Thermodynamic Equilibrium: Definition, Equation and Examples

Thermodynamic Equilibrium

Edited By Vishal kumar | Updated on Jul 02, 2025 07:49 PM IST

Thermodynamic equilibrium is a fundamental concept in physics, describing a system where all macroscopic flows of matter and energy cease, and the system's properties remain uniform and stable over time. It occurs when a system's temperature, pressure, and chemical potential are balanced, ensuring no net exchange of energy or matter with its surroundings. This equilibrium can be divided into three types: thermal, mechanical, and chemical.

This Story also Contains

Thermodynamic Equilibrium
Quasi-Static Process
Zeroth Law of Thermodynamics
Solved Examples Based on Thermodynamic Equilibrium
Summary

In real life, thermodynamic equilibrium is seen in everyday phenomena, such as a room reaching a stable temperature after being heated or cooled. When you leave a cup of coffee on the table, it eventually reaches the same temperature as the surrounding air, illustrating thermal equilibrium. Similarly, the pressure inside a sealed balloon equalizing with atmospheric pressure demonstrates mechanical equilibrium. These examples show how thermodynamic principles govern the balance of energy in natural and artificial systems.

Thermodynamic Equilibrium

When all the thermodynamic variables attain a steady value i.e. they do not change with respect to time, the system is said to be in the state of thermodynamic equilibrium. For the system to attain thermodynamic equilibrium, the following equilibrium must be attained

(i) Mechanical equilibrium: There is no unbalanced force between the system and its surroundings. There is no pressure gradient.

(ii) Thermal equilibrium: There is a uniform temperature in all parts of the system and is the same as that of the surroundings. There is no temperature gradient.

(iii) Chemical equilibrium: There is a uniform chemical composition throughout the system and the surroundings. There is no concentration gradient.

Quasi-Static Process

A quasi-static process is a thermodynamic process which happens slowly enough for the system such that each state will remain in internal equilibrium.

Example of quasi-static compression - when the volume of a system changes at enough rate to allow the pressure to remain constant throughout the system

Zeroth Law of Thermodynamics

If systems A and B are each in thermal equilibrium and B and C are in thermal equilibrium with each other, then A and C are in thermal equilibrium with each other.

Zeroth law leads to the concept of temperature. All bodies in thermal equilibrium must have a common property. This common property is called temperature.

Solved Examples Based on Thermodynamic Equilibrium

Example 1: A system can said to be in thermodynamic equilibrium if

1) The mass of the system does not change with time

2) The pressure of the system does not change with time

3) Macroscopic variables (Pressure, volume, temperature, mass and composition) that characterise the system do not change with time

4) None of these

Solution:

Thermodynamics Equilibrium - When Thermodynamics variables attain a steady state i,e, they are independent of time.

e.g. P, V, and T become independent of time.

Hence, the answer is the option (3).

Example 2: The condition for "mechanical equilibrium" in the thermodynamic process is

1) The temperature of the system and surroundings should remain the same

2) There should be no unbalanced force either within the system or between the system and its surroundings.

3) The mass of the system should be conserved.

4) The momentum of the system should be conserved.

Solution:

Mechanical Equilibrium

There is no unbalanced force between the system and its surroundings.

Fresultant =0

Hence, the answer is the option (2).

Example 3: "If the temperature of working substance must not differ appreciably from that of the surrounding of any stage of the cycle of the operations" is the condition of

1) Chemical equilibrium

2) Thermal equilibrium

3) Mechanical equilibrium

4) None of these

Solution:

Thermal Equilibrium

There is a uniform temperature in all parts of the system and is the same as that of the surroundings.

T is independent of time.

All parts of the system and surroundings should remain at the same temperature

Hence, the answer is the option (2).

Example 4: In the case of "chemical equilibrium" which statement is not true?

1) The internal structure of the system should not change due to chemical reactions.

2) No new product should formed in the process.

3) There should be uniform chemical composition throughout the system and surroundings.

4) None of these

Solution:

Chemical Equilibrium

There is a uniform chemical composition throughout the system and the surroundings.

