Gas molar specific heats

1
Gas molar specific heats
Mean kinetic energy of a gas molecule
If we have n moles of gas
Then molar specific heat at constant volume
should be
What molar specific heats, Cv, do we get
experimentally?
Monatomic gases He, Ne, Ar
Diatomic gas molecules H2, O2, N2
Polyatomic gas molecules NO2, SF6, C2H5OH
2
Gas molar specific heats
Equipartition theorem When a system is in
thermodynamic equilibrium the average energy per
molecule is ½kT per each degree of freedom.
It means that the molah heat capacity is ½R per
degree of freedom.
Monatomic molecules only have 3 translational
degrees of freedom.
Diatomicc molecules have 3 translational plus 2
rotational a total of 5. Polyatomic molecules
have 3 translational and 3 rotationla a total
of 6.
3
Is this the entire story?
Not really!!!
It takes a finite temperature to activate
rotational degrees of freedom. For H2, the 2
rotational degrees of freedom get activated at
100 K kT in molar specific heat at const.
volume. Below that temperature, H2 behaves as a
monatomic gas
At still higher temperatures, you activate
further degrees of freedom, which are due to
oscillations of the atoms along the axis
connecting the dumbbell an addition of 2 degrees
of freedom and another kT in Cv at 1000 K.
4
Reversibility.

• Where do we find reversible processes?
• In mechanics
• elastic collisions
• oscillations with no friction
  http//www.myphysicslab.com/pendulum1.html
• rotation of planets
• No mechanical energy is dissipated into
  heat-internal energy!
• You can run the movie back and it will still be a
  plausible process.

5
Irreversibility.
Where do we find irreversible processes?...
Pretty much everywhere, damn it!.. And we are not
getting any younger either!..
You cant possibly run that movie back
Losing, breaking, destroying, saying stupid
things.
6
Seriously.
Three common scenarios of irreversibility in
thermodynamics.
1) Mixing and loosing structural order in
general. Two molecularly mixed fluids never
unmix. http//mutuslab.cs.uwindsor.ca/schurko/an
imations/irreversibility/happy.htm A broken vase
never repairs itself
2) Conversion of mechanical energy into internal
energy (dissipation into heat). Ordered motion
of an object is converted into disordered motion
of its molecules. Never coming back
http//mutuslab.cs.uwindsor.ca/schurko/animations/
secondlaw/bounce.htm
3) Heat transfer from a hotter to a cooler object
never goes in the opposite direction.
7
Irreversibly lost opportunities...
1 Expanding gas On the way from a to b the gas
could be harnessed to do some mechanical work at
expense of its internal energy
Instead of that we have
Maxwells demon
8
2 Two systems with different temperatures
reaching equilibrium
There was an opportunity for a spontaneous
process heat flow from Th to Tc. It could be
used to run a heat engine between the two
reservoirs (hot and cold).
Maxwells demon high speed molecules go to the
right, low speed to the left.
9
Maxwell distribution after thermal equilibrium is
established Order is lost!
There is no way the molecules would spontaneously
split into two groups with high and low
temperatures.
10
Gas under a piston sliding without friction
Equilibrium of forces
Pressure from inside ? total weight of the piston
and shot from the outside
If I push the piston with a little force, f ,
what will be the work, W, to plug into the first
law?
As funny as it may be The work W is NOT directly
connected to the pushing force, f . It is work BY
THE GAS
Our system of interest is the gas, and we are
only concerned with the work done by or on it!
11
Pushing a piston. The gas heats up.
Three Forces involved, Due to the gas pressure
Due to the pushing hand
Due to the atmospheric pressure
12
Pulling a piston. The gas cools down.
Three Forces involved, Due to the gas pressure
Due to the pulling hand
Due to the atmospheric pressure