A sealed container holding $0\mathrm{.}652$ kg of liquid nitrogen at its boiling point of $77\mathrm{.}3$ K is placed in a large room at $19\mathrm{.}9$C$.$ Energy is transferred from the room to the nitrogen as the liquid nitrogen boils into a gas and then warms to the room's temperature. Liquid nitrogen has a latent heat of vaporization of $2\mathrm{.}01105$ J$/$kg$.$ The specific heat of N$2$ gas at constant pressure is

cN$2=1\mathrm{.}04103$

Jkg $$ K

$.$

HINT

$($a$)$

Assuming the room's temperature remains essentially unchanged at $19\mathrm{.}9$C$,$ calculate the energy $($in J$)$ transferred from the room to the nitrogen.