# Pre-Lecture Homework

By

Tee Kai Ze

,

Guan Xin

,

Jensie Low

,

Seow Ryan

●

Published 2022-08-27

Even before we had the statistical interpretation of quantum mechanics, statistics was applied to fundamental science to account for observations. Ludwig Boltzmann and other founders of statistical mechanics used methods of probability theory to bridge the microscopic world and macroscopic observations such as temperature, work, heat and chemical processes.

Say we have a macroscopic system at some temperature T. Suppose there exists a variety of possible "states" (state 1, state 2, etc), each with its characteristic energy (E_{1}, E_{2}, etc.). The probability of occurence of a state is related to the state's energy via the Boltzmann distribution:

\text{Probability of state } i \text{ occurring }=p_{i}\propto e^{-E_{i}/kT}

where k=1.38\times10^{23}\text{JK}^{-1} is the Boltzmann constant.

The space between stars is not empty. It is dotted with matter, at some places denser than others. As they exist in the regions between and around stars, they are known as the interstellar medium (ISM). The ISM can be made of clouds of hydrogen and helium gas, as well as "dust grains" that contain heavier elements. Interactions between matter and light within the ISM give rise to beautiful astronomical objects called nebulae.