# What is Thermal equilibrium: Definition and 103 Discussions

Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.
In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs.
Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.
A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.
In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.
Though not a widely named "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.

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1. ### B Heat exchange after thermal equilibrium

In screenshot below, systems A and B are separated by an adiabatic wall initially while each of them exchanges energy with system C via a diathermic wall. Once A and B reach thermal equilibrium with C, then A,B are allowed energy exchange via a diathermic wall, and energy exchange between A and...
2. ### I Concept of Thermal Equilibrium in the Context of Canonical Ensemble

Canonical ensemble can be used to derive probability distribution for the internal energy of the closed system at constant volume ##V## and number of particles ##N## in thermal contact with the reservoir. Also, it is stated that the temperature of both system and reservoir is the same, i.e...
3. ### I Estimating a thermal equilibrium on a custom made fridge

Hello, I'm trying to build a custom made fridge made by a cube by 120cm on each side. The material used to isolate the cube will be some polystyrene panels, with thickness s=4cm. Let's imagine to cool the dry air inside in order to reach the internal temperature of 8 degree Celsius, while the...
4. ### Energy of a crystal in thermal equilibrium

Homework Statement In a monatomic crystalline solid each atom can occupy either a regular lattice site or an interstitial site. The energy of an atom at an interstitial site exceeds the energy of an atom at a lattice site by an amount ε. Assume that the number of interstitial sites equals the...
5. ### Thermal equilibrium in open systems

Is it possible for an open system to reach thermal equilibrium? why/why not?
6. ### Thermal equilibrium formula

Hello all. Been a long time since I took a thermal course. I'm looking for a formula to work with the thermal stabilization of something. Specifically, I want to minimize the time required for thermal stabilization to occur and how to mathematically calculate what that set temperatures should...
7. B

### Thermal equilibrium and isolation

If two objects are at the same temperature, but thermally isolated from one another, are they still considered to be in thermal equilibrium with one another?
8. D

### Specific heat in the curve of equilibrium

Homework Statement Consider a system formed by two phases of a substance that consists of a single class of molecules. Determine the specific heat ##c## of a vapor pressure and temperature ##p## ##T## on the curve of liquid-vapor equilibrium. Consider the steam as an ideal gas. Data: ##c_p##...
9. ### I Inflation, horizon-problem and thermal equilibrium

Dear all, for the topic https://www.physicsforums.com/threads/problems-with-the-theory-of-inflation.905230/ I came across the following paper: https://arxiv.org/abs/1505.01456. In this paper the following arguments are given why the horizon problem is a fake problem. It raised by me the...
10. ### Two monatomic ideal gases are in thermal equilibrium with ea

Homework Statement Two monatomic ideal gases are in thermal equilibrium with each other. Gas A is composed of molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the average translational kinetic energies KA/KB is: Homework Equations KE=0.5xmxVavarage^2...
11. ### I Planck formula and density of photons

Hello! Let's consider again a system of atoms with only two permitted energy levels E_1 and E_2 > E_1. When electrons decay from E_2 level to E_1, they generate a photon of energy E_{21} = E_2 - E_1 = h \nu. The number of photons (per unit frequency, per unit volume) emitted by such a system in...
12. ### Sound in a gas of non-interacting particles?

Hi. In some statistical approaches (e.g. canonical ensemble), the particles of an ideal gas are non-interacting. Still, it's possible to derive the ideal gas law and other thermodynamic relations. Wikipedia gives an equation for the speed of sound in an ideal gas. How can there be waves in a...
13. ### Thermal Equilibrium of Hot Iron & Water

Homework Statement A hot (800 K) iron nail of mass 150 g is placed into a 1.0 kg of water at 25°C. What is the common temperature of the 2 objects once they have reached thermal equilibrium? Assume no change of state of the water. Heat capacity of iron nail is 450 J/kg/K Heat capacity of...
14. ### Thermal Equilibrium Temperature Question Sodium and Water

Homework Statement Expose the error: When sodium is placed in water, a violent reaction always occurs; therefore sodium and water can never be at the same temperature. Homework Equations Thermal equilibrium and temperature. Zeroth law. Isotherms. The Attempt at a Solution My Answer: The...
15. ### I Pn junction to reach thermal equilibrium

Hello! Some of the processes caused by a pn junction are not clear for me. Just after the contact between the p and the n region, a migration of charges happens in a semiconductor junction in order to reach an equilibrium condition. A valence band and a conduction band are present in both...
16. ### Some questions on heat transfer

Hello, forum! I'm just starting a new course on heat transfer and we're using Incropera's book. Last time I studied heat transfer was in my transport phenomena course, using BSL, so it was kind of a culture shock using the new book, because the methods used are kind of different in some cases...
17. ### Black Body radiation and thermal equilibrium

Wikipedia writes: "Black-body radiation is the type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment". Why does it write "thermodynamic equilibrium"? If it is not in a thermodynamic equilibrium, then what changes as far as the absorption...
18. ### Equilibrium temperature of three different substances

