Transcription of 4. Canonical ensemble
{{id}} {{{paragraph}}}
Example: tourism industry
4. Canonical ensemble
4. Canonical ensembleIn this chapter we will formulate statistical physics for subsystemsthat are held at constant temperature. In the next chapter we willwork at constant temperature and constant chemical potential. Thecalculations are different from those we have done so far, and oftenfar simpler. For systems at fixed temperature there are very usefulnumerical techniques, Monte Carlo methods, that we will :Gibbs gave odd names to methods involving subsystemsin contact with reservoirs. In closed system, with fixed energy we estimate time averages bysampling uniformly over the energy shell, as we have done untilnow. Gibbs called this themicrocanonicalensemble. In a system which can exchange energy at fixed temperature weaverage using the Boltzmann factor of Eq. ( ). This is calledthecanonicalensemble. In a system which can exchange both energy and number withreservoirs, we have a different method of averaging that we willderive below. This is called thegrand Averages and the partition functionIn this section we study systems which are subsystems of a largersystem: they are held at constant temperature by contact with a (muchlarger) heat bath.
The angular momentum vector L should be regarded as having two components – in our classical picture we neglect the moment of inertia around the molecular axis. Thus we have two more degrees of freedom, and E =3N(k B T/2)+2N(k B T/2) = (5/2)Nk B T. The first term is the translational part and the second rotational. Thus C V =(5/2)Nk B ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: