$)$ A large cylindrical tank contains $0\mathrm{.}760$ m$3$ of nitrogen gas at $25\mathrm{.}0$C and $8150$ Pa $($absolute pressure$).$ The tank has a tight$-$fitting piston that allows the volume to be changed. Calculate the pressure in the tank if the volume is decreased to $0\mathrm{.}490$ m$3$ and the temperature is increased to $154$C$.(10$ marks$)$ ii$)$ A $15\mathrm{.}2$ g bullet traveling horizontally at $875$ m$/$s passes through a tank containing $14\mathrm{.}4$ kg of water and emerges with a speed of $542$ m$/$s$.$ Find the maximum temperature increase that the water could have as a result of this event. Assume heat capacity of water $4\mathrm{.}186$ J$/($g $$C$).$