Cryogenic liquids (liquid N2, He, etc) are typically stored in Dewar flasks (fan

Question

Cryogenic liquids (liquid N2, He, etc) are typically stored in Dewar flasks (fancy thermos bottles) that consist of mirrored glass walls (to reduce radiative heating) separated by vacuum (a cylinder within a cylinder). How long would a liter sample of liquid helium last in a flat bottomed cylindrical Dewar with an inner radius of 8 cm and height of 20cm and an outer radius of 10cm and height of 25 cm assuming negligible thickness for the glass and that the only energy transfer that occurs is radiative between the walls of the Dewar (the top surface does not receive any radiation). The emissivity of silvered glass is 0.02 over all wavelengths, the outer surface of the dewar is at 77K, (the Dewer sits in a vat of liquid nitrogen) the temperature of liquid Helium is 4 K, the density of liquid He is 0.125 g cm3 , and the latent heat of vaporization is 83 J/mol. , The latent heat of vaporization is a measure of how much “extra” energy is required to vaporize a substance at its boiling point (the boiling point of He is 4K). (Assume that all of the energy impinging on the inner cylinder is used to vaporize the Helium).

Explanation / Answer

mass of He = 0.123*1*10^-6*10^3 = 0.125*10^-3g

heat require = mLv

Q = 0.125*10-3*83 = 10.375*10^-3J

heat given per second =eAdT = 0.02*565.48*10^-4*74 = 836.91*10^-4

time require to convert He in gas = 103.75*10^-4/836.91*10^-4 = 0.123sec

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