## Thermodynamics Questions

#### Unanswered

• How do reflected beams sum to form standing waves in blackbody (cavity) radiation?
• What is the kinetic theory of capillary action?
• Why is the Boltzmann factor in the partition function for Fermi-Dirac and Bose-Einstein statistics instead of their distributions? In other words, explain why \bar{n_s} = N P(s) is true or false, where P(n) is the Boltzmann factor applied to a single particle.
• Why does it give you a different answer if you pretend that particles are distinguishable when they aren't? It seems like if you simulated a gas in a computer then the computer would be able to label each particle with a number and tell you where it is. This should still give you the right answer unless there is some mechanism that the computer isn't accounting for.
• Is it possible that the gas in a container will never collect in one half? So basically this would mean that the gas would cycle back to its exact initial state before collecting in one half.
• Why is it h instead of hbar in the expression for the classical partition function?
• What is the connection between symmetry with respect to particle interchange and symmetry with respect to coordinate inversion?
• What is the heat capacity of a van der Waals gas?
• Doesn't Reif's derivation of the free expansion of a van der Waals gas assume it is quasistatic in equation (5.7.1)/(5.8.4)? Or is this a different type of quasistatic?
• Is there a more correct way to count momentum states between Reif's k = 2nPi/L versus the more obvious k = nPi/L?

#### Answered

• How do you know if you have a complete set of variables for a thermodynamic problem? There is no theory for this, all current justification comes from experiment.
• Why is Boltzmann's Law true? I reasoned this one out myself and later found supporting evidence in a book called Introduction to Laser Physics by Bela Lengyel page 171. When atoms with high kinetic energy collide, they can transfer their energy to an excitation of an electron. And if a collision occurs with an excited atom that has not yet had a chance to decay via photon emission, then the energy of the excitation can be released as kinetic energy of the atoms. If the atom does decay, the photon will be reabsorbed by another atom, which creates the same situation again. These two mechanisms allow there to be a fixed relationship between the energy of electrons and the kinetic energy of the atoms as stated in Boltzmann's Law. For further information search for "inelastic collisions of the second kind", but it won't be too easy to find.
• How do Van der Waals forces work? Each atom or molecule has an oscillating electric dipole moment and the mutual interactions cause the oscillations of nearby molecules to be in phase. This causes opposite charges to be closer together, which causes mutual attraction between nearby atoms or molecules.
• Does an ideal gas violate the third law of thermodynamics? Yes, the entropy approaches negative infinity as the temperature approaches zero. This is discussed in the Wikipedia article "Ideal Gas".
• What aspect of indistinguishability is responsible for the spin singlets and triplets to combine up-down with down-up? It is the indistinguishability under measurements of the total z component of angular momentum. Even though the two states up-down and down-up maybe be distinguishable in principle, they are certainly not distinguishable to a device that can only measure J_z. So the basis you choose determines the counting of indistinguishability.
• What is the molecular theory of why a gas cools down upon expansion? For a free expansion an ideal gas doesn't cool down. But when an ideal gas expands quasistatically it does work on a piston and with each collision with the piston the velocities of the particles slow down.
• Is dQ = TdS only true for quasistatic processes? Yes
• Can T be less than zero? Yes, but only for systems with an upper bound to their energy. See Reif page 105.