A cryogenic storage container holds liquid helium, which boils at 4.2 K. Suppose

Question

A cryogenic storage container holds liquid helium, which boils at 4.2 K. Suppose a student painted the outer shell of the container black, turning it into a pseudo-blackbody, and that the shell has an effective area of 0.36 meters squared and is at 3.1e+02 K

(a) Determine the rate of heat loss due to radiation. (The Stefan-Boltzmann constant is 5.67e-08)

(b) What is the rate at which the volume of the liquid helium in the container decreases as a result of boiling off? The latent heat of vaporization of liquid helium is 20.9 kJ/kg. The density of liquid helium is 0.125 kg/L.

Explanation / Answer

a)q = σT4A where

q = heat transfer per unit time (W)

σ = 5.670 10-8 (W/m2K4) - The Stefan-Boltzmann Constant

T = absolute temperature Kelvin (K)

A = area of the emitting body (m2)

evaluating the answer q=237.35 W

b)now heat gained by He =heat radiated

Ï(dV/dt)x20.9x1000=q=237.35 Ï=0.125

so dV/dt=0.090806495389649 m3/s or 90.80 l/s

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