a$)$ Calculate the $S$ of mixing of $5\mathrm{.}5$mol of hydrogen with $5\mathrm{.}5$mol of helium at $25C,$ assuming that they behave as ideal gases.

b$)$ Determine $S$ when helium at $25C$ and $\frac{1\mathrm{.}00}{b}ar$ in a cylinder of volume $0\mathrm{.}500d{m}^3$ is allowed to expand to $1\mathrm{.}300d{m}^3$ and is simultaneously heated to $145C.$