Year 1 Sem 2/LC Temperature and Matter/Lecture 14
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Stefan-Boltzmann Law
We can integrate across the whole spectrum to work out total energy emitted per unit time:
Where $\sigma = 5.67 \times 10^{-8} \mathrm{W m^{-2} K^{-1}}$ is the Stefan-Boltzmann constant, $\epsilon$ is the emissivity, $A$ is the surface area of the radiating body and $T$ 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 $\sim 10^{23}$ 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:
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 $>1$. 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 $<0$.
The rest of the lecture then turned into a fun tangent on statistics which isn’t examinable and needs no notes.