I've been asked to find the final temperature of different in an insulated container. A combination of 0.25kg water at 20C, 0.4kg aluminum at 26C, and 0.1kg copper at 100C are combined, and allowed to come to thermal equilibrium. Finding the equilibrium temperature for two substances is...
19. ### Thermal Equilibrium and Longitudinal Relaxation

Homework Statement Problem 6.2 from Magnetic Resonance Imaging: Physical Principles and Sequence Design. Show that M_o \approx \rho_o \frac{s(s+1)\gamma^2\hbar^2}{3kT}B_o Homework Equations M_o = \rho_o \gamma \hbar \frac{\sum m_s e^{m_s(\hbar w_o / kT)}}{\sum e^{m_s(\hbar w_o / kT)}} ...
20. ### Assumption of thermal equilibrium for ensembles

Take for example a canonical ensemble, to use the derived distributions and probabilities, the considered system has to be in thermal equilibrium with the heat bath. Where in the derivation of the probabilities and distributions do we usually assume this? There is a point that I can identify...
21. ### Thermal Equilibrium: How Objects Reach Balance

Hello, What "path" do objects take to reach thermal equilibrium? Does heat from a hot part sitting in room temperature air like to travel through the most thermally conductive portions? My thought is that it is similar to current in a circuit taking the path of least resistance (where the most...
22. ### How Can We Calculate Accurate Temperature Drops in an Unstirred Tank?

Hello all, I'm stuck with following problem: At our plant we have a tank filled with a liquid maintained on 80°C with a steam coil. During the night the steam is switched off and the liquid temperature start to drop. Tank mass not taken into account atm. mass liquid: 20000 kg cp liquid...
23. ### Maxwell distribution in thermal equilibrium

Homework Statement In thermal equilibrium, the particle in a gas are distributed in velocity space according to the Maxwell distribution f(v) = A*exp(-mv^2/(2KT)) What is the average velocity ? What is the most probable velocity ? Homework Equations <v> = ∫∫∫vf(v)d3v = (0 to infinty)...
24. ### Question on thermal equilibrium?

So I'm not too sure about the answer to this question: explain why it is advisable to add water to an overheated automobile engine only slowly, and only with the engine running? So if something is overheating, it makes sense to want to cool it. Since the water's temperature is less than that...
25. ### Thermal Equilibrium: Why Does Car Get Hotter Inside?

So you take some boiling water and drop a metal cube into it and the cube will reach the temp of the water. Or you leave some hot water out on a desk and the water will eventually become room temperature, right? Then why, in the summer time, does the inside of the car get way hotter than the...
26. ### Heat Capacity and Thermal Equilibrium

Homework Statement A 3.50-kg block of iron initially at 8.00 × 10^2 K is placed on top of a 6.25-kg block of copper initially at 4.00 × 10^2 K. Assume the blocks are thermally insulated from their surroundings but not from each other and that they constitute a closed system. How much energy is...
27. ### Temperature of gas and solid in thermal equilibrium

Hello I got to thinking about temperature when i prepared a lecture for my high school class. For a monoatomic ideal gas the temperature is proportional with the average kinetic energy of the atoms. For a diatomc gas we also have rotational energy (vibrations assumed to be freezed out), and for...
28. ### Why Do Gases Need Same Speed for Thermal Equilibrium?

When two gases are mixed, if they are to be in thermal equilibrium, they must have the same average molecular speed. Why or why not?
29. ### Two Objects In Thermal Equilibrium

Hello everyone, I was wondering, is there any way of calculating the time it takes for two objects in thermal contact to come to thermal equilibrium?
30. ### Thermal Equilibrium With Insulated Liquid And Gas Containers

Homework Statement A beaker with a metal bottom is filled with 20g of water at 20∘C. It is brought into good thermal contact with a 4000 cm^3 container holding 0.40mol of a monatomic gas at 10atm pressure. Both containers are well insulated from their surroundings. What is the gas pressure...
31. ### Show that the total weight w of an assembly in thermal equilibrium is

Homework Statement Show that the total weight w of an assembly in thermal equilibrium is a maximum. Homework Equations S= k ln W? dS = dQ/ T ? S is maximize when thermal equilibrium is reached. The Attempt at a Solution First of all, i don't know what does "total weight w" means...
32. ### Thermal Equilibrium of a system

Homework Statement A combination of .25kg of H2O at 20C, .4kg of Al at 26C and .1kg of Cu at 100C is mixed in an insulated container and allowed to come to thermal equilibrium. Ignore any energy transfer to or from the container and determine the final T of the mixture. Homework Equations...
33. ### Thermal equilibrium for ice being added to liquid water

Homework Statement 0.05625 m^3 of H2O(s) is added to a thermally isolated system of 20 L of H2O (l). If the ice was initially at 0 C and the liquid water was initially at 95 C, what is the final state and temperature? The Attempt at a Solution I missed class for this so I'm going by...
34. ### Does Temperature Affect the Time to Reach Thermal Equilibrium?

