Here you are on top of Mt. McKinley, at 20,300 ft. You would like to know the at

ID: 767868 • Letter: H

Question

Here you are on top of Mt. McKinley, at 20,300 ft. You would like to know the atmospheric pressure, since you seem to have trouble breathing, but your manometer has fallen down an ice cave. Fortunately, your thermometer wasn't lost, and you use it to measure the boiling point of water as you boil a cup to make some tea. You find 75 degree C. What is the atmospheric pressure? Use this pressure to estimate the altitude. It will help to remember the barometric formula, which says that the pressure of a gas decreases exponentially with altitude (A) as: P = P0 exp(-cA), where c = Mg/(RT), where M is the molar mass (~30 g/mol for air) and g is the acceleration of gravity (9.8 m/s2).

Explanation / Answer

(a)

Using antonie equation

log(P) = 8.07131 - (1730.63/(233.426 + Tb))

log(P) = 8.07131 - (1730.63/(233.426 + 75))

log(P) =2.46

P = 10^(2.46) torr

P =288.5 torr = 0.38 atm

(b)

c = Mg/RT = 0.030*9.8/(8.314*288)

Po = 1 atm

P/Po = e^(-cA)

A = -(1/c)*ln(P/Po)

A = ((8.314*288)/(0.030*9.8))*ln(0.38)

A =7880 m

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