28 PROBLEMS
4.53 Critical Parameters (Stony Brook)
Consider a system described by the Dietrici equation of statewhere A, B, R are constants and P, V, and are the pressure, volume,
temperature, and number of moles. Calculate the critical parameters, i.e.,
the values ofP, V, and at the critical point.
Mixtures and Phase Separation
4.54 Entropy of Mixing (Michigan, MIT)
A 2-L container is divided in half: One half contains oxygen at 1
atm, the othernitrogen at the same pressure, and both gases may
be considered ideal. The system is in an adiabatic enclosure at a
temperature K. The gases are allowed to mix. Does the
temperature of the system change in this process? If so, by how
much?Does the entropy change? If so, by how much?
How would the result differ if both sides contained oxygen?
Now consider one half of the enclosurefilled with diatomicmolecules
of oxygenisotope andthe otherhalfwith Will theanswer
be different from parts (a) and (b)?4.55 Leaky Balloon (Moscow Phys-Tech)
Sometimeshelium gas in a low-temperaturephysics lab iskepttemporarily
in a large rubber bag at essentially atmospheric pressure. A physicist left a
40-L bag filled with He floating near the ceiling before leaving on vacation.
When she returned, all the helium was gone (diffused through the walls of
the bag). Find the entropy change of the gas. Assume that the atmospheric
helium concentration is approximately. What is the minimum
work needed to collect the helium back into the bag?
4.56 Osmotic Pressure (MIT)
Consider an ideal mixture of monatomic molecules of type A and
monatomicmolecules of type B in a volume V.
b)
c)a)