No variation of the chemical composition.

All statements are true for chemical equilibrium

Hence, the answer is the option (4).

Example 5: Zeroth law of thermodynamics is related to the concept of

1) Pressure

2) Heat

3) Temperature

4) Energy

Solution:

Concept of Temperature

Zeroth law leads to the concept of temperature. All bodies in thermal equilibrium must have a common property.

This common property is called temperature.

Hence, the answer is the option (3).

Summary

Thermodynamic equilibrium occurs when a system's temperature, pressure, and chemical composition remain constant over time, with no net exchange of matter or energy with its surroundings. It consists of three types: mechanical, thermal, and chemical equilibrium. The Zeroth Law of Thermodynamics introduces the concept of temperature, stating that if two systems are in thermal equilibrium with a third, they are also in equilibrium with each other. Quasi-static processes allow systems to transition slowly while maintaining equilibrium at each state.

Frequently Asked Questions (FAQs)

1. What is quasi-static equilibrium in thermodynamics?

Quasi-static equilibrium is a theoretical concept where a system undergoes changes so slowly that it remains infinitesimally close to equilibrium at all times. While not physically achievable, it's a useful idealization for analyzing thermodynamic processes and calculating work done on or by a system.

2. What is the relationship between thermodynamic equilibrium and reversibility?

A system in thermodynamic equilibrium can undergo only reversible processes. Any spontaneous change would move the system away from equilibrium. Conversely, for a process to be truly reversible, the system must remain infinitesimally close to equilibrium at all times, which is only possible in the limit of infinitely slow changes.

3. What is the role of pressure in thermodynamic equilibrium?

Pressure is a key variable in thermodynamic equilibrium. Mechanical equilibrium requires uniform pressure throughout a system (in the absence of external fields). Pressure also affects phase equilibria, chemical equilibria, and many other thermodynamic properties. In multi-phase systems, the pressures of each phase must be equal at equilibrium.

4. How does the concept of thermodynamic equilibrium apply to stars?

Stars are not in true thermodynamic equilibrium due to ongoing nuclear reactions and energy loss through radiation. However, many stars maintain a state of hydrostatic equilibrium, where gravitational collapse is balanced by internal pressure. Local thermodynamic equilibrium is often assumed for different layers within a star to simplify analysis.

5. What is local thermodynamic equilibrium, and how does it differ from global equilibrium?

Local thermodynamic equilibrium (LTE) is a state where small regions of a system are in equilibrium with their immediate surroundings, but the entire system may not be in equilibrium. Global equilibrium, on the other hand, refers to the entire system being in equilibrium. LTE is often used in analyzing systems that are not in full thermodynamic equilibrium, such as in astrophysics or plasma physics.

6. What is thermodynamic equilibrium?

Thermodynamic equilibrium is a state where a system has no tendency to change its macroscopic properties over time. It occurs when thermal, mechanical, and chemical equilibrium are all achieved simultaneously within the system and between the system and its surroundings.

7. How does thermal equilibrium differ from thermodynamic equilibrium?

Thermal equilibrium is just one component of thermodynamic equilibrium. It refers to a state where two systems have the same temperature and no net heat transfer occurs between them. Thermodynamic equilibrium, however, requires thermal equilibrium plus mechanical and chemical equilibrium.

8. Can a system be in thermal equilibrium but not in thermodynamic equilibrium?

Yes, a system can be in thermal equilibrium without being in full thermodynamic equilibrium. For example, a compressed gas in a cylinder might have the same temperature as its surroundings (thermal equilibrium) but still be under pressure (not in mechanical equilibrium).

9. What are the three types of equilibrium that make up thermodynamic equilibrium?

The three types of equilibrium that constitute thermodynamic equilibrium are:

10. How does the concept of thermodynamic equilibrium apply to phase changes?

During a phase change, such as melting or boiling, a system is in thermodynamic equilibrium when the rates of the forward and reverse processes are equal. For example, in a liquid-vapor equilibrium, the rate of evaporation equals the rate of condensation, maintaining a constant vapor pressure and temperature.

