Phys 215A Hw 3A
1. Calculate the entropy of the two-states system (energies 0 and ) at temperature T.
2. Find the specific heat of a system with discrete, equally spaced, non-degenerate energy
levels (i.e. the quantum harmonic oscillator). Give expression
Phys 215A Hw 5
5.1 Consider N Hydrogen atoms in a volume V. 0 is the ionization energy; consider only
two states: H atom in the ground state, and ionized state (i.e. proton and electron go their
own separate ways). Calculate the number of dissociated atom
Phys 215A Hw 1
1. Which way does heat flow. Show that from the 2nd Law (in the form: S is max at
equilibrium for a closed system) follows that heat flows from the warm to the cold body.
2. Lagrange multipliers. Show that the max (or min) of f (x, y) under
Phys 215A Hw 4A
3.6 Consider an ideal gas in equilibrium in a uniform gravitational field (the isothermal
atmosphere). Using the chemical potential, find how the pressure changes with height.
3.7 For a system at temperature T (i.e. in contact with a heat
Phys 215A Hw 6
6.1 For an atom of a monoatomic classical ideal gas at temperature T, find the mean
square fluctuations of the velocity and of the energy.
6.2 Find the ground state energy for a relativistic ideal Fermi gas.
6.3 Find the first order correct
Phys 215A Hw 2
1. One mole of a monoatomic gas performs a Carnot cycle between the temperatures 400
K and 300 K. On the upper isothermal transformation, the initial volume is 1 L and the
final volume 5 L (liters). Find the work performed during one cycle,