THERMODYNAMICS AND STATISTICAL PHYSICS 13
c)Find the height at which the drag on the rocket is at a maximum.
4.20 Adiabatic Atmosphere (Boston, Maryland)
The lower 10–15 km of t h e atmosphere, the troposphere, is often in a con-
vective steady state with constant entropy, not constant temperature
is independent of the altitude, where
Find the change of temperature in this model with altitude
Estimate in K/km. Consider the average diatomic molecule
of air withmolarmass
4.21 Atmospheric Energy (Rutgers)
The density of the Earth’s atmosphere, varies with height above
the Earth’s surface. Assume that the “thickness” of the atmosphere is
sufficiently small so that it is in a uniform gravitational field of strength
Write an equation to determine the atmospheric pressure given
the function
In a static atmosphere, each parcel of air has an internal energy
and a gravitational potential energy To a very good approxima-
tion, the air in the atmosphere is an ideal gas with constant specific
heat. Using this assumption, the result of part (a), and classical
thermodynamics,show that the total energy in a vertical column of
atmosphere of cross-sectional area A is given by
and that the ratio of energies is
where T is the temperature, is the pressure at the Earth’s surface,
is the molar mass, is the molar specific heat at constant pres-
sure, and is the ratio of specific heats.
Hint: The above results do not depend on the specific way in which
and vary as a function of (e.g.,isothermal,adia-
batic, or something intermediate). They depend only on the fact that
is monotonically decreasing. At some step of the derivation, you
might find it useful to do an integration by parts.
a)
b)
a)
b)