A well$-$insulated piston$-$cylinder contains $3\mathrm{.}5$ mol of an ideal gas $($C$\_$P $=28$ J$/($mol K$)).$ Its pressure of $4\mathrm{.}8$ bar is obtained by a $90.-$kg weight on the piston, which weights $10.$ kg$.$ The gas is at a temperature of $55$C$.$ Suppose a $100.-$kg weight was suddenly added to the piston. What is the final temperature and pressure of the gas?