Notes
• Colloquium Tomorrow: “To the Terascale and
B
Beyond:
d N
New physics,
h i electroweak
l t
k symmetry
t
breaking, and the LHC”, 4pm, NSH 118
– Office hours will be 5-6pm tomorrow
• Regular Office Hours, Help Sessions otherwise
Results from Maxwell’s Velocity Distr.
Some more results from Maxwell
For molecular oxygen and molecular hydrogen,
compute the temperatures at which the rms speed is
equal to the escape velocity from Earth, 11.2 km/s.
Do the same for the moon, assuming ve = 2.3 km/s.
The average temperature in the upper atmosphere is
about 1000K for the earth. The average daily
temperature on sunlit parts of the moon is 380K.
380K What
does this tell you about the relative populations of
oxygen and hydrogen near these celestial bodies?
Current experiments in atomic trapping and cooling can create
low-density gases of elements like rubidium with temperatures in
the nano-Kelvin range. These atoms are trapped and cooled
using magnetic fields and lasers in ultra-high
ultra high vacuum chambers.
chambers
One method that is used to measure the temperature of a trapped
ggas is to turn off the trap
p and measure the time it takes for the
molecules of gas to fall a given distance. Consider a gas of
rubidium (85g/mol) at a temperature of 120nK. Calculate how
long it would take an atom traveling at the rms speed of the gas to
fall 0.1m if it were initially moving (a) directly upward (b)
directly downward.
downward
The temperature in interstellar space is 2.7K. Find the
rms speed of hydrogen molecules at this temperature.
The latent heat of vaporization for water at room
temperature is 2430 J/g. Consider one water molecule at
the surface of a glass of liquid, moving upward with
sufficiently high speed that it will be the next molecule to
join the vapor. (a) Find its translational kinetic energy.
(b) Find its speed. (c) Now, consider a thin gas made of
molecules just like this one. What is the temperature of
the gas? (d) Given what you calculated, why aren’t you
burned by water evaporating from a glass at room
temperature?
A cylinder is filled with 0.10 mol of an ideal gas at standard
t
temperature
t
andd pressure, andd a 1.4-kg
1 4 k piston
i t seals
l the
th gas in
i the
th
cylinder with a frictionless seal. The trapped column of gas is
2.4-m
2.4
m high. The piston and cylinder are surrounded by air, also at
standard temperature and pressure. The piston is released from
rest and starts to fall. The motion of the piston ceases after the
oscillations stop with the piston and the trapped air in thermal
equilibrium with the surrounding air. (a) Find the height of the
gas column.
l
(b) Suppose
S
th
thatt the
th piston
i t is
i lifted
lift d above
b
its
it
equilibrium position by a small amount and then released.
Assuming that the temperature of the gas remains constant, find
the frequency of vibration of the piston.
Internal Energy of an Ideal Gas
Equipartition Theorem