I am trying to derive certain formulas and and I feel like the following expression is good for my derivation. ( ∂ u ∂ T ) p = ( ∂ u ∂ T ) V I am trying to say that the above expression is true because of first law of thermodynamics. any suggestions weather if this approach is good or not

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I am trying to derive certain formulas and and I feel like the following expression is good for my derivation.            (                        ∂          u                          ∂          T                    )        p    =            (                        ∂          u                          ∂          T                    )        V  I am trying to say that the above expression is true because of first law of thermodynamics. any suggestions weather if this approach is good or not

adwelirlz · Accepted Answer

d  U  =            (                        ∂          U                          ∂          T                    )        V    d  T  +            (                        ∂          U                          ∂          V                    )        T    d  V  d  V  =            (                        ∂          V                          ∂          T                    )        P    d  T  +            (                        ∂          V                          ∂          P                    )        T    d  Pso  d  U  =      [                  (                              ∂            U                                ∂            T                          )            V        +                  (                              ∂            U                                ∂            V                          )            T                      (                              ∂            V                                ∂            T                          )            P        ]    d  T  +            (                        ∂          U                          ∂          V                    )        T              (                        ∂          V                          ∂          P                    )        T    d  PSo,            (                        ∂          U                          ∂          T                    )        P    =      [                  (                              ∂            U                                ∂            T                          )            V        +                  (                              ∂            U                                ∂            V                          )            T                      (                              ∂            V                                ∂            T                          )            P        ]  According to this, your equation is correct for an ideal gas, but not for a real gas beyond the ideal gas region.

I am trying to derive certain formulas and and I feel like the following expression is good for my derivation. (du/dT)_p=(dU/dT)_V I am trying to say that the above expression is true because of first law of thermodynamics. any suggestions weather if this approach is good or not

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