A Rigid Cylinder $15 \mathrm{~cm}$ Radius $15 \mathrm{~cm}$ Height) Contains Nitrogen Gas

A rigid cylinder ( $15 \mathrm{~cm}$ radius, $15 \mathrm{~cm}$ height) contains nitrogen gas $\left(\mathrm{N}_{2}\right)$ at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $\left.1 \mathrm{~atm}\right)$ . What heat input is required to increase the average translational kinetic energy of the nitrogen molecules by $15 \%$ ?

A) $77 \mathrm{~J}$
B) $260 \mathrm{~J}$
C) $130 \mathrm{~J}$
D) $86 \mathrm{~J}$
E) $51 \mathrm{~J}$
F) $403 \mathrm{~J}$