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State Functions

State Functions

Edited By Shivani Poonia | Updated on Jul 02, 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)

1. How does a state function differ from a path function?
A state function depends only on the initial and final states of a system, while a path function depends on the specific path taken between those states. State functions are independent of the route, whereas path functions are influenced by the process used to change the system's state.
2. Can you give examples of state functions in thermodynamics?
Common examples of state functions include internal energy (U), enthalpy (H), entropy (S), and Gibbs free energy (G). These properties depend only on the current state of the system, not on how it reached that state.
3. Why is pressure considered a state function?
Pressure is a state function because its value depends only on the current condition of the system. Regardless of how the system reached a particular pressure, the value remains the same for that specific state.
4. Is work a state function? Why or why not?
Work is not a state function. It is a path function because the amount of work done depends on the specific path taken between the initial and final states. Different paths between the same two states can result in different amounts of work being done.
5. How does the concept of state functions relate to the First Law of Thermodynamics?
The First Law of Thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). Since internal energy is a state function, its change depends only on the initial and final states, regardless of the path taken.
6. What is a state function in thermodynamics?
A state function is a property of a system that depends only on its current state, regardless of how the system reached that state. The value of a state function is independent of the path taken to achieve it and only depends on the initial and final states of the system.
7. Can you explain why temperature is a state function?
Temperature is a state function because it is a measure of the average kinetic energy of particles in a system. This value depends only on the current state of the system and not on how it reached that state. Two identical systems at the same temperature will have the same average kinetic energy, regardless of their history.
8. How do state functions relate to the Second Law of Thermodynamics?
The Second Law of Thermodynamics introduces entropy, a state function, as a measure of the disorder in a system. The law states that the total entropy of an isolated system always increases for spontaneous processes, highlighting the importance of state functions in determining the direction of natural processes.
9. Can you explain why chemical potential is considered a state function?
Chemical potential is a state function because it represents the change in the Gibbs free energy of a system when the amount of a component is changed, keeping temperature, pressure, and other component amounts constant. Its value depends only on the current state of the system, not on how that state was reached.
10. Why is Gibbs free energy considered a state function?
Gibbs free energy (G) is a state function because it is defined in terms of other state functions: enthalpy (H), temperature (T), and entropy (S). The equation G = H - TS shows that G depends only on the current state of the system, not on its history.
11. How do state functions relate to the Third Law of Thermodynamics?
The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero is zero. This law establishes an absolute reference point for the state function entropy, allowing for the calculation of absolute entropy values for substances.
12. Can you explain why fugacity is considered a state function?
Fugacity is a state function because it is a measure of the tendency of a substance to escape from a phase, which depends only on the current state of the system. It's often used as a replacement for pressure in non-ideal gas calculations, maintaining the state function properties.
13. How do state functions relate to the concept of partial molar quantities?
Partial molar quantities, such as partial molar volume or partial molar enthalpy, are state functions. They represent the change in the total property (e.g., volume or enthalpy) of a system when one mole of a component is added at constant temperature, pressure, and amounts of other components.
14. Why is the Helmholtz free energy considered a state function?
Helmholtz free energy (A) is a state function because it is defined in terms of other state functions: internal energy (U), temperature (T), and entropy (S). The equation A = U - TS shows that A depends only on the current state of the system, not on its history.
15. How does the concept of state functions apply to electrochemical cells?
In electrochemical cells, state functions like Gibbs free energy are crucial for determining the cell potential. The change in Gibbs free energy for the cell reaction is related to the cell potential through a state function relationship, regardless of the specific cell construction or pathway of the reaction.
16. Can you explain why compressibility factor (Z) is considered a state function?
The compressibility factor (Z) is a state function because it is a measure of how much the behavior of a real gas deviates from that of an ideal gas under given conditions. Its value depends only on the current state of the gas (temperature, pressure, and composition), not on how that state was reached.
17. How do state functions relate to the concept of chemical affinity?
Chemical affinity, which drives chemical reactions, is related to the change in Gibbs free energy (a state function) of a reaction. The negative of the change in Gibbs free energy at constant temperature and pressure gives the maximum work that can be extracted from a process, independent of the path taken.
18. Why is molar volume considered a state function?
Molar volume is a state function because it depends only on the current state of the system. For a given substance under specific conditions of temperature and pressure, the volume occupied by one mole of the substance will be the same, regardless of how that state was achieved.
19. How does the concept of state functions apply to non-equilibrium thermodynamics?
In non-equilibrium thermodynamics, state functions are still valid, but their values may vary within the system. The local equilibrium assumption allows for the definition of state functions at each point in the system, even when the system as a whole is not at equilibrium.
20. How does the concept of state functions apply to surface tension?
Surface tension is a state function because it depends only on the current state of the interface between two phases. For a given substance under specific conditions of temperature and pressure, the surface tension will be the same, regardless of how the interface was formed.
21. How do state functions relate to the concept of thermodynamic stability?
Thermodynamic stability is determined by the values of state functions like Gibbs free energy. A system is at its most stable when its Gibbs free energy is at a minimum for the given conditions. The state function nature of Gibbs free energy allows for the prediction of stability regardless of the path taken to reach a particular state.
22. Can you explain why the Seebeck coefficient is considered a state function?
The Seebeck coefficient, which describes the thermoelectric voltage induced in response to a temperature difference across a material, is a state function. Its value depends only on the current state of the material and the temperature gradient, not on how that state was achieved.
23. How do state functions relate to the concept of thermodynamic degrees of freedom?
