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Thermodynamics Maxwell relation

  1. Jun 26, 2013 #1
    When can be used
    [tex](\frac{\partial S}{\partial V})=\frac{P}{T}[/tex]?
  2. jcsd
  3. Jun 26, 2013 #2


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    The fundamental relation is, if I recall correctly,
    ##\mathrm dE = T \, \mathrm dS - p \, \mathrm dV + \mu \, \mathrm dN##

    So setting dE = 0, you obtain P/T = dS/dV when dN = 0, so if the number of particles and the energy in the system don't change.
    For convenience you can put this in the subscript:
    ##\left( \frac{\partial S}{\partial V} \right)_{E, N} = \frac{P}{T},##
    as a reminder that E and N should be kept constant.
  4. Jun 26, 2013 #3
    And could you get this relation without using first law of thermodynamics?
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