1.
(50%) WeBWorK set
# 10.
2.
(25%) In 1988 telescopes viewed Pluto as it crossed in
front of a distant star. As
the star emerged from behind the planet, light from the star was slightly
dimmed as it went through Pluto's atmosphere. The
observations indicated that the atmospheric density at a height of
50 km above the surface of Pluto is about one-third the density at
the surface. The mass
of Pluto is known to be about 1.5 x 1022 kg, and its radius
is about 1200 km. Spectroscopic
data indicate that the atmosphere is mostly nitrogen (N2). Estimate the temperature of Pluto's atmosphere. State
what approximations and/or simplifying assumptions you made.
3.
(25%) A nano particle consisting of four iron atoms (object
1) initially has 1 quantum of energy. It is brought into contact with another nano particle, consisting
of two iron atoms (object 2), which has 2 quanta of energy. The mass of one mole of iron is 56 gram.
a.
Using the Einstein model of a solid, calculate and plot ln(W1) versus q1 (the
number of quanta of object 1), ln(W2)
versus q1, and ln(Wtotal) versus q1 (put all three plots on the same graph). Show
your work and explain how you obtained the results shown.
b.
Calculate the approximate temperature of the objects when they are
in equilibrium. State clearly what assumptions or approximations
you made.
4.
(Optional; 25% extra credit)
You can download the gasModel program from glowscript.org. This
program simulates the motion of 50 gas molecules in a container. The
simulations start with all molecules having the same speed but random
directions. How
long does it take for the system to obtain a speed distribution that
mimics the Maxwell-Boltzmann speed distribution?
Modify the program to run various simulations
with different masses (for example, use tin and lead atoms) and different
temperatures (for example, 100 K, 200 K, 500 K, 1,000 K, and 10,000K)
and use graphs to compare the average speed obtained with the program
with the average speed expected for the Maxwell-Boltzmann speed distribution. Do they agree for all masses and temperature? If
they disagree, make sure that the disagreement is not due to numerical
problems (e.g. is the step size consistent with the expected range
of velocities)? Send the graphs and a brief description
of your conclusions via email to Professor Wolfs (wolfs@pas.rochester.edu).
