A rigid vessel containing three moles of nitrogen gas at $30$C is heated to $250$C$.$ Assume the average capacities of nitrogen to be Cp $=29\mathrm{.}1$ J$/$mole$.$C and, Cv $=20\mathrm{.}8$ J$/$mole$.$C$.$ The heat required, neglecting the heat capacity of the vessel, is

$13728$ J

$19206$ J

$4576$ J

$12712$ J