Page 1 Thermodynamic Relations Page 2 Thermodynamic Relations Some Mathematical Theorem • Theorem 1- If the relation exists among relations x, y and z, then z may be expressed as a function of x and y. Where Where z, M and N are functions of x and y. Differentiating M partially with respect to y , and N with respect to x. The order of differentiation is immaterial for properties since they are continuous point functions and have exact differentials. Therefore, the two relations above are identical: This is the condition of exact differential. In thermodynamics, this relation forms the basis for the development of the Maxwell relations discussed in the next section. Page 3 Thermodynamic Relations Some Mathematical Theorem • Theorem 1- If the relation exists among relations x, y and z, then z may be expressed as a function of x and y. Where Where z, M and N are functions of x and y. Differentiating M partially with respect to y , and N with respect to x. The order of differentiation is immaterial for properties since they are continuous point functions and have exact differentials. Therefore, the two relations above are identical: This is the condition of exact differential. In thermodynamics, this relation forms the basis for the development of the Maxwell relations discussed in the next section. THE MAXWELL RELATIONS • The equations that relate the partial derivatives of properties P , v, T, and s of a simple compressible system to each other are called the Maxwell relations. Since U,H ,F and G are thermodynamics properties and exact differential of the type dz = Mdx + Ndy, then Page 4 Thermodynamic Relations Some Mathematical Theorem • Theorem 1- If the relation exists among relations x, y and z, then z may be expressed as a function of x and y. Where Where z, M and N are functions of x and y. Differentiating M partially with respect to y , and N with respect to x. The order of differentiation is immaterial for properties since they are continuous point functions and have exact differentials. Therefore, the two relations above are identical: This is the condition of exact differential. In thermodynamics, this relation forms the basis for the development of the Maxwell relations discussed in the next section. THE MAXWELL RELATIONS • The equations that relate the partial derivatives of properties P , v, T, and s of a simple compressible system to each other are called the Maxwell relations. Since U,H ,F and G are thermodynamics properties and exact differential of the type dz = Mdx + Ndy, then Helmholtz and Gibbs Function • The Gibbs free energy or Gibbs function is a thermodynamic function of a certain system , it is equal to the enthalpy H of the system minus the product of the entropy S of this system and its thermodynamic temperature T . Page 5 Thermodynamic Relations Some Mathematical Theorem • Theorem 1- If the relation exists among relations x, y and z, then z may be expressed as a function of x and y. Where Where z, M and N are functions of x and y. Differentiating M partially with respect to y , and N with respect to x. The order of differentiation is immaterial for properties since they are continuous point functions and have exact differentials. Therefore, the two relations above are identical: This is the condition of exact differential. In thermodynamics, this relation forms the basis for the development of the Maxwell relations discussed in the next section. THE MAXWELL RELATIONS • The equations that relate the partial derivatives of properties P , v, T, and s of a simple compressible system to each other are called the Maxwell relations. Since U,H ,F and G are thermodynamics properties and exact differential of the type dz = Mdx + Ndy, then Helmholtz and Gibbs Function • The Gibbs free energy or Gibbs function is a thermodynamic function of a certain system , it is equal to the enthalpy H of the system minus the product of the entropy S of this system and its thermodynamic temperature T . Helmholtz and Gibbs Function • The Helmholtz free energy or Helmholtz function is a thermodynamic function of a certain system equal to internal energy U of the system minus the the entropy S of this system multiplied by its thermodynamic temperature T .Read More

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