A mole of a van der Waals gas is expanded isothermally from V 1 to V 2 . Derive the expressions for the changes in the Helmholtz free energy and internal energy.

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A mole of a van der Waals gas is expanded isothermally from       V    1   to       V    2  . Derive the expressions for the changes in the Helmholtz free energy and internal energy.

hospitaliapbury · Accepted Answer

For 1 mole van der Waals equation is written as:  P  =            R      T              V      −      b        −      a          V      2          (            d      P              d      T            )    V    =      R          V      −      b      The equation for internal energy change is:  d  U  =      C    V    d  T  +  [  T  (            d      P              d      T            )    V    −  P  ]  d  VAt constant T, equation becomes:  d  U  =  [            R      T              V      −      b        −  P  ]  d  V    d  U  =      a          V      2      Equation for Isothermal Helmholtz free energy change  A  ≡  U  −  T  SAt constant  △  A  =  △  U  −  T  △  S    △  A  =  a  [      1          V      1        −      1          V      2        ]  −  R  ln  ⁡  (                    V        2            −      b                      V        1            −      b        )

A mole of a van der Waals gas is expanded isothermally from V 1 </msub> to V

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