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Ok, so I was reading a chapter on thermodynamics (introduction), which built its content on the idea that two systems separated by a diathermic wall will tend to attain thermal equilibrium with each other and the surrounding ( in case they are also separated by surrounding with diathermic wall). I have a simple question in my mind, why do systems tend to attain thermal equilibrium anyway? Any explanation, bulk or microscopic will do, both are also welcome.

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    $\begingroup$ It is the most likely state: physics.stackexchange.com/a/377428/137289 $\endgroup$ – user137289 Oct 27 '18 at 16:16
  • $\begingroup$ @Pieter thanks for the help, but I think it does not answer the exact "why" question I asked $\endgroup$ – Aditya Oct 27 '18 at 16:30
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    $\begingroup$ There is no purpose, systems do not "strive" to "attain" equilibrium, no real reason "why". It is just random exchanges of energy. Until the probability is maximal. $\endgroup$ – user137289 Oct 27 '18 at 16:45
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    $\begingroup$ @Adi Regarding AbhirupMukherjee and dmckee discussion below, check out the Hyperphysics web site on "What is Temperature". It shows how entropy change provides a "more reliable approach to temperature" than the more intuitive idea of high speed molecules hitting low speed molecules. Hope this helps. $\endgroup$ – Bob D Oct 27 '18 at 17:42
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If one system, say a fluid, is at a higher temperature, it will have more kinetic energy than the other fluid. Hence it will continue to impart kinetic energy to the other fluid through the diathermal wall, via collisions. Of course the fluid at lower temperature also transfers kinetic energy to the 'hotter' fluid, but the former process is more intense. The result is a net transfer of energy from hotter to cooler, via collisions. This happens until their average thermal energies become equal; the rate of transfer of energies become equal on either side.

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  • $\begingroup$ No. Equal temperature does not imply equal energy or equal kinetic energy or equal average thermal energy. $\endgroup$ – user137289 Oct 27 '18 at 16:10
  • $\begingroup$ @Peter, isn't kinetic energy proportional to temperature? $\endgroup$ – Abhirup Mukherjee Oct 27 '18 at 16:17
  • $\begingroup$ No, not necessarily. It is only valid in classical systems. It is not how temperature is defined. Quantum effects are important also in melting ice etc. $\endgroup$ – user137289 Oct 27 '18 at 16:18
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    $\begingroup$ Levels of fundamentalness are not well defined. A fundamental definition (one suited to classical thermodynamics and many uses in statistical mechanics) is as the partial derivative of internal energy with respect to entropy. But of course, you can't use the definition until you have good definition of entropy and into the rabbit hole you go. $\endgroup$ – dmckee --- ex-moderator kitten Oct 27 '18 at 16:46
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    $\begingroup$ Yes, and my preferred teaching approach starts that way. But look at the historical development of thermal physics to see just how late that notion came along. People dealt with the subject using the equilibrium and heat-engines model for lifetimes before the statistical basis got off the ground. $\endgroup$ – dmckee --- ex-moderator kitten Oct 27 '18 at 16:54

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