Mathematical Thinking
Table of Contents
Introduction
Fermi's Piano Tuner Problem
How Old is Old?
If the Terrestrial Poles were to Melt...
Sunlight Exerts Pressure
Falling Eastward
What if an Asteroid Hit the Earth
Using a Jeep to Estimate the Energy in Gasoline
How do Police Radars really work?
How "Fast" is the Speed of Light?
How Long is a Light Year?
How Big is a Trillion?
"Seeing" the Earth, Moon, and Sun to Scale
Of Stars and Drops of Water
If I Were to Build a Model of the Cosmos...
A Number Trick
Designing a High Altitude Balloon
Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water
Calendar Calculations
Telling Time by the Stars - Sidereal Time
Fields, an Heuristic Approach
The Irrationality of
The Irrationality of
The Number (i)i
Estimating the Temperature of a Flat Plate in Low Earth Orbit
Proving that (p)1/n is Irrational when p is a Prime and n>1
The Transcendentality of
Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions
Maxwell's Equations: The Vector and Scalar Potentials
A Possible Scalar Term Describing Energy Density in the Gravitational Field
A Proposed Relativistic, Thermodynamic Four-Vector
Motivational Argument for the Expression-eix=cosx+isinx
Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics


Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water

Problem:
The space suits worn by Lunar astronauts are cooled by the sublimation of water through specially designed, porous surfaces on the suit. The rate of water loss is approximately one pound per hour. If

A = .06m2

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:
The rate of water loss is approximately one pound per hour. This value corresponds to a mass loss of

1.4 x 10-4 kg/sec

1.

or a particle loss of

dN/dt = 5 x 1021 /sec

2.

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

nv = (dN/dt)/A

3.

or

nA = (dN/dt)/v

3a.

where A = the area from which sublimation is occurring. Substituting for dN/dt and v in the second expression, we find that

nA = 1019 /m

4.

Setting A = .06m2, we find

n = 2 x 1020/m3

5.

and the pressure p = (2 x 1020/m3)/(2 x 1025/m3) atm = 2 x 10-5 atm, (where n0 =2 x 1025/m3 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.]