Thermodynamic Properties of Fluid

Thermodynamic Properties of Fluid Classified as follows

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1. The Reference Properties
2. The Energy Properties
3. The Derived Properties

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The Reference Properties

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Properties are used to defined the state of the system are called the reference properties.

The Reference Properties are allso known as Primary Properties

• The Reference Properties have absolute values.
• Pressure \((P)\), Volume \((V)\), Temperature \((T)\), Entropy \((S)\) are the primary properties or reference properties.
• Pressure and Temperatue are Intensive Properties, and Volume and Entropy are Extensive Properties
• The composition is also refered as primary property when we deal with the solutions.

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The Energy Properties

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• Internal Energy\((U)\), Enthalpy\((H)\), Helmholtz Free Energy\((A)\), and Gibbs Free Energy\((G)\) are the energy properties.
• All the energy poroperties are extensive properties.
• All the energy poroperties can be evaluted with respect to some reference plane.
• Why these properties are called as energy properties?

Changes in these properties indicate useful work under certain conditions, thats why they are called as energy properties.

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The Derived Properties

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• The derived properties are the partial derivative of the reference properties or the energy properties.
• Specific Heat \((C)\), Coefficient of Expansion \((\beta)\), Joule-Thomson Coefficient \((\mu)\) are the derived properties.

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Fundamental Property Relations

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\[dU= T dS - P dV --------- (1)\] \[dH = T dS + V dP --------- (2)\] \[dA = -S dT - P dV --------- (3)\] \[dG = -S dT + V dP --------- (4)\]

Derivation of Fundamental Property Relation

• First law of thermodynamics for closed syatem.
\[dU = dQ - dW--------- (5)\]

We know,

\[dQ = T dS\] \[dW = P dV\]

Put these values in equation no (5).

We get,

\[dU = TdS - PdV --------- (1)\]
• As per the defination of Enthalpy,
\[H = U + PV --------- (6)\]

Taking differential of equation no. (6)

\[dH = dU + PdV + VdP --------- (7)\]

Put value of \(dU\) form equation no. (1) to equation no (7).

\[dH = TdS - PdV + PdV + VdP\] \[dH = TdS + VdP --------- (2)\]
• As per the defination of Helmholtz free energy,
\[A = U - TS --------- (8)\]

Taking differential of equation no. (8)

\[dA = dU - TdS - SdT --------- (9)\]

Put value of \(dU\) form equation no. (1) to equation no (9).

\[dA = TdS - PdV - TdS - SdT\] \[dA = - SdT - PdV --------- (3)\]
• As per the defination of Gibbs free energy,
\[G = H - TS --------- (10)\]

Taking differential of equation no. (10)

\[dG = dH - TdS - SdT --------- (9)\]

Put value of \(dH\) form equation no. (2) to equation no (10).

\[dG = TdS + VdP - TdS - SdT\] \[dA = - SdT + VdP --------- (4)\]

Here, Energy Properties are functionally related to special pair of reference properties.

\(S\) and \(V\) are the canonical variables (special variables) of internal energy \(U.\)

\[U = f(S,V)\]

\(S\) and \(P\) are the canonical variables (special variables) of enthalpy \(H.\)

\[H = f(S,P)\]

\(V\) and \(T\) are the canonical variables (special variables) of internal energy \(A.\)

\[A = f(T,V)\]

\(P\) and \(T\) are the canonical variables (special variables) of internal energy \(G.\)

\[G = f(T,P)\]

Read Also:
Duhem’s Theorem
Basic Concepts of Chemical Engineering Thermodynamics
Laws of Thermodynamics
Important Unit Operations of Chemical Engineering
Fundamentals of Heat Transfer
Newtonian and Non-Newtonian Fluids
Hydrostatic Equilibrium

Manometers