Question $4$

a$)$ A metal flask for storing liquid nitrogen is spherical and of hollow$-$

walled construction, with a small vent. The cavity is evacuated so that

convection and conduction in the annular space are negligible. The

flask may be modelled as two concentric spherical shells with an

annular space. The inner radius of the annular space is $15cm$ and the

outer is $15\mathrm{.}5cm.$ The emissivities of both surfaces are $0\mathrm{.}06.$ Nitrogen

boils at $77K$ and its heat of vaporisation is $200kJk{g}^{-1}.$ If the outer

annular surface is at $298K,$ calculate the rate of nitrogen loss from the

flask.

Grey body interchange: $F_{12}=\frac{1}{(\frac{1}{{}_1}-1)+\frac{A_1}{A_2}(\frac{1}{{}_2}-1)+\frac{1}{\frac{?}{\text{b}\text{a}\text{r}}(F_{12})}}$

Data: The Stefan Boltzmann constant is $5\mathrm{.}663{10}^{-8}W{m}^{-2}{K}^{-4}.$