Question

Liquid oxygen (LOX) for the space shuttle can be stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology’s Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is 20°C on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.

Answer 1

The thermal conductivity

$K = QL/AΔT$

A - area ($4\pi$r²)

$L = KAΔT/Q$

Q = $213*200/3600$ = 153360000 J

L = $0.00012*4*3.14*4*203 / 153360000$

L = 0.103 m = 10.3 cm