Weakly Coupled Systems

The discussion in section 2.3 showed that thermodynamic concepts such as temperature are not required for the discussion of the behaviour of a single particle in a conservative system, since the energy of the particle is constant. When the isolated system consists of a number of particles (such as molecules of a gas) however, the individual particle energies change after each collision in such a way that the energy of the entire system (E) is conserved. <m:math display='block'> <m:mrow> <m:mi>E</m:mi><m:mo>=</m:mo><m:msub> <m:mo>&#x2208;</m:mo> <m:mn>1</m:mn> </m:msub> <m:mo>+</m:mo><m:msub> <m:mo>&#x2208;</m:mo> <m:mn>2</m:mn> </m:msub> <m:mo>+</m:mo><m:mn>...</m:mn><m:mo>+</m:mo><m:msub> <m:mo>&#x2208;</m:mo> <m:mi>N</m:mi> </m:msub> </m:mrow> </m:math>]] </EquationSource><EquationSource Format="TEX"><![CDATA[$$E = { \in _1} + { \in _2} + ... + { \in _N}$$ In general it is no longer possible (or indeed interesting) to discuss the exact behaviour of each molecule. In thermal equilibrium the macroscopic properties of the system become independent of time and at the molecular level it is postulated that the fraction of the molecules with a given range of energies is also independent of time. An individual molecule will leave the chosen energy range after a collision but elsewhere in the gas another molecule will on average also make a collision such that it enters the energy range.