PHYSICS 313
Problem set 2 2002
Given Sept 16
Due Sept 25

Problem 1: The pressure in the atmosphere decreases with altitude according to

$$\frac{dP}{dz}=-\frac{mgP}{kT}$$

(see e.g problem 1:16 of text for derivation, $m$ is the mass of a molecule, i.e. molecular weight divided by Avogadro's number).
a: Integrate the above formula assuming the temperature $T=T_o=const.$ and that the pressure at ground level is $P_o$.
b: Find the pressure at height $z$ if the temperature decreases with height according to

$$T=T_o-lz$$

where $l$ is the lapse rate.
c: Plot the pressure in the range z=0 to 10 km assuming $T_0=300 K$ $P_o=1$ bar, $l=10^{-2}$ K m$^{-2}$. Take the molecular weight of air to be 29. g mol$^{-1}$.
Problem 2: How long will it take to bring 1 liter of water to boil in a 600 W microwave oven starting with tap water at 10$^oC$. Assume that all the microwave energy is absorbed by the water
Problem 3:. Suppose you flip 5 fair coins. List the probabilities for the different outcomes (5 heads, 4 heads 1 tail, 3 heads 2 tails etc.)