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 102.1 kpa at sea level and 87.8 kpa at h = 1,000 m. (round your answers to one decimal place.) (a) what is the pressure at an altitude of 4500 m? kpa (b) what is the pressure at the top of a mountain that is 6165 m high?

(a) 37.8 kPa

First of all, we need to find the rate of change of pressure per meter.

We know that:

at h = 0 m, the pressure is 102.1 kPa

at h = 1,000 m, the pressure is 87.8 kPa

So, the rate of change of pressure is

And so now we can calculate the pressure at any altitude by using the equation:

where

is the pressure at sea level

m is the rate of change of pressure

h is the altitude

Substituting h = 4500 m, we find

(b) 13.9 kPa

As before, we can calculate the pressure at the top of the mountain by using the equation:

where

is the pressure at sea level

m is the rate of change of pressure

h is the altitude

Substituting this time h = 6165 m, we find

260 miles per hour

explanation: