In a piston$-$cylinder system, initially $0\mathrm{.}15$ m of nitrogen gas is at a temperature of $350$ K$.$ The mass of the piston is $250$ kg and the cross$-$sectional area is $0\mathrm{.}1$ m$.$ The ambient pressure is $1$ bar and the gravitational acceleration is $10$ m$/$s$.$ Assuming that nitrogen gas obeys the Redlich$-$Kwong equation, calculate the heat transferred to the gas for the following situations.

a$)$ The piston is fixed at the initial level and the final temperature and pressure are $365$ K$.$ and $1\mathrm{.}32$ bar, respectively.

b$)$ The piston is released and the temperature reaches $361$ K$.$

Cv $20\mathrm{.}8$ J$/$mol$.$K

C$-29\mathrm{.}0$ J$/$mol$.$K

NOTE: In the calculations, it is expected that the numerical value of each parameter in the equations will be substituted and detailed calculations will be shown.