Chapter 1, Problem 1.49P

Liquid oxygen, which hems a boiling point of 90 K and a latent heat of vaporization of 214 kJ/kg, is stored in a spherical container whose outer surface is of 500-mm diameter and at a temperature of $-10°\text{C}\text{.}$ The container is housed in a laboratory whose air and walls are at $25°\text{C}\text{.}$

1. If the surface emissivity is 0.20 and the heat transfer coefficient associated with free convection at the outer surface of the container is $10{\text{W/m}}^{\text{2}}\cdot \text{K,}$ what is the rate, in kg/s, at which oxygen vapor must be vented from the system?
2. Moisture in the ambient air will result in frost formation on the container, causing the surface emissivity to increase. Assuming the surface temperature and convection coefficient to remain at $-10°\text{C}$ and $10{\text{W/m}}^{\text{2}}\cdot \text{K,}$ respectively, compute the oxygen evaporation rate (kg/s) as a function of surface emissivity over the range $0.2\le \epsilon \le \mathrm{0.94.}$