Homework

Liquid nitrogen is stored in a thin spherical vessel of diameter $D_i=1m.$ The vessel is positioned concentrically within a larger, thin$-$walled spherical container of $D_0=1\mathrm{.}1m,$ and the intervening cavity is filled with atmospheric helium. Under normal operating conditions, the inner and outer surface temperatures are $T_i=77K$ and $T_0=283K.$ If the latent heat of vaporization of nitrogen is $2{10}^5\frac{J}{k}g,$ what is the mass rate $(k\frac{g}{s})$ at which gaseous nitrogen vented from the system? $($For He at $180$ K and $1$ atm : $v=51\mathrm{.}3{10}^{-6}\frac{m^2}{s},k=0\mathrm{.}107\frac{W}{m}.K,=76\mathrm{.}2{10}^{-6}\frac{m^2}{s},Pr=0\mathrm{.}673)$