B. How much power would be required to desalinate ocean water to provide
for the fresh water requirements of the human race? Compare to the total
power requirement of the human race today.
C. Neutron star crusts are said to be like jello. Explain why using
order-of-magnitude arguments.
D. What is the thermal diffusion time of a white dwarf?
E. What determines the voltage of household batteries?
F. Estimate the velocity of electrons running through a household lamp.
Explain why the value you estimate does or does not trouble you.
G. A circumstellar ring is composed of particles whose vertical, geometric,
optical depth is equal to tau. Estimate the kinematic viscosity of the ring
in the tau << 1 and tau >> 1 limits.
H. Derive an expression for the electrical conductivity of a plasma
in the absence of an external magnetic field and see that it is independent
of the plasma density.
I. A plasma is threaded with a uniform external magnetic field. Estimate the
electrical conductivity perpendicular to the field.
J. Temperature as a function of time and depth near the lunar surface.
(for HW---or lecture/notes on solving equations without solving them).
K. Why can an insect but not a human walk on water?
L. Provide a quantitative explanation for why glass dishes are likely to crack
if used as cooking vessels.
M. Bathyspheres are spherical vessels designed to withstand the pressure
at great depths in the ocean. How thick must the wall of a 2-m radius
bathysphere be for it to safely travel to the deepest parts of the ocean, depth
10 km? Would such an empty bathysphere float?
N. Electromagnets: Estimate the strongest magnetic field that one could make by
passing an electric current through copper. Consider in turn limitations
due to: (a) yield strength of copper, and (b) ability of copper to conduct
away the power dissipated by ohmic loss.
O. (a) Estimate the surface tension of a nuclear fluid. The radius of an atomic
nucleus of atomic number A is 1.2e-13 A^{1/3} cm.
(b) Show that the electrostatic plus surface energy of nuclei with A < A_{max}
is increased by fission, so fission will not occur spontaneously for such A, but that
for A > A_{max}, the energy is reduced by fission. Estimate A_{max}. Use Z/A = 0.4.
(c) Estimate the maximum possible angular momentum of a tin nucleus (A = 120,
Z = 50) in units of h-bar.
P. Full refrigerators, empty refrigerators, and urban myths: do empty fridges turn on more
frequently than full ones? Explain your answer quantitatively.
Q. A superball has a diameter of 4.2 cm and a mass of 38 g. Resting on a hard
surface, the radius of the circle of contact is measured to be 0.13 cm.
(a) What is the elastic modulus of the ball?
(b) When you drop the rubber ball, it bounces with decreasing height and increasing
frequency until it stops bouncing and begins to vibrate. What is the minimum time
between bounces of the ball?
R. Estimate the electrical conductivity of the air, assuming that electrons are absorbed
by micron-size aerosols and positive ions are free.
S. In regions of fair weather, a so-called "fair weather electric field" exists that
transports current from the positively charged ionosphere to the negatively charged ground.
The fair-weather field has strength of order 100 V/m.
Assume that the return current is provided by lightning discharges in thunderstorms, completing
the so-called "global circuit." Using your answer to (R), estimate the amount
of current flowing through this global circuit. Estimate also the amount of current
flowing through a typical thunderstorm.
T. Estimate the strength of the electric field in a thunderstorm required to generate lightning.
U. How much warmer is a big city [say 1e7 people in a square 20 km on a side]
than the surrounding countryside? [Hint: average American uses 10 kW].
Treat two cases:
(a) City is trapped under a breezeless inversion layer, so all heat must be radiated.
(b) Heat is convected up into atmosphere and carried away by horizontal winds.
V. If a T-rex dinosaur trips and falls, landing on its back and head,
would it suffer a life-threatening concussion?
W. Estimate the maximum size of a mountain on the Earth. Repeat for a neutron star.
X. Estimate the mass of a zero-temperature, hydrogen-rich planet above which the hydrogen
in the planet's interior is ionized.
Y. Light bulb filaments are made of refractory metals (e.g., Tungsten) so that when
heated enough to radiate at optical wavelengths, they don't sublimate.
(a) The resistance of a light bulb measured with a 3 V battery tester is about 10
times lower than it is when measured at 120 V line voltage. Why? Can you think of
a consequence from your personal experience?
(b) Predict the length and thickness of the filament of a 100 W light bulb.
Z. Estimate the time required for perfume to diffuse across our classroom. Does this
time accord with your experience?
AA. The specific metabolic rates (energy consumed per unit time per unit volume) of most single and multi-celled organisms are intermediate between those of a sedentary and an actively exercising human being. (a) Estimate those specific metabolic rates in erg cm^{-3} s^{-1}. (b) Estimate the required oxygen consumption (in g of O2 cm^{-3} s^{-1}. (c) By considering diffusion of oxygen into an organism, calculate the size of the largest water-dwelling organism without a circulatory system. In water in equilibrium with air at 25 C, the equilbrium dissolved oxygen content is 8e-6 g of O2 per gram of water.