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 0.73 m2 and is at 3.1 102 K. (a) Determine the rate of heat loss due to radiation. (The Stefan-Boltzmann constant is ? = 5.67 10-8 W/(m2 K4).) (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 = T4A where

q = heat transfer per unit time (W)

= 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=268.967 W

b)now heat gained by He =heat radiated

(dV/dt)x20.9x1000=q=268.967   =0.125

so dV/dt=0.102954 m3/s or 102.954 l/s

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