SOLUTION: At constant temperature, the atmospheric pressure p (in Pa) at an altitude h (in m) is given by Ph = Poe^(-mgh/RT), where Po is the pressure where h = 0 (atmospheric pressure at se

Algebra ->  Finance -> SOLUTION: At constant temperature, the atmospheric pressure p (in Pa) at an altitude h (in m) is given by Ph = Poe^(-mgh/RT), where Po is the pressure where h = 0 (atmospheric pressure at se      Log On


   

Question 788870: At constant temperature, the atmospheric pressure p (in Pa) at an altitude h (in m) is given by Ph = Poe^(-mgh/RT), where Po is the pressure where h = 0 (atmospheric pressure at sea level). Given that Po = 1013.25 hPa (atmospheric pressure at sea level) and Ph = 900 hPa, find the value of h.
Where P0 is the atmospheric pressure at some reference level
Ph is the atmospheric pressure at altitude h (m) above the reference level.
m is the molecular mass of air (0.0289644 kg/mol)
g is acceleration due to gravity (9.80665 ms-2)
R is the gas constant constant (8.314462 JK-1mol-1)
T is the temperature in Kelvin. In the lower altitudes temperature reduces with altitude at a rate of about 6.5 Kelvin per km of altitude.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
P%5Bh%5D+=+P%5B0%5D%2Ae%5E%22%28-mgh%2FRT%29%22
P%5Bh%5D%2FP%5B0%5D=e%5E%22%28-mgh%2FRT%29%22 or P%5B0%5D%2FP%5Bh%5D=e%5E%22%28mgh%2FRT%29%22
ln%28P%5Bh%5D%2FP%5B0%5D%29=-mgh%2FRT or ln%28P%5B0%5D%2FP%5Bh%5D%29=mgh%2FRT
ln%281013.25%2F900%29=mgh%2FRT --> h=%28RT%2Fmg%29%2Aln%281013.25%2F900%29
Assuming that T is the temperature at sea level, or it does not change much from 0 to h meters above sea level,
h=%288.314462%2A6.5%2F%280.0289644%2A9.80665%29%29%2Aln%281013.25%2F900%29 gives us the height in meters (because those would be the units of RT%2Fmg} with, R, T, m, and g in the units given).
I do not have a temperature, so I will assume 20%5EoC (293 kelvins)
h=%288.314462%2A293%2F%280.0289644%2A9.80665%29%29%2Aln%281013.25%2F900%29=1017%29
So the height is about 1,000 meters.