Ash: Import converted Year 1 Semester 2 lecture notes from 443937a7d37850a3c57dfa863f35e80d07f2ccbc

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Import converted Year 1 Semester 2 lecture notes from 443937a7d37850a3c57dfa863f35e80d07f2ccbc

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<b>Lecture 14: Statistical Physics I: Introduction</b><br>
Thu 05 Mar 2026 13:00
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[[Year 1 Sem 2/LC Temperature and Matter/Lecture 13|← Previous lecture]] · [[Year 1 Sem 2/LC Temperature and Matter|Module]] · [[Year 1 Sem 2/LC Temperature and Matter/Lecture 15|Next lecture →]]

== Stefan-Boltzmann Law ==

We can integrate across the whole spectrum to work out total energy emitted per unit time: <div class="pn-import-equation"><nowiki>$$\dot{Q} = \epsilon \sigma A T^4$$</nowiki></div>

Where <nowiki>$\sigma = 5.67 \times 10^{-8} \mathrm{W m^{-2} K^{-1}}$</nowiki> is the Stefan-Boltzmann constant, <nowiki>$\epsilon$</nowiki> is the emissivity, <nowiki>$A$</nowiki> is the surface area of the radiating body and <nowiki>$T$</nowiki> is the temperature.

== Kinetic Theory of Gases ==

We’ve now finished the module on temperature and move into statistical physics. We start wth a kinetic theory of the motion of gas molecules. Gas molecules move “randomly” (effectively, it’s not computationally viable to determine what’s actually going on), with vastly different velocities and positions.

We would love to describe a gas using the individual molecules that make it up, but that’s really difficult to do for <nowiki>$\sim 10^{23}$</nowiki> molecules so it’s not viable and we have to use statistical physics to describe it.

We’ve previously touched upon the Maxwell-Boltzmann distribution to describe the velocities of particles as a statistical distribution wrt temperature:

[[File:TM-Y1S2-lec07-1.png|thumb|center|800px]]

These statistical approximations improve as we increase the number of particles, and for very large numbers they become good approximations. We can in statistical physics have a probability <nowiki>$>1$</nowiki>. This seems mathematically strange, but we interpret it to mean that (if the probability represents the probability of an event occurring in a measurement), the event will take place multiple times. We still cannot have any probabilities <nowiki>$<0$</nowiki>.

The rest of the lecture then turned into a fun tangent on statistics which isn’t examinable and needs no notes.

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Ash: Import converted Year 1 Semester 2 lecture notes from 443937a7d37850a3c57dfa863f35e80d07f2ccbc