On 02/10/2011 08:28 AM, Jed Rothwell wrote: > <jwin...@cyllene.uwa.edu.au <mailto:jwin...@cyllene.uwa.edu.au>> wrote: > > > What you wrote is true when there is liquid water and steam > together in a container - the combination cannot be heated to a > temperature higher than 100 deg C without raising the pressure. > However once all the liquid has turned to gas there is no longer > any limit to what temperature it can be raised to until the > molecules dissociate into their component elements. > > > What would keep the molecules in the kettle, assuming the top or spout > is open? What would prevent the gas density from declining > indefinitely until it is close to a vacuum? > > My understanding is that the temperature does not rise as long as the > volume is free to expand.
Your understanding appears to be incomplete. Ideal gases, and, to a good approximation, all real gases, obey the law: PV = nRT That means, for a given quantity of gas, the pressure on the gas, times the volume it occupies, is equal to the number of moles of gas (the quantity), times a constant 'R', times the absolute temperature (degress Kelvin). A "mole" of gas is about 6.02 * 10^23 molecules. If we have a ten gallon tank filled with air, with a small opening, then, when the tank is at room temperature (300 degrees, roughly), we'll have 15 psi * 10 gallons = n0 * R * 300 where the number of *molecules* of gas in the tank is n0 * 6.02 * 10^23. (I leave it to someone else to calculate what the numeric value of "n0" is, and I don't know the value of the constant "R" when we're using pounds per square inch and gallons, so I'll just continue to call it 'R'.) If I then heat the tank to 400 degrees, the air inside will also be heated, by conduction from the walls of the tank. The air will, of course, expand, and we'll probably notice a whistling sound as air rushes out of the tank through the small opening. When it all comes to equilibrium there will be less gas in the tank -- a smaller number of moles. Since we've heated the gas to 4/3 the original temperature, the volume will have expanded by 4/3, so a lot of the gas will have escaped, and the number of moles which will still fit inside the tank will be 3/4 what it was before. So, for the gas which remains inside the tank, we'll have 15 psi * 10 gallons = (3/4)*n0 * R * 400 The temperature has increased by 4/3, the number of moles remaining in the tank has dropped by a factor of 3/4, the pressure and volume are the same as they were to start with, and the equation balances. But you can't make it balance if you assume the temperature didn't increase! As the tank is heated, gas expands and escapes -- you can hear it whistling out. That means "n", the number of moles of gas inside the tank, gets smaller. Since the pressure and the volume inside the tank haven't changed, in order for PV = nRT to continue to balance, the temperature *must* have increased.
