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Homework Help: Derive the entropy of an ideal gas

  1. Oct 22, 2006 #1

    Lee

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    THe Question asks 'Derive the entropy of an ideal gas when its molar specific heat at constant volume is constant.'

    So I've taken

    [tex] \Delta S = \int_{S_0}^{S} dS = \int_{T_0}^{T} \frac{\partial_S} {\partial_V} dT + \int_{V_0}^{V} \frac{\partial_S}{\partial_V} dV [/tex]

    in this context what would be the next best step?
     
  2. jcsd
  3. Oct 22, 2006 #2

    Andrew Mason

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    Homework Helper

    If the specific heat remains constant at all temperatures, then it is possible to integrate from temperature 0 to T.

    Since [itex]dQ = TdS = dU + PdV = nC_vdT + PdV[/itex] at constant volume [itex]nC_vdT = TdS[/itex]

    so:

    [tex]\int_0^T dS = \int_0^T nC_v dT/T = S_T - S_0[/tex]

    If you let the entropy of the gas at 0 K be 0: [itex]S_0 = 0[/itex], then ST represents the entropy of the gas at temperature T.

    AM
     
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