Available online
Description
The programme examines the way in which the special behaviour of liquid helium can be explained by the way atoms are counted in the various energy levels available to them.
The programme examines the way in which the special behaviour of liquid helium can be explained by the way atoms are counted in the various energy levels available to them.
| Module code and title: | TM361, "Graphs, networks and design" |
|---|---|
| Item code: | TM361; 04 |
| First transmission date: | 22-04-1981 |
| Published: | 1981 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:22:38 |
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| Producer: | Andrew Millington |
| Contributors: | Allan I.,1936-2013 Solomon; Robin Wilson |
| Publisher: | BBC Open University |
| Keyword(s): | Atoms; Counting; Energy levels; Entropy; Liquid helium; Transition |
| Footage description: | Close up film shots of boiling liquid helium in a capillary tube. Allan Solomon, at the Clarendon Laboratory, Oxford, introduces the programme. He points out some remarkable properties of liquid helium. Robin Wilson points out, briefly, that the behaviour of liquid helium can be explained by the way its atoms are counted in their quantum energy states. He then goes on, by placing various snooker balls into pigeon holes, to discuss some basic facts about counting. Wilson identifies four types of selection and distribution problems and examines each in turn. Having worked out these four problems he explains that just one of them is the correct model for the behaviour of superfluid helium but he cannot tell which. In order to determine which of the four mathematical models above is the correct one for helium, Allan Solomon discusses the physics of helium. He begins by deriving an equation for determining the entropy of a system and also explains what entropy is. Solomon uses a blackboard and a pack of cards as aids. Solomon goes on to explain that helium atoms obey the laws of quantum mechanics and so are found at discrete energy levels. He cites, as an analogy, people walking up and down steps and then explains that the way helium atoms are distributed is also analogous to the snooker ball - pigeon hole set up seen earlier in the programme. Solomon eliminates two of the four possible arrangements, and works out an expression for the entropy of the remaining two, the Fermi-Dirac model and the Bose-Einstein model. Robin Wilson, with the aid of animated graphics, takes the expressions worked out by Allan Solomon above and evaluates them more explicitly in terms of logarithms of different combinatorial functions Allan Solomon takes the expression for entropy for the two arrangements and plots them on graphs. Then, with the aid of these graphs and another look at the people on steps analogy, he explains why the Bose-Einstein model but not the Fermi-Dirac model fits the observed properties of liquid helium, particularly of helium in its superfluid state. |
| Production number: | FOUT078J |
| Videofinder number: | 1525 |
| Available to public: | no |
