# Thermodynamic equilibrium of an isolated system

When an arbitrary system is isolated and left to itself, its property will in general change in time. ....after a sufficiently long time,the temperature will become the same at all points and then the system is in thermal equilibrium. - Sears and Salinger.

Now, if the system is isolated, how has it changed to bring the equilibrium?

It is an axiom of thermodynamics that when a body of material starts from a non-equilibrium,state of non-homogeneity or chemical non-equilibrium and by thermodymamic operation,is then isolated,it spontaneously towards its own internal state of equilibrium. - Wikipedia.

Now how does an isolated system attain thermodynamic equilibrium-thermal and mechanical especially in course of time?? Do each particle in the isolated system have same energy and no net force? No, each particle collide and there is force and energy of each particle changes. So,if force exists and energy changes,how can there be equilibrium?

And the wiki page also mentions :

In a macroscopic equilibrium,almost or exactly balanced microscopic exchanges occur.

What does this mean?

• Just a clarification: equilibrium means that you can define (and describe the system using) some variable (which can be some average) that does not change with time, equilibrium doesn't mean "absence of change" for every variable.
– user65081
Dec 28, 2014 at 16:11
• Related question by OP: physics.stackexchange.com/q/155271/2451 Dec 28, 2014 at 23:39

First of all I will address your last concern, which translates into: equilibrium doesn't necessarily mean that nothing is moving. As an example, particle in a solution at equilibrium can move from one side to the other as long as almost the same number of particle move the opposite direction (this usually happens, say, because of thermal agitation/Brownian motion...). What doesn't change with time is then the average concentration of particles in the solution. Now using again this analogy, suppose you have an isolated system made of, say, sea water and distilled water. When you first mix them you can still distinguish them, as one has a higher concentration of salts. After a while, internal gradients, that arise because the system is out of equilibrium, will drive the salts to homogenise and the end result is water with a homogeneous concentration of salts, after a suitably long relaxation time. Same happens with temperature: if you replace sea and distilled water with hot and cold water, the same mechanism will homogenize your system. Temperature gradients will mix water around until the temperature is the same everywhere. Then gradients disappears and dynamical equilibrium settles in (water is not completely static, but molecules flow around because of thermal agitation).

• So, equilibrium means the macroscopic property is not changing though microscopic properties are changing,right?
– user36790
Dec 29, 2014 at 4:30
• And sir, can you tell me how mechanical equilibrium is dynamic? Forces are always present,when particles collide. So,how can there be mechanical equilibrium??
– user36790
Dec 29, 2014 at 4:32
• There is no reference to mechanical equilibrium in what you have quoted. Consider that, strictly speaking, even for a rigid body at rest, you can always find motion within it (atoms in a crystal vibrate because of the internal energy, even if the crystal is "at rest"). Dec 29, 2014 at 9:49

Now, if the system is isolated, how has it changed to bring the equilibrium??

The system is isolated from its surroundings, but different parts of it can exchange matter and energy within in. Take, for example, a long metal ruler. Put one extremity on hot water and the other on ice and wait a certain time. A thermal gradient will be established along the ruler. Now, isolate the ruler. You see that the hot end of it will become colder, and the cold end will become warmer. Although the ruler is isolated, there is energy transfer WHITHIN it.

At thermodynamic macroscopic equilibrium, not all particles must have the same energy. The energy of each one can vary, but in a way such that in average over a REV, energy and composition remain constant.

For REV, please consult this Wikipedia article and remember that macroscopic mechanics relies on the continuum hypothesis.

• +1. Can you please explain me the last line that I 've quoted?
– user36790
Dec 29, 2014 at 4:34
• Consider, for example, a liquid-vapour equilibrium. If a molecule go from the vapour phase to the liquid phase at the same time as another one goes from the liquid phase to the vapour phase, there is no noticeable macroscopic change, an "exactly balanced microscopic exchanges occurs". Dec 29, 2014 at 9:53