Is there a name for this sort of thermo relationship? H v a p / s u b / c o n d ( T ′ ) − H v a p / s u b / c o n d ( T ) = ∫ T T ′ Δ C p , m d T

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Is there a name for this sort of thermo relationship?      H          v      a      p                    /                  s      u      b                    /                  c      o      n      d        (      T    ′    )  −      H          v      a      p                    /                  s      u      b                    /                  c      o      n      d        (  T  )  =      ∫          T                      T        ′              Δ      C          p      ,      m          d  T

hottchevymanzm · Accepted Answer

The relation arises from integrating the general partial-derivative expansion  d  H  =            (                        d          H                          d          T                    )        P    d  T  +            (                        d          H                          d          P                    )        T    d  P  ,or replacing the partial derivatives with the corresponding material properties  d  H  =      C    P      d  T  +  V  (  1  −      α    T  )  d  P  ,with constant-pressure heat capacity       C    P  , temperature T, bulk modulus K, thermal expansion coefficient   α, and volume V , for the specific cases of an ideal gas, for which   α  =  1      /    T, or constant pressure (  d  P  =  0), thus giving   d  H  =      C    P      d  T and then   Δ  H  =  ∫      C    P      d  TTo calculate   Δ  S for instance, you&#039;d express dS in the variables you wish to use, e.g.,  d  S  =            (                        d          S                          d          T                    )        P    d  T  +            (                        d          S                          d          P                    )        T    d  P  .Then you&#039;d figure out what material properties those partial derivatives refer to, simplify, and integrate over the temperature range of interest. Here,       C    P    ≡  T            (                        ∂          S                          ∂          T                    )        P  , so at constant pressure   d  S  =            C      P        T    d  T and then   Δ  S  =  ∫            C      P        T    d  TThe same general strategy would be applied to calculate   Δ  G

Is there a name for this sort of thermo relationship? H_(vap sub cond)(T')-H_(vap sub cond)(T)= int_(T)^(T')Delta C_(p,m)dT

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