This is an extra credit assignment that is due at the beginning of the final on Monday, $12/09/24.$ A bottle of mass mb $=0\mathrm{.}1$ kg and volume V $=0\mathrm{.}1$ m$3.$ The bottle is full of atomic hydrogen $($mH $=1\mathrm{.}671027$ kg$)$ and is at atmospheric pressure and a temperature of T$0=20$C$.($a$)$ What are the number of moles and the initial rms velocity of the hydrogen? $(2$ points$)($b$)$ The temperature of the oxygen in the bottle is now increased to T $=100$C$.$ What is the new pressure inside the bottle? $(2$ points$)($c$)$ What is the change in internal energy, work, heat transfer, and entropy for the bottle? $(8$ points$)$