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Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant WaterProblem: A =
.06m^{2}
is the approximate area of the porous space suit surfaces, predict the gas pressure in the immediate vicinity of the suit. Assume a temperature of 273°K. Solution:
where N = the total number of water particles available. If we assume that the temperature T = 273°K, and set the velocity v of the sublimating water particles equal to (2kT/m)^{1/2} (with m = 3 x 10^{-26} kg for water), then v = 500 m/sec approximately. Now if n is the number density of the water vapor at the surface where sublimation from the suit into space is occurring, then
where A = the area from which sublimation is occurring. Substituting for dN/dt and v in the second expression, we find that
Setting A = .06m^{2}, we find
and the pressure p = (2 x 10^{20}/m^{3})/(2 x 10^{25}/m^{3}) atm = 2 x 10^{-5} atm, (where n_{0} =2 x 10^{25}/m^{3} is Loschmidt's number, ie., the number density of an ideal gas at STP). [Nota Bene: This calculated value of pressure may be used in estimating the probability of Paschen breakdown occurring in the immediate vicinity of an astronaut who might be working near an exposed high voltage if the Paschen curve of water vapor under the specified conditions is known.] |
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