homework #2

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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 1st Law. Rewrite the 1st law under each one
of these processes.
2. The equation of state when considering a dry atmosphere is: P  RT , where P is
pressure, T is temperature,  is the air density, and R is the Gas Constant 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:
 1000hPa 
  T

P


R / Cp
Derive 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. 200hPa. 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 cyclic processes. Explain what is
meant by a cyclic process. Next using the pressure, volume diagram below 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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