1. There is liquid nitrogen in a hemispherical tank at a certain temperature (T=73K). The radius of the spherical tank is 5m. The ambient pressure is 1 atm. The hemispherical tank is half full and is open to the atmosphere. The relationship between the liquid level h and the radius of the liquid in the tank is given as:

R²=(R-h)²+X²

In the equation above X is the radius of the liquid level, h is the liquid level and R (=5m) is the radius of the hemispherical tank. The volume of the liquid in the tank is given as below:

pR²h-1/3ph³

The vapor of nitrogen as a function of temperature is given below:

Pvap=10^{(A-B/(C+T(oC)))} where Pvap is in mmHg.

A=6.94 , B=330.2 , C=277.2

1. Derive steady state evaporation rate for nitrogen in terms of R, h ,P, Pvap , Diffusivity of nitrogen, T 25 pts
2. Determine the value of diffusivity of nitrogen gas in air by using Fuller method10 pts

Determine the value of evaporation rate initially when the evaporation just started15 pts