$0\mathrm{.}0107$mol of nitrogen $($diatomic ideal gas, $C_p=7\frac{R}{2})$ is expanded in a piston$-$cylinder assembly from an initial volume of $210c{m}^3$ to a final volume of $430c{m}^3.$ The initial temperature of the nitrogen is $40C.$ Assume the expansion is done reversibly, meaning there are no frictional losses.

Determine the properties listed in the table below for three cases:

a$.$ the expansion is done isobarically

b$.$ the expansion is done isothermally

c$.$ the expansion is done adiabatically

$\backslash$table$[[$Case$,T_f(K),P_f(Pa),\backslash$table$[[Q$