(@) If z denotes the height above sea level, show that the change of atmos- pheric pressure p with height is given by dp R7 dz where T is the absolute temperature at the height z. (b) If the decrease of pressure in (a) is due to an adiabatic expansion, show that dp Y dT y -iT (c) From (a) and (b) calculate dT/dz in degrees per kilometer. Assume the atmosphere to consist mostly of nitrogen (Na) gas for which y- 1.4. (d) In an isothermal atmosphere at temperature T, express the pressure pat height z in terms of the pressure po at sea level. (e) If the sea-level pressure and temperature are po and Te, respectively, and the atmosphere is regarded as adiabatic as in part (6), find again the pressure
(@) If z denotes the height above sea level, show that the change of atmos- pheric pressure p with height is given by dp R7 dz where T is the absolute temperature at the height z. (b) If the decrease of pressure in (a) is due to an adiabatic expansion, show that dp Y dT y -iT (c) From (a) and (b) calculate dT/dz in degrees per kilometer. Assume the atmosphere to consist mostly of nitrogen (Na) gas for which y- 1.4. (d) In an isothermal atmosphere at temperature T, express the pressure pat height z in terms of the pressure po at sea level. (e) If the sea-level pressure and temperature are po and Te, respectively, and the atmosphere is regarded as adiabatic as in part (6), find again the pressure
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Transcribed Image Text:Consider the earth's atmosphere as an ideal gas of molecular weignt u in a
uniform gravitational field. Let g denotc the acceleration due to gravity.
(a) If z denotes the height above sea level, show that the change of atmos-
pheric pressure p with height is given by
dp
where T is the absolute temperature at the height z.
(6) If the decrease of pressure in (a) is due to an adiabatic expansion, show
that
dp
Y dT
Y -iT
(c) From (a) and (b) calculate dT/dz in degrees per kilometer. Assume
the atmosphere to consist mostly of nitrogen (N) gas for which y - 1.4.
(d) In an isothermal atmosphere at temperature T, express the pressure
p at height z in terms of the pressure po at sea level.
(e) If the sea-level pressure and temperature are po and To, respectively, and
the atmosphere is regarded as adiabatic as in part (b), find again the pressure
p at height z.
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