11. What is the zeroth law of thermodynamics, and how does it relate to thermodynamic equilibrium?

The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law is fundamental to understanding thermodynamic equilibrium, as it establishes the transitive property of thermal equilibrium and allows for the definition of temperature.

12. How long does it take for a system to reach thermodynamic equilibrium?

The time it takes for a system to reach thermodynamic equilibrium varies depending on the system's properties and initial conditions. Some systems may reach equilibrium quickly, while others may take a very long time or never truly reach perfect equilibrium. The approach to equilibrium is often exponential, with the rate of change slowing as the system gets closer to equilibrium.

13. How does the Gibbs free energy relate to thermodynamic equilibrium?

At constant temperature and pressure, a system reaches thermodynamic equilibrium when its Gibbs free energy is minimized. Any spontaneous change in the system will result in a decrease in Gibbs free energy until equilibrium is reached. At equilibrium, the change in Gibbs free energy for any process becomes zero.

14. What is the difference between thermodynamic equilibrium and steady state?

Thermodynamic equilibrium is a state where all flows and changes within a system have ceased. A steady state, on the other hand, is a condition where the system's properties remain constant over time despite ongoing processes. Steady states require a continuous input of energy or matter to maintain, while equilibrium does not.

15. How does the concept of thermodynamic equilibrium apply to the atmosphere?

The Earth's atmosphere is not in true thermodynamic equilibrium due to constant energy input from the Sun and varying conditions across the globe. However, local regions can be approximated as being in thermodynamic equilibrium for short time scales. Understanding deviations from equilibrium is crucial for meteorology and climate science.

16. How does the concept of entropy relate to thermodynamic equilibrium?

Entropy is a measure of the disorder in a system. In thermodynamic equilibrium, a system reaches its maximum entropy state for its given energy and volume. This means that the system has reached its most probable macrostate, with no tendency to change spontaneously.

17. How does the presence of external fields affect thermodynamic equilibrium?

External fields, such as gravitational or electromagnetic fields, can influence the conditions for thermodynamic equilibrium. In the presence of these fields, equilibrium may involve gradients in properties like pressure or chemical potential. For example, in a gravitational field, the pressure in a fluid at equilibrium increases with depth, even though the temperature remains constant.

18. How does the concept of thermodynamic equilibrium apply to living organisms?

Living organisms are open systems that are never in true thermodynamic equilibrium, as they constantly exchange matter and energy with their environment. However, they maintain a steady state far from equilibrium through complex metabolic processes. This state is sometimes called dynamic equilibrium or homeostasis.

19. What is the significance of the Maxwell-Boltzmann distribution in thermodynamic equilibrium?

The Maxwell-Boltzmann distribution describes the distribution of particle velocities in a gas at thermodynamic equilibrium. It is a consequence of statistical mechanics and provides a link between the microscopic properties of particles and macroscopic thermodynamic quantities like temperature and pressure.

20. What is the role of temperature in determining thermodynamic equilibrium?

Temperature plays a crucial role in thermodynamic equilibrium. It determines the distribution of energy among particles and affects the rates of processes that lead to equilibrium. At higher temperatures, systems generally reach equilibrium faster due to increased molecular motion and collision rates.

21. How does the concept of thermodynamic equilibrium apply to black holes?

In black hole thermodynamics, a black hole is considered to be in thermodynamic equilibrium when its Hawking radiation is in equilibrium with the cosmic microwave background radiation. This equilibrium determines the black hole's temperature and entropy, linking concepts from general relativity with thermodynamics.

22. How does the third law of thermodynamics relate to thermodynamic equilibrium?

The third law of thermodynamics states that as a system approaches absolute zero temperature, it reaches a state of minimum entropy. This implies that perfect thermodynamic equilibrium is theoretically achievable only at absolute zero, where all molecular motion ceases. However, this state is practically unattainable.