Is there a relationship between increasing temperature in one test tube and keeping the other temperature constant and the time it takes to reach thermal equilibrium Homework Statement Is there are relationship between increasing the temperature of water and keeping the other same and the...
35. ### Heat transfer and time needed to reach thermal equilibrium

I was hoping someone could lend a hand with a question about thermodynamics. It's been years since I've done work on thermodynamics. Let's say I have a plastic 275 gallon liquid container, filled with a mixture of Propylene Glycol and Water (50/50 by volume). The container is placed inside of...
36. ### Why is the Fermi level a constant in thermal equilibrium?

Why is the Fermi level a constant in thermal equilibrium? just like PN diode (P=material 1 ; N=material 2) the fermi levels are the same (Ef1=Ef2) in thermal equilibrium i confused that why there is no energy transfer so that can judge each energy E will obey rate from 1 to 2 ~...
37. ### Is thermal equilibrium possible by the Law of Cooling?

Law of cooling states that the rate of loss of heat by a body is directly proportional to the excess temperature of the body above that of its surroundings. The equation of determining temperature in time T(t)=Ta+(T0-Ta)*e^kt (Ta-ambient temperature, T0-initial temperature, k-heat transfer...
38. ### Affleck-Dine and thermal equilibrium

Hi, I am currently studying Cosmology on my own, and I am learning about the Affleck-Dine mechanism of baryogenesis. I understand that in this case the baryon asymmetry is generated by the decay of a supersymmetric flat direction carrying B, which is excited during inflation. Regarding...
39. ### Heat gained and lost by aluminium and water in thermal equilibrium

Homework Statement A physicist pours 100g of water at 100'C into a 20g aluminium cup which already contains 50g of water at 20'C. The final equilibrium temperature of the water is 71.847. C(water)=4186J/kgC C(aluminium)=900J/kgC 1. the amount of heat lost by the hot water 2. the amount...
40. ### Heat loss and thermal equilibrium of underground aquifer

Homework Statement I am working on a project where I have to design and size an aquifer. There are two which either store hot or cold water for 6 months which is then pumped up to be used in either the summer or winter. The aquifer is going to be 80 meters under the ground. The rest is...
41. ### Ideal gas-thermodynamics, thermal equilibrium

Homework Statement Two ideal gases are separated by a partition which does not allow molecules to pass from one volume to the other. Gas 1 has: N1, V1, T1, Cv1 for the number of molecules, volume it occupies, temperature in kelvin, and specific heat per molecule at constant volume...
42. ### Common temperature for thermal equilibrium

Homework Statement One mole of copper at a uniform temp. of 0 Celsius is placed in thermal contact with a second mole of copper which, initially, is at a uniform temperature of 100 Celsius. The pressure in the system is maintained at 1 atm. The two moles of copper are thermally insulated from...
43. ### Calculating Total Internal Energy of a System in Thermal Equilibrium

Homework Statement Consider a system in thermal equilibrium consisting of N particles that have 2 energy states E1 and E2 separated by an energy ΔE. Given that $$N_1 = \frac{N}{exp(-ΔE/k_BT)},\,\,N_2 = \frac{N exp(-ΔE/k_BT)}{1+exp(-ΔE/k_BT)}$$ show that in the case of the lowest energy...
44. ### What is Maxwell Distribution, Thermal Equilibrium, Fluctuation and Wein's law?

I was reading a book, 'Introducing Quantum Theory' by J.P.McEvoy, and I find it difficult to understand in details of Maxwell Distribution, Thermal Equilibrium, Fluctuation, Wein's law and Planck's quantum theory, so I am finding it difficult to follow Einstein's explanation of photoelectric...
45. ### A question about position of piston after achieving thermal equilibrium

A vertical cylindrical container contains some helium gas that is in thermodynamic equilibrium with the surroundings. The gas is confined by a movable heavy piston. the piston is slowly elevated a distance H from its equilibrium position and then kept in the elevated position long enough for the...
46. ### Thermal Equilibrium between a Hot and Cold Body

Just a quick question relating to thermal equilibrium between a hot and cold body. If a hot body and cold (closed systems) are opened up to each other, the thermal energy will be transfer from the hot body to cold body through conduction. So even when thermal equilibrium is reached, the...
47. ### Highschool Question on Thermal Equilibrium

Hi guys, I'm having a bit of trouble with following thermal equilibrium question... Homework Statement Create an equation representing energy transfers of thermal energy equilibrium, that will enable one to determine the latent heat of fusion for ice. One conducts an experiment mixing ice...
48. ### Thermal equilibrium through radiation and Stefan Boltzmann

Hey Guys, so I had a longish discussion with colleagues and on reddit about thermal equilibrium and the sun and how you cannot heat up anything above the surface temperature of the sun using clever mirrors and stuff. However, somebody came up with Napkin calculations of the Stefan Boltzmann...
49. ### Thermal equilibrium - Entropy driven

Hey there. We are struggling with a problem from an old exam about statistical mechanics. I hope you can help us or give any clues. Here is the problem. Homework Statement A chamber is divided by a wall into two sections of equal volume. One section of the chamber is initially filled by an...
50. ### Thermal Equilibrium - in a microwave?

hi, i don't quite know how to pose this question but i'll try my best. if you have an object and heat one end of it, energy will move from an area of high energy, to an area of low energy. By this method, heat transfer will stop when all regions of the object are at the same temperature...