Physics 441/541: Homework Questions Due March 29th

Problem 9.6

The summit of Mauna Kea, Hawaii (4200m above sea level), is considered one of the world's premier observing sites. It is especially good as an infrared site because of the low water vapor and carbon dioxide content in the atmosphere above this altitude. (Water and carbon dioxide have many infrared wavelength absorption bands.) However, working at these altitudes can be hard on astronomers who are not acclimated to the lower abundance of molecular oxygen.
a) To understand both of these effects, calculate the scale height for H2O, CO2, and O2 in the Earth's atmosphere.
b) What percentage of each of these gases in the atmosphere is below 4200m? (Assume that the content decreases uniformly for each gas.)

Show that for an ideal monatomic non-degenerate gas, delta grad rho divided by rho is equal to delta grad temperature divided by the temperature.

Problem 9.17

Show that if the entire solar luminosity were carried by convection through the midway point of the sun with a mixing length of 10**9 cm., the required excess of the temperature gradient would only be about 10**-6 of the temperature gradient itself.