Transfer of Heat: mass of liquid helium that boils?

[MKM]

Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical container (r = 0.251 m). The container is a perfect blackbody radiator. The container is surrounded by a spherical shield whose temperature is 72.8 K. A vacuum exists in the space between the container and shield. The latent heat of vaporization for helium is 2.1 x 104 J/kg. What mass of liquid helium boils away through the venting valve in 19.2 hours?


I have tried calculating the net Powere first withthe equation Pnet =e sigma (5.67*E -8) A(.251*.251*pi) ( T^4-Tenvirnment^4) this gives me
.315210793711 as my Pnet. then I plug it into the formula Q=Pt Q=P*69120 secs) = 21787.3700613. My last step is to plug it into Q=mLv which is my new specific heat divided by my liquid heat of vaoprization of helium which is 2.1*E4 I get 1.03749, which is incorrect. I am not sure where I am going wrong . should I be calculating separate Q values from the beginning with different e values?

 

[Astronuc]

For one thing the area of a sphere is 4$\pi$r².

So one calculates the P (W) from the Stefan-Boltzmann Law - using the correct area.

Then with power * time = Q, and one can then use the latent heat to find the mass.