PPT: Thermodynamic Relations | Thermodynamics - Mechanical Engineering PDF Download

 Page 1


Thermodynamic Relations
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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 .