23. What is the significance of the Boltzmann factor in thermodynamic equilibrium?

The Boltzmann factor, e^(-E/kT), describes the relative probability of a system being in a particular energy state E at temperature T. It is fundamental to statistical mechanics and explains how energy is distributed among particles in a system at thermodynamic equilibrium, forming the basis for many equilibrium properties.

24. What is the relationship between thermodynamic equilibrium and the second law of thermodynamics?

The second law of thermodynamics states that the entropy of an isolated system always increases until it reaches a maximum at thermodynamic equilibrium. This law explains why systems spontaneously move towards equilibrium and why certain processes are irreversible.

25. How does the concept of thermodynamic equilibrium apply to phase diagrams?

Phase diagrams represent the equilibrium states of a system under various conditions of temperature, pressure, and composition. Each point on a phase diagram represents a state of thermodynamic equilibrium, while the lines represent conditions where multiple phases can coexist in equilibrium.

26. How does the concept of thermodynamic equilibrium apply to quantum systems?

In quantum systems, thermodynamic equilibrium is described by a density matrix that maximizes the von Neumann entropy subject to constraints on observables. The principles of quantum statistical mechanics, such as the quantum version of the equipartition theorem, govern the equilibrium properties of these systems.

27. How does the concept of thermodynamic equilibrium apply to superconductors?

Superconductors exhibit a unique thermodynamic equilibrium state below their critical temperature, characterized by zero electrical resistance and perfect diamagnetism (Meissner effect). This state represents a macroscopic quantum phenomenon where electron pairs condense into a coherent state, minimizing the system's free energy.

28. What is the significance of the Helmholtz free energy in describing thermodynamic equilibrium?

The Helmholtz free energy (F = U - TS) is minimized at equilibrium for systems at constant volume and temperature. It represents the useful work obtainable from a system and is particularly important for describing equilibrium in situations where volume, rather than pressure, is held constant.

29. What is the role of the grand canonical ensemble in describing thermodynamic equilibrium?

The grand canonical ensemble is used to describe systems in thermal and chemical equilibrium with a reservoir, allowing for fluctuations in both energy and particle number. It is particularly useful for describing open systems and phase equilibria, providing a framework for calculating thermodynamic properties when both temperature and chemical potential are fixed.

30. What is the difference between stable and metastable equilibrium in thermodynamics?

Stable equilibrium is a state where small disturbances cause the system to return to its original state. Metastable equilibrium is a state that appears stable but can transition to a more stable state if given enough energy. For example, supercooled water is in metastable equilibrium and can suddenly freeze if disturbed.

31. What is the role of fluctuations in thermodynamic equilibrium?

Even in thermodynamic equilibrium, microscopic fluctuations constantly occur due to the random motion of particles. These fluctuations are typically small and average out over time and space in macroscopic systems. However, they become more significant in small systems or near critical points, leading to phenomena like critical opalescence.

32. How does the equipartition theorem relate to thermodynamic equilibrium?

The equipartition theorem states that in thermal equilibrium, energy is shared equally among all accessible degrees of freedom of a system. This principle is a consequence of the system being in thermodynamic equilibrium and helps explain many phenomena, such as the specific heat capacities of gases.

33. How does the concept of thermodynamic equilibrium apply to chemical reactions?

In chemical equilibrium, which is part of thermodynamic equilibrium, the forward and reverse reaction rates are equal, resulting in no net change in the concentrations of reactants and products. The equilibrium constant, derived from the law of mass action, quantifies this balance and is related to the change in Gibbs free energy of the reaction.

34. What is the role of chemical potential in thermodynamic equilibrium?

Chemical potential is a measure of how the Gibbs free energy of a system changes with the addition or removal of a particular component. In thermodynamic equilibrium, the chemical potential of each component must be uniform throughout the system. This principle is crucial for understanding phase equilibria and chemical reactions.

35. How does the concept of thermodynamic equilibrium apply to the early universe?

In the early universe, matter and radiation were in thermal equilibrium due to frequent interactions. As the universe expanded and cooled, different particle species fell out of equilibrium at different times. Understanding these departures from equilibrium is crucial for explaining phenomena like Big Bang nucleosynthesis and the cosmic microwave background.

