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The rate of change of atmospheric pressure P with respect to altitude h is proportional to P, provided that the temperature is constant. At a specific temperature the pressure is 101.5 kPa at sea level and 87.3 kPa at h = 1,000 m. (Round your answers to one decimal place.)

(a) What is the pressure at an altitude of 3500 m? kPa
(b) What is the pressure at the top of a mountain that is 6154 m high?

Respuesta :

Answer:

[tex]P = 101.5 e^{-0.00015h}[/tex]

Step-by-step explanation:

dP/dh = kP

dP/P = k dh

ln P = kh + C

Now, using the points given,

ln 101.5 = C, so C = 4.62

ln 87.3 = k*1000 + 4.62

k = -0.00015

So, we have

ln P = -0.00015 h + ln 101.5

P = 101.5 e^(-0.00015h)

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