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Have you tried circulating the air in the bottom chamber? I'd like to know if putting a computer fan down there would work. Also, what kind of alcohol are you using in the upper section?
It's the universal gas constant. Quoting from wikipedia, it is "the constant of proportionality that happens to relate the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered."
If you are ok with an electronic setup, you could use a float switch with a solenoid valve. It may need a relay to work opposite to the normal application.
This seems like a homework question. What have you tried? A globe valve doesn't suddenly open. It takes quite a few rotations of the handle to fully separate the plug from the seat. Assuming you have a valve that can be suddenly opened fully, try assuming that your final temp and pressure equalize, then figure out the volume of each species now in each cylinder.
