  The next section specializes to the simplest case of monatomic gases and also provides a more complete specification of the problem he aims to solve. The gas molecules are modelled as hard spheres, contained in a fixed vessel with perfectly elastic walls (WA I, 320). Boltzmann represents the state of the gas by a time-dependent distribution function \(f_t(\vec{v})\) which gives us, at each time \(t\), the relative number of molecules with velocity \(\vec{v}\).[11] He also states three more special assumptions: