(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
[tex]m=\frac{\Delta p}{\Delta h}=\frac{87.8 kPa-102.1 kPa}{1000 m-0 m}=-0.0143 kPa/m[/tex]
And so now we can calculate the pressure at any altitude by using the equation:
[tex]p(h) = p_0 + m h[/tex]
where
[tex]p_0 = 102.1 kPa[/tex] is the pressure at sea level
m is the rate of change of pressure
h is the altitude
Substituting h = 4500 m, we find
[tex]p=102.1 kPa + (-0.0143 kPa/m)(4500 m)=37.8 kPa[/tex]
(b) 13.9 kPa
As before, we can calculate the pressure at the top of the mountain by using the equation:
[tex]p(h) = p_0 + m h[/tex]
where
[tex]p_0 = 102.1 kPa[/tex] 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
[tex]p=102.1 kPa + (-0.0143 kPa/m)(6165 m)=13.9 kPa[/tex]
