State Functions: The volume of water in a pond can increase naturally by rainwater or by artificially supplying water through pipes. The volume of water increased in the pond is important in the way in which water is increased in the pond. So, here change in the volume depends only on the initial and final state and not on the path through which change is brought about. Such functions are called the State Function.

What is a State Function?

It refers to the state of the system and not on the path through which it gets to the state.

A temperature of one litre of water can be changed either by heating or by cooling. Here, change in temperature is more important than the path in which change is brought about.

Based on this example, a state function can be defined as a function whose value depends only upon the initial and final states of the system and not upon the path through which this state has been attained.

In other words, a physical quantity is said to be a state function if the change in its value during the process depends only upon the initial and the final state of the system and does not depend upon the path or route by which this change has been brought about.

Examples for State Function

The changes in the system can be measured in terms of pressure, volume, temperature, etc. These are known as state functions. These are also called state variables along with thermodynamic parameters, and the state of the system is also known as a thermodynamic state. A list of the state variables which describe the state of a system is:

1. Pressure \(\left( {\rm{P}} \right)\)
2. Temperature \(\left( {\rm{T}} \right)\)
3. Volume \(\left( {\rm{V}} \right)\)
4. Internal Energy (\({\rm{U}}\) or \({\rm{E}}\))
5. Enthalpy \(\left( {\rm{H}} \right)\)
6. Entropy \(\left( {\rm{S}} \right)\)
7. energy \(\left( {\rm{G}} \right)\)

How is Pressure, Temperature and Volume State Function?

1. Temperature \(\left( {\rm{T}} \right)\) is a measure of the hotness or coldness of an object. It is also defined as a measure of the kinetic energy of an object.
2. Pressure is defined as force per unit area.
3. Volume is defined as the amount of space taken up by the substance.

The change in temperature, pressure and volume does not depend on the path by which change occurs; therefore, these are state functions.

How Internal Energy is a State Function?

The total energy within a substance or a system is called its internal energy.

That is the sum of transitional energy \(\left( {{{\rm{U}}_{\rm{t}}}} \right){\rm{,}}\) electronic energy \(\left( {{{\rm{U}}_{\rm{e}}}} \right){\rm{,}}\) nuclear energy \(\left( {{{\rm{U}}_{\rm{n}}}} \right){\rm{,}}\) chemical bond energy \(\left( {{{\rm{U}}_{\rm{c}}}} \right){\rm{,}}\) potential energy \(\left( {{{\rm{U}}_{\rm{p}}}} \right){\rm{,}}\) and kinetic energy \(\left( {{{\rm{U}}_{\rm{k}}}} \right){\rm{.}}\)

\({\rm{U}} = {{\rm{U}}_{\rm{t}}} + {{\rm{U}}_{\rm{e}}} + {{\rm{U}}_{\rm{n}}} + {{\rm{U}}_{\rm{c}}} + {{\rm{U}}_{\rm{p}}} + {{\rm{U}}_{\rm{k}}}\)

Unit of internal is Joule \(\left( {{\rm{1}}\,{\mkern 1mu} {\rm{J = 1}}{{\rm{0}}^{\rm{7}}}{\mkern 1mu} {\rm{ergs}}} \right){\rm{.}}\)

Internal energy is a state function because the internal energy of a system depends upon the state of the system and not upon how the system attains that state.

The change in the internal energy \(\left( {\Delta {\rm{U}}} \right)\) depends only upon the initial and final states of the system and upon the intermediate states.

\(\Delta {\rm{U}} = {{\rm{U}}_{{\rm{final}}\,{\rm{state}}}} – {{\rm{U}}_{{\rm{initial}}\,{\rm{state}}}}\)
\(\Delta {\rm{U}} = {{\rm{U}}_2} – {{\rm{U}}_1}\)

The change in the internal energy in a chemical reaction is given by

\(\Delta {\rm{U}} = {{\rm{U}}_{{\rm{products}}}} – {{\rm{U}}_{{\rm{reactants}}}}\)

If \({{\rm{U}}_{\rm{1}}} < {{\rm{U}}_{\rm{2}}}{\rm{,}}\) energy is absorbed by the system, then \(\Delta {\rm{U}}\) will be positive. If \({{\rm{U}}_{\rm{1}}}{\rm{ > }}{{\rm{U}}_{\rm{2}}}{\rm{,}}\) energy is released by the system, then \(\Delta {\rm{U}}\) will be negative.

Is Enthalpy a State Function?

The enthalpy is also called heat content and is denoted by \({\rm{H}}{\rm{.}}\) The enthalpy of a system may be defined as the sum of the internal energy \(\left( {\rm{U}} \right)\) and pressure volume \(\left( {{\rm{PV}}} \right)\) energy, under a set of conditions.

\({\rm{H}} = {\rm{U}} + {\rm{PV}}\)

Enthalpy is a state function. Therefore, the change in enthalpy \(\left( {\Delta {\rm{H}}} \right)\) depends only upon the initial and final states of the system.

