Space Station Pressure
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 4
4-9-2016
1500
Space Station Pressure
A space station consists of a large cylinder of radius R0 filled with air. The cylinder spins about its symmetry axis at an angular speed Ω providing an acceleration at the rim equal to g. If the temperature τ is constant inside the station, what is the ratio of air pressure Pc at the center of the station to the pressure P0 at the rim?
SOLUTION
The rotation of the station around its axis is equivalent to the appearance of an energy U = -mΩ2R2/2, where m is the mass of an air particle and R is the distance from the center. Therefore, the particle number density satisfies the Boltzmann distribution (similar to the Boltzmann distribution in a gravitational field):
Where nc is the number density at the center and τ ≡ kBT is the temperature in energy units. The pressure is related to the number density n simply by P = nτ. So, at constant temperature,
Using the condition that the acceleration at the rim is Ω2R0 = g, we have
الاكثر قراءة في مواضيع اخرى
اخر الاخبار
اخبار العتبة العباسية المقدسة
