Problem $4.$ A well$-$insulated piston$-$cylinder contains $3\mathrm{.}5$mol of an ideal gas $\frac{J}{\text{m}\text{o}\text{l}\text{K}}.$ Its pressure of $\frac{4\mathrm{.}8}{b}ar$ is obtained by a $90.-kg$ weight on the piston, which weights $10.kg.$ The gas is at a temperature of $55C.$ Suppose a $100.-kg$ weight was suddenly added to the piston. What is the final temperature and pressure of the gas?