\(\Delta {\rm{H}} = {{\rm{H}}_{{\rm{final}}\,{\rm{state}}}} – {{\rm{H}}_{{\rm{initial}}\,{\rm{state}}}}\)
\(\Delta {\rm{H}} = {{\rm{H}}_2} – {{\rm{H}}_1}\)

The change in the enthalpy in a chemical reaction is given by

\(\Delta {\rm{H}} = {{\rm{H}}_{{\rm{products}}}} – {{\rm{H}}_{{\rm{reactants}}}}\)

In the exothermic process (energy is released by the system), \(\Delta {\rm{H}}\) is negative, and in the endothermic process (energy is absorbed by the system), \(\Delta {\rm{H}}\) is positive.

What is Entropy?

Entropy \(\left( {\rm{S}} \right)\) is defined as a measure of randomness or disorder of the system. The greater the randomness, the higher is the entropy. The order of randomness or entropy of solid, liquid, and gas is \({\rm{Gas}} > {\rm{Liquid}} > {\rm{Solid}}{\rm{.}}\)

The physical state, temperature, volume, and number of particles are the factors that affect entropy.

The value of entropy depends only on the initial and final state of temperature, volume and number of particles of the reaction and does not depend upon the path of the reaction. Hence, entropy is a state function.

The SI unit of change in entropy is Joules per Kelvin per mole, i.e., \({\rm{J}}{{\rm{K}}^{ – 1}}{\rm{mo}}{{\rm{l}}^{ – 1}}.\)

What is Energy?

J. Williard Gibbs has introduced the term energy to predict the direction of spontaneity. energy \(\left( {\rm{G}} \right)\) is defined as the amount of energy available for doing useful work.

\({\rm{G}} = {\rm{H}} – {\rm{TS}}\)

Here, \({\rm{H}}\) is the enthalpy of the system, \({\rm{S}}\) is the entropy of the system, and \({\rm{T}}\) is the temperature of the system on the Kelvin scale.

energy (Gibbs energy) is a state function. Therefore, the change in Gibbs energy depends only upon the initial and final states of the system and does not depend upon the path by which the change has been carried out. The change in Gibbs energy is presented by \(\Delta {\rm{G}}{\rm{.}}\)

The Gibbs energy, \({\rm{G}} = {\rm{H}} – {\rm{TS}}\)
We know that enthalpy, \({\rm{H = U + PV}}\)
Therefore, \({\rm{G = U + PV – TS}}\)

The change in Gibbs energy can be expressed as

\(\Delta {\rm{G = }}\Delta {\rm{U + }}\Delta \left( {{\rm{PV}}} \right){\rm{ – }}\Delta \left( {{\rm{TS}}} \right)\)
\(\Delta {\rm{G = }}\Delta {\rm{U + P}}\Delta V + {\rm{V}}\Delta {\rm{P}} – {\rm{T}}\Delta {\rm{S}} – {\rm{S}}\Delta {\rm{T}}\)

If the change is carried out at a constant temperature and constant pressure \(\Delta {\rm{T}} = 0\) and \(\Delta {\rm{P}} = 0\)

Therefore, \(\Delta {\rm{G}} = \Delta {\rm{U}} + {\rm{P}}\Delta {\rm{V}} – {\rm{T}}\Delta {\rm{S}}\)

Since, \(\Delta {\rm{H}} = \Delta {\rm{U}} + {\rm{P}}\Delta {\rm{V}}\)
\(\Delta {\rm{G}} = \Delta {\rm{H}} – {\rm{T}}\Delta {\rm{S}}\)

The equation \(\Delta {\rm{G}} = \Delta {\rm{H}} – {\rm{T}}\Delta {\rm{S}}\) is called Gibbs- Helmholtz equation.

Difference Between State Function and Path Function

The state function and path are two different quantities. They are differentiated as follows,

State Function	Path Function
1. Its values are independent of the path followed.	1. Its values are dependent on the path followed.
2. It is an exact differential.	2. It is not an exact differential
3. Its cyclic integral is always zero.	3. Its cyclic integral is not zero.
4. Example: Enthalpy, Entropy, Internal energy, etc.	4. Example: Heat, Work, etc.

Summary

In the article State Functions, you have understood the entropy, enthalpy, Gibbs energy, internal energy, etc., are state functions in terms of thermodynamics aspects. This knowledge is helpful in clarifying thermodynamic laws, chemical equilibrium and many more.

FAQs on State Function

Q.1. Which of the following is not a state function? Temperature, pressure, enthalpy, density, heat.
Ans: Heat is not a state function because its value depends upon the path by which change has occurred.

Q.2. What is meant by state function? Give an example.
Ans: The state function is defined as a thermodynamic function whose value depends only upon the initial and final states of a system and does not depend upon the path by which this state has been attained.
Example: Entropy.

Q.3. Explain the importance of state function.
Ans: A state function is important because it helps to calculate the change in the value of physical quantities like entropy, enthalpy, energy, etc., only by considering its initial and final values.

Q.4. What are state functions and state variables?
Ans: Certain quantities like temperature, pressure, volume, concentration, etc., are used to describe the properties of the system called state variables. State functions are physical quantities that depend only on the initial and final values.

Q.5. What is a state function? Is work a state function?
Ans: The state function is defined as a thermodynamic function whose value depends only upon the state of the system and not on the path by which this state has been attained.
Work is not a state function since magnitude of work depends on the path followed by the system to reach the final state. Work is the product of force and displacement. Both these quantities are dependent on the path.

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