1. The following shows the fundamental equation of internal energy (U), [ d U=T d S-p d V ] Using this equation, derive fundamental equations of a) enthalpy (H), b) Helmholtz energy (A), and c) Gibbs free energy (G). d) Using the derived differential equations, prove the followings: [ begin{array}{l} left( frac{ partial T}{ partial V} right)_

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1. The following shows the fundamental equation of internal energy (U),  [ d U=T d S-p d V  ] Using this equation, derive fundamental equations of a) enthalpy (H), b) Helmholtz energy (A), and c) Gibbs free energy (G). d) Using the derived differential equations, prove the followings:  [  begin{array}{l}  left( frac{ partial T}{ partial V} right)_{S}=- left( frac{ partial p}{ partial S} right)_{V}     left( frac{ partial p}{ partial T} right)_{V}= left( frac{ partial S}{ partial V} right)_{T}  end{array}  ]

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(Solved): 1. The following shows the fundamental equation of internal energy (U), \[ d U=T d S-p d V \] Using ...

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