36. What is the significance of the partition function in describing thermodynamic equilibrium?

The partition function is a central quantity in statistical mechanics that encapsulates all the statistical properties of a system in thermodynamic equilibrium. It allows for the calculation of macroscopic thermodynamic quantities from microscopic properties and is essential for understanding the behavior of systems at equilibrium.

37. How does the concept of thermodynamic equilibrium apply to non-ideal gases?

For non-ideal gases, interactions between particles become significant, complicating the conditions for thermodynamic equilibrium. These interactions lead to deviations from the ideal gas law and can result in phenomena like phase transitions. The van der Waals equation and other equations of state attempt to account for these non-ideal behaviors in describing equilibrium states.

38. What is the role of fluctuation-dissipation theorem in thermodynamic equilibrium?

The fluctuation-dissipation theorem relates the response of a system in thermodynamic equilibrium to a small applied force to the spontaneous fluctuations of the system. It provides a deep connection between microscopic fluctuations and macroscopic dissipative processes, and is fundamental to understanding transport phenomena and linear response theory.

39. What is the significance of the Onsager reciprocal relations in near-equilibrium thermodynamics?

The Onsager reciprocal relations describe symmetries in the coefficients that relate thermodynamic forces to their corresponding fluxes in systems close to equilibrium. These relations are a consequence of microscopic reversibility and provide important constraints on the behavior of systems slightly perturbed from equilibrium.

40. How does the concept of thermodynamic equilibrium apply to magnetic systems?

In magnetic systems, thermodynamic equilibrium involves the alignment of magnetic moments. The competition between the tendency of moments to align (minimizing energy) and the tendency towards disorder (maximizing entropy) leads to phenomena like paramagnetism, ferromagnetism, and phase transitions, all of which can be described using equilibrium thermodynamics.

41. What is the role of ergodicity in thermodynamic equilibrium?

Ergodicity is the assumption that, over long periods, the time average of a system's properties equals the ensemble average. This concept is crucial for connecting microscopic dynamics to macroscopic equilibrium properties. In ergodic systems, a single trajectory will eventually explore all accessible microstates, justifying the use of statistical ensembles to describe equilibrium.

42. How does the concept of thermodynamic equilibrium apply to the oceans?

The Earth's oceans are not in true thermodynamic equilibrium due to constant energy input from the Sun, tidal forces, and interactions with the atmosphere. However, local regions can be approximated as being in quasi-equilibrium. Understanding deviations from equilibrium is crucial for studying ocean circulation, heat transport, and the carbon cycle.

43. What is the role of the canonical ensemble in describing thermodynamic equilibrium?

The canonical ensemble is a statistical ensemble used to represent the possible states of a system in thermal equilibrium with a heat bath at a fixed temperature. It provides a probabilistic description of the system's microstates and allows for the calculation of macroscopic thermodynamic properties, bridging microscopic and macroscopic descriptions of equilibrium.

44. How does the concept of thermodynamic equilibrium apply to glasses and amorphous solids?

Glasses and amorphous solids are non-equilibrium systems that are trapped in metastable states. They do not reach true thermodynamic equilibrium on observable timescales but instead undergo extremely slow relaxation processes. Understanding their behavior often requires concepts from non-equilibrium thermodynamics.

45. What is the significance of the Le Chatelier's principle in thermodynamic equilibrium?

Le Chatelier's principle states that when a system at equilibrium is subjected to a change in conditions (temperature, pressure, concentration), the system will respond by shifting the equilibrium to counteract the change. This principle is crucial for predicting how equilibrium systems will respond to perturbations.

46. How does the concept of thermodynamic equilibrium apply to the Earth's climate system?

The Earth's climate system is not in true thermodynamic equilibrium due to constant energy input from the Sun and internal dynamics. However, it can reach a steady state or "energy balance" where incoming and outgoing energy fluxes are equal. Understanding deviations from this balance is crucial for climate science and predicting climate change.

47. How does the concept of thermodynamic equilibrium apply to nuclear reactions?

In nuclear reactions, thermodynamic equilib