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State Functions

State Functions

Shivani PooniaUpdated on 02 Jul 2025, 06:31 PM IST

State functions are such properties of the system that depend only on the current state of the system and not on the path taken to achieve that state. These functions provide fundamental information about the equilibrium state of a system and do not turn either upon the process or transformation that the system undergoes. All the important state functions of thermodynamics include internal energy, enthalpy, entropy, Gibbs free energy, Helmholtz free energy, volume, pressure, and temperature. Each of these functions can be used to describe something about the properties and behaviors of a system.

This Story also Contains

  1. Types of Thermodynamic Process
  2. Some Solved Examples
  3. Summary
State Functions
State Functions

Path and State Function


It is the path along which a change of state occurs. It is a path of change of a system from one equilibrium state or another which is usually accompanied by a change in energy or mass.

Types of Thermodynamic Process


1. Isothermal Process

Here the temperature is kept constant during each step of the process. Example,

ΔT=0,ΔE=0

  • It is achieved by using a thermostatic control.

  • Heat can be absorbed or evolved here that is, can be exchanged with the surroundings.

For example, Freezing, melting, evaporation, and condensation.

2. Isobaric Process
Here the pressure is kept constant (ΔP=0) during each step of the process.
For example, the Expansion of gas in an open system.

  • Vaporization and heating of water up to its boiling point occur at the same atmospheric pressure.

  • 3. Isochoric Process

    Here volume is kept constant. (ΔV=0) during each step of the process.

    For example, the Heating of substance in a closed vessel (system) or non-expanding chamber.

    4. Adiabatic Process

    • Here no exchange of heat takes place between the system and the surroundings that is, (Q = 0)

    • It is achieved by insulating the system or in closed insulated containers (thermos).

  • 5. Cyclic Process

    • Here the System undergoes a series of changes but finally comes back to the initial state.

  • ΔE=0,ΔH=0

    Recommended topic video on(State Functions)


Some Solved Examples

Example 1: Which one of the following is a state property or function?

1)Heat

2)Work

3)Loss of energy due to friction

4) Potential energy.

Solution

Path and state function- It is the path along which a change of state occurs. It is a path of change of a system from one equilibrium state or another which is usually accompanied by a change in energy or mass. A physical quantity is said to be a state function if its value depends only upon the state of the system and does not depend upon the path by which this state has been attained For example, a person standing on the roof of a five-storeyed building has fixed potential energy, irrespective of the fact whether he reached there by stairs or lift. Thus, the potential energy of the person is a state function.
Hence, the answer is the option (4).

Example 2: Internal energy is an example of

1)Path function

2) State function

3)Both A and B

4)None of these

Solution

State Function - Any property of the system is dependent only on the state of the system and not on the path by which the system is obtained. Internal energy, Enthalpy, Entropy, Pressure, temperature, volume, etc. The function whose value depends only on the state of a system is known as the state function.

Hence, the answer is the option (2).

Example 3: Which of the following is the path function?

1)Temperature

2)Enthalpy

3) Heat

4)Entropy

Solution

Quantities are dependent on the Path by which the system has achieved a particular state. e.g. Heat, Work, Heat capacity Hence, heat is a path function.

Hence, the answer is the option (3).

Example 4: U is equal to :

1) Adiabatic work

2) Isothermal work

3) Isochoric work

4)Isobaric work

Solution

Adiabatic Process -

Heat exchange between the system and surroundings is zero.

So,

ΔE=q+w

q=0

ΔE=w

No change in internal energy = Adiabatic work

Hence, the answer is an option (1).

Example 5: A process in which volume remains constant is called:

1) Isochoric process

2)Isothermal process

3)Adiabatic process

4)Isobaric process.

Solution

Isochoric Process- Here volume is kept constant. (ΔV=0) during each step of the process, For example, the Heating of substance in a closed vessel (system) or non-expanding chamber. The process is termed isochoric in which volume remains constant throughout the change, i.e., dV=0.

Hence, the answer is the option (1).

Summary

State functions in thermodynamics are necessary to define the equilibrium state of a system regardless of the path. Internal energy, U, encompasses all kinds of energy, kinetic and potential energies, present in the system. In contrast, enthalpy, H, is defined as the sum of internal energy and the product of pressure and volume, so it expresses the total heat content. Entropy, S, comes with disorder and increases in spontaneous processes according to the second law of thermodynamics. Gibbson free energy, G, merges enthalpy with entropy to calculate the spontaneity of a process at constant temperature and pressure, with ΔG < 0 being spontaneous. Helmholtz free energy, A, does the same thing but is used at constant volume and temperature and thus gives the maximum work available. Volume, V, and pressure, P, describe both the amount of space that a substance occupies, as well as the force per unit area respectively.

Frequently Asked Questions (FAQs)

Q: How do state functions relate to the concept of thermodynamic coupling?
A:
Thermodynamic coupling occurs when a change in one state function leads to changes in others. For example, the Maxwell relations describe how changes in different state functions are related. These relationships are possible because state functions depend only on the system's state, allowing for consistent connections between different properties.
Q: How does the concept of state functions apply to phase diagrams?
A:
Phase diagrams represent the states of matter as a function of state variables like temperature and pressure. The boundaries between phases on these diagrams represent conditions where state functions like Gibbs free energy are equal for two phases, illustrating the importance of state functions in understanding phase behavior.
Q: Why is the isothermal compressibility considered a state function?
A:
Isothermal compressibility is a state function because it represents the fractional change in volume of a substance with pressure at constant temperature. Its value depends only on the current state of the system, not on how that state was reached.
Q: Can you explain why the coefficient of thermal expansion is not strictly a state function?
A:
The coefficient of thermal expansion is not strictly a state function because it can depend on the path taken to change the temperature. However, for small temperature changes, it can be approximated as a state function for many materials.
Q: How does the concept of state functions apply to adiabatic processes?
A:
In an adiabatic process, no heat is exchanged with the surroundings. Even though the path is restricted (no heat transfer), state functions like internal energy and entropy still only depend on the initial and final states, not on the specific adiabatic path taken.
Q: Why is volume considered a state function?
A:
Volume is a state function because it depends only on the current state of the system. For a given amount of substance under specific conditions of temperature and pressure, the volume will be the same regardless of how the system reached that state.
Q: How do state functions contribute to the concept of thermodynamic equilibrium?
A:
At thermodynamic equilibrium, all state functions remain constant over time. This stability of state functions is a key indicator of equilibrium, and changes in state functions can be used to predict the direction of spontaneous processes towards equilibrium.
Q: Can you explain the relationship between state functions and thermodynamic potentials?
A:
Thermodynamic potentials, such as internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy, are all state functions. They provide different ways of expressing the energy of a system and are chosen based on which variables (like temperature, pressure, or volume) are held constant in a given process.
Q: Why is heat capacity not considered a state function?
A:
Heat capacity itself is not a state function because it can depend on the path taken to heat the substance. However, the change in heat capacity between two states is a state function, as it depends only on the initial and final states.
Q: How does the concept of state functions apply to open systems?
A:
In open systems, where matter can be exchanged with the surroundings, state functions still apply. However, additional terms must be considered to account for the flow of matter. For example, the change in internal energy must include terms for mass transfer as well as heat and work.
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