Understanding Gas Molar Specific Heats & Thermodynamic Processes

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 ½·kT per each degree of freedom. It means that the molah heat capacity is ½·R 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 Cvat ~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 can’t 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/animations/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 Maxwell’s 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). Maxwell’s 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