Thermodynamic degrees of freedom represent the number of independent variables needed to fully define the state of a system. State functions provide a way to describe these degrees of freedom, as each independent state function corresponds to a degree of freedom in the system.
24. Why is the bulk modulus considered a state function?
The bulk modulus, which describes a substance's resistance to uniform compression, is a state function because it depends only on the current state of the material. For a given substance under specific conditions, the bulk modulus will be the same, regardless of how that state was reached.
25. How does the concept of state functions apply to statistical mechanics?
In statistical mechanics, state functions are derived from the partition function, which describes the statistical properties of a system in thermodynamic equilibrium. The partition function itself is a function of state variables, ensuring that the derived properties maintain their state function character.
26. Can you explain why the Grüneisen parameter is considered a state function?
The Grüneisen parameter, which relates the volume dependence of vibrational properties to thermal properties in solids, is a state function. It depends only on the current state of the material, not on how that state was achieved, and is crucial in understanding the thermodynamic behavior of solids at high pressures and temperatures.
27. Why is the magnetic susceptibility considered a state function?
Magnetic susceptibility, which describes how a material responds to an applied magnetic field, is a state function because it depends only on the current state of the material. For a given substance under specific conditions, the magnetic susceptibility will be the same, regardless of how that state was reached.
28. How does the concept of state functions apply to quantum thermodynamics?
In quantum thermodynamics, state functions are defined in terms of the density matrix of the system, which contains all the information about the quantum state. The von Neumann entropy, for example, is a quantum analog of the classical entropy and maintains its state function character in the quantum realm.
29. Can you explain why the Peltier coefficient is considered a state function?
The Peltier coefficient, which describes the heat absorbed or released when an electric current passes through a junction between two different materials, is a state function. Its value depends only on the current state of the materials and the junction, not on how that state was achieved.
30. How do state functions relate to the concept of thermodynamic fluctuations?
Thermodynamic fluctuations represent small, spontaneous deviations from equilibrium values of state functions. The study of these fluctuations is based on the properties of state functions, as the probability of a given fluctuation is related to the change in state functions like entropy or free energy associated with that fluctuation.
31. How do state functions simplify thermodynamic calculations?
State functions simplify calculations because they allow us to determine changes in system properties without needing to know the exact path taken between states. This means we can focus on initial and final conditions rather than tracking every step of a process.
32. What is the significance of Hess's Law in relation to state functions?
Hess's Law states that the enthalpy change for a reaction is independent of the pathway between the initial and final states. This law is a direct consequence of enthalpy being a state function, allowing us to calculate overall enthalpy changes by combining individual steps, regardless of the actual reaction pathway.
33. How does the concept of state functions apply to cyclic processes?
In a cyclic process, the system returns to its initial state after undergoing a series of changes. Since state functions depend only on the system's state, the net change in any state function over a complete cycle is zero. This principle is crucial in understanding the efficiency of heat engines and refrigeration cycles.
34. Why is heat not considered a state function?
Heat is not a state function because the amount of heat transferred depends on the specific path taken between initial and final states. Different paths can result in different amounts of heat transfer, even if the initial and final states are the same.
35. How do state functions relate to the concept of reversibility in thermodynamics?
State functions are independent of the path taken, including whether that path is reversible or irreversible. However, reversible processes are often used to calculate changes in state functions because they allow for simpler mathematical treatment and represent the maximum efficiency possible for a given process.
36. Can you explain the relationship between state functions and exact differentials?
State functions are associated with exact differentials in mathematics. An exact differential is one that can be integrated independently of the path, which aligns with the path-independent nature of state functions. This property allows for the use of powerful mathematical tools in thermodynamic analysis.
37. How does the concept of state functions apply to phase changes?
During phase changes, such as melting or vaporization, the values of state functions like enthalpy and entropy change discretely. These changes are independent of the path taken to achieve the phase change, reinforcing the state function concept even in processes involving discontinuous property changes.
38. Why is volume considered a state function?
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.
39. How do state functions contribute to the concept of thermodynamic equilibrium?
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.
40. How does the concept of state functions apply to adiabatic processes?
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.
41. Can you explain the relationship between state functions and thermodynamic potentials?
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.
42. Why is heat capacity not considered a state function?
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.
43. How does the concept of state functions apply to open systems?
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.
44. Can you explain why the Joule-Thomson coefficient is not a state function?
The Joule-Thomson coefficient, which describes the temperature change of a gas during an isenthalpic expansion, is not a state function. It depends on the specific path taken during the expansion process and can vary depending on the initial conditions and the exact nature of the expansion.
45. How do state functions relate to the concept of exergy?
Exergy, which represents the maximum useful work that can be extracted from a system as it reaches equilibrium with its environment, is a state function. It depends only on the current state of the system and the state of the environment, not on the path taken to reach that state.
46. Why is the speed of sound in a gas considered a state function?
The speed of sound in a gas is a state function because it depends only on the current properties of the gas, such as temperature, pressure, and composition. For a given state of the gas, the speed of sound will be the same, regardless of how that state was achieved.
47. Can you explain why the coefficient of thermal expansion is not strictly a state function?
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.
48. Why is the isothermal compressibility considered a state function?
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.
49. How does the concept of state functions apply to phase diagrams?
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.
50. How do state functions relate to the concept of thermodynamic coupling?
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.

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