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It is well known that the temperature of the atmosphere
Chapter 3, Problem 137P(choose chapter or problem)
Problem 137P
It is well known that the temperature of the atmosphere varies with altitude. In the troposphere, which extends to an altitude of 11 km, for example, the variation of temperature can be approximated by where T0 is the temperature at sea level, which can be taken to be 288.15 K, and β = 0.0065 K/m. The gravitational acceleration also changes with altitude as where g0 = 9.807 m/s2 and z is the elevation from sea level in m. Obtain a relation for the variation of pressure in the troposphere (a) by ignoring and (b) by considering the variation of g with altitude.
Questions & Answers
QUESTION:
Problem 137P
It is well known that the temperature of the atmosphere varies with altitude. In the troposphere, which extends to an altitude of 11 km, for example, the variation of temperature can be approximated by where T0 is the temperature at sea level, which can be taken to be 288.15 K, and β = 0.0065 K/m. The gravitational acceleration also changes with altitude as where g0 = 9.807 m/s2 and z is the elevation from sea level in m. Obtain a relation for the variation of pressure in the troposphere (a) by ignoring and (b) by considering the variation of g with altitude.
ANSWER:
Part (a)
Step 1:
To obtain the relation for the variation of pressure in the troposphere by taking constant acceleration due to gravity
The change in pressure P at troposphere is given by
=
----(1)
Where is density of the air
g is the acceleration due to gravity (assuming constant)
z is the vertical height (altitude)