AOS 330
Homework #2
Due: 10/05/09
1. State the First Law of Thermodynamics and define/explain each term in the equation.
Next define/explain the following: adiabatic process, isobaric process, isothermal
process, and isochoric process in terms of the 1
st
Law. Rewrite the 1
st
law under each one
of these processes.
2. The equation of state when considering a dry atmosphere is:
, where P is
pressure, T is temperature,
is the air density, and R is the Gas Constan
t of dry air.
a.)
Calculate R, only taking into account the volume fractions of the atmospheric
constituents: N2, O2, Ar, and CO2
b.)
Repeat the process but for the surface of Mars
3. Poisson’s equation for potential temperature is:
Der
ive Poisson’s equation for potential temperature from the First Law of
Thermodynamics.
a.)
Define/explain “
”
b.)
A trans

continental airline cruises at an altitude of approx. 12km, where the
temperature may be

55C and the pressure approx. 2
00hPa. Compute the potential
temperature of air at this altitude.
c.)
For a potential temperature of 310K compute the corresponding “T” at 700hPa,
300hPa, 100hPa
4
. Prove mathematically that the potential temperature is constant for adiabatic processes
i.e.
= 0. (Hint
:
use the 1st Law of Thermo. and the equation for potential temp.)
5
. Of specific interest in thermodynamic theory are cy
clic processes. Explain what is
meant by a cyclic process. Next using
the
pressure, volume diagram b
elow explain what
happens to a gas as it goes from Point A to Point B. Then, explain what happens as the
gas goes from Point B to Point A. Hash out the work done on the gas and write out
mathematically the net work done on this cyclic process.
6
. Please
define/explain the Second Law of Thermodynamics.
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