Thermodynamic Potential: Fundamental Functions Of Thermodynamics

The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions.

Thermodynamic potential have the dimensions of energy. Therefore, they are used to measure the energy of a system in terms of various variables because often we can only measure certain properties of the system, not all. For example, we can know the pressure and temperature of the system but not the volume or entropy.  

In this article, we will learn about thermodynamic potential / fundamental functions in detail. The thermodynamic potential or fundamental functions allow us to measure more state variables of the system.

Thermodynamic Potentials 

In thermodynamics, thermodynamic potentials are parameters associated with a thermodynamic system and have the dimensions of energy. Thermodynamic potential/ fundamental functions are scalar quantities used to represent the thermodynamic state of a system. 

We have four fundamental functions: Internal energy (U), Enthalpy (H), Helmholtz free energy (A) & Gibbs free energy (G). All four functions have units of energy. Any one of these functions can be used to characterize the thermodynamic properties of a macroscopic system. These four functions are sometimes called "Thermodynamics Potentials".

Thus, three extensive state functions with dimensions of energy are: Enthalpy, Helmholtz energy, and Gibbs energy. These functions, together with internal energy, are called "Thermodynamic Potentials". 

Four quantities called thermodynamic potentials are useful in the chemical thermodynamics of reactions and non-cyclic processes.

Let Us Discuss All These Functions (Thermodynamic Potentials) One By One In Detail

(1) INTERNAL ENERGY [U]

In thermodynamics, "Internal energy (also called the thermal energy) is associated with the microscopic forms of energy. Thus, It is defined as the energy associated with the random, disordered motion of molecules within the system". 

1. It is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system.
2. It is an extensive quantity, it depends on the size of the system, or on the amount of substance it contains. The SI unit of internal energy is the joule (J). It involves energy on the microscopic scale.
3. For an ideal monoatomic gas, this is the translational kinetic energy of the linear motion of "Hard Sphere" type atoms. However, for polyatomic gases there is rotational and vibrational kinetic energy as well. 
4. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance. None of these forms of energy can be measured or evaluated directly.

(2) ENTHALPY [H]

In thermodynamics, "Enthalpy is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the total heat content of a system". 

.......Enthalpy of a thermodynamic system is defined as a state function that is calculated at constant pressure condition. The unit of enthalpy is the same as energy, i.e., "Joule"........

........The total enthalpy of a system cannot be measured directly hence we calculate the change in enthalpy.........

In many thermodynamic analyses, the sum of the internal energy (U) and the product of pressure (P) and volume (V) appears, therefore it is convenient to give the combination a name, Enthalpy, and a distinct symbol, H.

➩ [ H = U + PV ]

Thus, the enthalpy is defined to be the sum of the internal energy (U) plus the product of the pressure (P) and volume (V) in a mathematical way. 

Enthalpy is then a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables. It is somewhat parallel to the first law of thermodynamics for a constant pressure system

➩ [ Q = ΔU + PΔV ] 

Since in this case, Q = ΔH

It is a useful quantity for tracking chemical reactions.

(3) HELMHOLTZ FREE ENERGY [A]

In thermodynamics, "Helmholtz free energy is a thermodynamic potential that is defined as the internal energy of the system minus the product of the temperature times the entropy of the system". It measures the maximum amount of useful work (non PV-work) obtainable from a closed thermodynamic system at a constant volume and pressure. 

Sometimes, Helmhotz free energy is also called Work Function as it measures the work. It is defined as;

              ➩ [ A ＝ U – TS ]

    Here,

          U- Internal Energy of a system

          T- Absolute temperature of surrounding

          S- Final Entropy of the system

TS- Energy, you can get from the system's environment on heating

The internal energy (U) has an exact physical meaning, it is the sum of all the kinetic and potential energies of all the particles in the system. The second term (TS) is the amount of spontaneous energy transfer.

For a constant temperature process the Helmholtz free energy gives all the reversible work.

(4) GIBBS FREE ENERGY [G]

The free energy concept was developed by Willard Gibbs in 1870s. 

In thermodynamics, "Gibbs free energy is a thermodynamic potential that is defined as the energy associated with a chemical reaction that can be used to do work". Thus, it is a measure of chemical energy. It determines whether or not a reaction is favorable.

• Gibbs free energy is a quantity used to measure the maximum work-done (reversible work) in thermodynamic system when temperature and pressure are kept constant. This work can be done on the surrounding by a system.

• All chemical systems tend naturally toward states of Minimum Gibbs free energy. Free energy is a thermodynamic function related to spontaneity and is useful in dealing with temperature dependence of spontaneity, defined by the relationship;

➩ [ G = H –TS ]

   ➩ [ G = U –TS +PV = H –TS = A +PV ]

       Here,

             T= Absolute Temperature

             S= Final Entropy of the system 

             P= Absolute Pressure

             V= Final Volume 

The change in Gibbs free energy, ΔG, in chemistry, is a very useful parameter. It can be thought of as the maximum amount of work obtainable from a reaction. 

For a process that occurs at constant temperature, the changes in free energy (∆G) is given by the equation;

            ➩ [∆G = ∆H –T∆S = ∆A +P∆V ]

CONDITIONS 

∆G ≻0; The reaction is Non-spontaneous & endo-thermic 

∆G ≺0; The reaction is Spontaneous & Exothermic 

∆G =0 ; The reaction is at equilibrium condition 

∆G serves as the single master variable that determine whether a given chemical change is thermodynamically possible or not. 

!!!!!When A Physicists Say “Free Energy” Without Indicating Helmholtz Or Gibbs, They Usually Means Helmholtz Free Energy. On The Other Hand, When A Chemists Say “Free Energy” They Almost Always Means Gibbs Free Energy!!!!!!

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