1.
(50%) WeBWorK set
# 11.
2.
(25%) In this problem we use the results of measurements
of the temperature dependence of the heat capacity of Hydrogen gas
(H2) at constant volume to determine the molecular properties
of Hydrogen.
a.
At temperatures below 80 K the heat capacity (at constant volume) is
(3/2)k per molecule, but at higher temperatures the heat
capacity increases to (5/2)k per
molecule due to contributions from rotational energy states. Use these observations to estimate the
distance between the hydrogen nuclei in an H2 molecule.
b.
At about 2000 K the heat capacity (at constant volume) increases to
(7/2)k per molecule due to contributions from vibrational
energy states. Use these
observations to estimate the stiffness of the "spring" that
approximately represents the inter-atomic force.
3.
(25%) A rigid, thermally insulated container with a volume
of 22.4 liters is filled with one mole of helium gas (4 grams per mole)
at a temperature of 0 Celsius (273 K). The
container is sitting in a room, surrounded by air at standard temperature
and pressure (STP: 1 atmosphere and 0 Celsius).
a.
Calculate the pressure inside the container in N/m2.
b.
Calculate the root-mean-square speed of the helium atoms.
c.
Now open a tiny square hole in the container, with area 10-8 m2. After 5 seconds, how many helium atoms
will have left the container?
d.
During the same 5 seconds, some air molecules from the room will enter
the container through the same hole. How
many air molecules will enter the container?
e.
Does the pressure inside the container increase or decrease during
this 5 seconds period?
