Consider an ideal gas of N atoms following classical statistics. Find the contribution to the average Helmholtz free energy and entropy from the internal electronic level structure considering the atoms as two-level systems with the ground state energy 0 and excited state energy E. The system's temperature is T. The internal electronic energy levels are non-degenerate.
The Helmholtz free energy is defined as F = U - TS. F = -NkBT ln(Z).
A log of length L and radius r is weighted at one end with a lump of lead so it
can float vertically in water (of density ρwater). The total mass is
M. The log is pushed in the water by a small amount compared to the equilibrium
position.
(a) Find the equation of motion for the log and describe the motion.
(b) If the motion is periodic, give an expression for the period.
Consider that the Universe is spherical and an adiabatic expansion of a
mono-atomic hydrogen gas
(γ = 5/3). The current Universe's radius is at least 46 billion light years,
and its temperature is 2.7 K. Estimate the temperature when the Universe had
the size of a cherry (1 cm radius).
Find the heat capacity CV of:
(a) one mole of argon in the gas phase,
(b) a carbon dioxide (CO2) molecule in the gas phase (a linear
molecule),
(c) an alcohol molecule (C2H6O) in the gas phase (NB,
not a linear molecule),
(d) 0.1 mol of lead atoms in a lead crystal,
all in the high temperature limit. Assume ideal gases in (a) through (c).