Question 515108: At constant temperature, the atmospheric pressure p (in Pa) at an altitude h (in m) is given by p = p0e^kh, where p0 is the pressure where h = 0 (atmospheric pressure at sea level). Given that p0 = 101.3 kPa (atmospheric pressure at sea level) and p = 68.9 kPa for h = 3050 m, find the value of k.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! At constant temperature, the atmospheric pressure p (in Pa) at an altitude h (in m) is given by p = p0e^kh, where p0 is the pressure where h = 0 (atmospheric pressure at sea level). Given that p0 = 101.3 kPa (atmospheric pressure at sea level) and p = 68.9 kPa for h = 3050 m, find the value of k.
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p = p0e^(kh)
Rearrange the equation to solve for k:
p/p0 = e^(kh)
Take the natural log of both sides:
ln(p/p0) = kh
So k = (1/h)*ln(p/p0)
Putting in the numbers, we get
k = ln(68.9/101.3)/3050 = -0.0001264
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