An isothermal irreversibly expanded gas of $1$ mol of a monatomic ideal gas at $0\backslash$deg C $1$ atm, resulting in a volume of $44\mathrm{.}8$dm$3,$ and working at $418\mathrm{.}4$ J$.$ Find the change in entropy of the system $(\backslash$Delta S$)[$J$/$K$].$