When a filament is placed inside an adiabatic $2$ L piston filled with N$2$ gas at $2$ atm pressure and room temperature $(25$ C$)$ and $200$ J of energy is added;a$)$ Initially, the piston takes over its position. Find how much the temperature increased. Find how much work was done. Find what your new pressure will be$.$b$)$ After being released, the piston's stiffness will slowly decrease when the volume expands reversibly by $2$ atm external pressure. Your task is to find the final temperature, find it$))$Important note: For the N$2$ molecule, Cm$=20\mathrm{.}8$ J$/$ mol K Cem $=29\mathrm{.}1$ J$/$ mol KN$2$ behaves as an ideal gas$))$