a solid liquid, or solid vapor or liquid vapor
  indicates where the phase changes these are not
  transformations.

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REAL GASES

• What equation is used for real gases?
• van der Waals equation
• p a(n/V)2 V/n b RT
• a f(intermolecular forces)
• b f(finite molecular size)
• n number of moles
• Another form is p RT/(V/n b) a/(V/n)2

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REAL GASES

• Two other equations used for real gases
• Redlich-Kwong equation
• p RT/(V/n b) - a/V/n(V/n b)T1/2
• where a and b are different constants.
• Beattie-Bridgeman equation
• p RT/(V/n) ß/(V/n)2 ?/(V/n)3 d/(V/n)4
• ß, ? and d are determined by five other
  experimental constants.

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Blackbody Radiation

• When charged particles accelerate they produce
  electromagnetic waves. This is the condition of
  an body above absolute zero and the waves that
  are generated is called Black Body Radiation.
• As T increases the radiated energy becomes more
  intense and the average energy increases. Since
  the particles which generate the waves have a
  distribution of velocities, so does the
  radiation.

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Blackbody Radiation

• The distribution of radiated energy per unit
  volume with a frequency between f and f?f is
  given by Plancks Formula
• u(f,T) ?f (8ph/c3) f3?f /(ehf/kT
  -1)
• where h 6.625 x 10-34 Js c 3 x 108 m/s
• Implies E hf is a quantized energy photon
• If one considers the total power radiated from a
  hole in a hot enclosure by integrating u(f,T)
  over all frequencies,

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Blackbody Radiation

• then this produces the Stephan-Boltzmann formula.
• R(T) s T4 (Watts/m2)
• where s 2 p5 k4/(15 c2 h3)
• having a value of 5.67 x 10-8 W/(m2 K4)
• To obtain the total radiated energy one
  integrates over the surface.
• If R constant then, E(T) R A

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Blackbody Radiation

• At very low energies compared to kT
• u(f,T) 8pf2kT/c3
• At very high energies compared to kT
• u(f,T) (8phf3/c3) e-hf/kT
• (Raleigh-Jeans Catastrophe)
• If expressed as u(?,T) f c/?
• u(?,T) (8phc)/ ?5(ehf/kT -1)

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