(Solved): There is liquid nitrogen in a hemispherical tank at a certain temperature (T= ...

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There is liquid nitrogen in a hemispherical tank at a certain temperature $$(\mathrm{T}=73\mathrm{K})$$. The radius of the spherical tank is $$5\mathrm{m}$$. The ambient pressure is 1 atm. The hemispherical tank is half full and is open to the atmosphere. The relationship between the liquid level $$\mathrm{h}$$ and the radius of the liquid in the tank is given as: $${\mathrm{R}}^2=(\mathrm{R}?\mathrm{h}{)}^2+{\mathrm{X}}^2$$ In the equation above $$X$$ is the radius of the liquid level, $$h$$ is the liquid level and $$R(=5\mathrm{m})$$ is the radius of the hemispherical tank. The volume of the liquid in the tank is given as below: $$?{\mathrm{R}}^{2}h?1/3?{\mathrm{h}}^3$$ The vapor of nitrogen as a function of temperature is given below: $$\mathrm{Pvap}=10^{(\mathrm{A}?\mathrm{B}/(\mathrm{C}+\mathrm{T}(\mathrm{oC})))}$$ where $$\mathrm{Pvap}$$ is in $$\mathrm{mmHg}$$. $$\mathrm{A}=6.94,\mathrm{B}=330.2,\mathrm{C}=277.2$$ a) Derive steady state evaporation rate for nitrogen in terms of $$\mathrm{R},\mathrm{h},\mathrm{P},\mathrm{Pvap}$$, Diffusivity of nitrogen, $$\mathrm{T}$$.....25 pts b) Determine the value of diffusivity of nitrogen gas in air by using Fuller method...10 pts c) Determine the value of evaporation rate initially when the evaporation just started...15 pts