Chocolate fireguard
Active member
andrewmc said:Adding hot water will cause the air to expand, as already described. You don't actually need to think about the addition of water vapour by evaporation (although this will add to the partial pressures I think); just heating the air will cause expansion. This will take a bit of time; adding hot water and then immediately closing the lid means the trapped cold air will attempt to expand as it heats, but can't, so the pressure goes up. But if you let the air heat and then _then_ closed the lid then you would get no further expansion but would get a partial vacuum/pressure drop as the water and air slowly cooled.
The expansion of the air due to the increase in temperature will contribute of course, but for the temperature changes here the presence of the water vapour will be the dominant factor.
This is because thermal expansion of air (at constant pressure, ie before the flask is closed) is determined by the increase in the Absolute (Kelvin) temperature, which is obtained by adding 273 to the Celsius temperature.
If the flask contains only air an increase from 20C (293K) to 90C (363K) expands the air by a factor of 363/293 or 1.24 so about a fifth of the air is pushed out of the flask.
When the flask is closed and cooled back to 20C the 80% of the original air left in the flask will suffer a reduction in pressure (now at constant volume) to 0.8 atmospheres.
Now with some hot water in the open flask: the increase in the partial pressure of water vapour is (almost) exponential in the 0 to 100C range and goes from about zero up to 1 atmosphere in that range ? reasonable considering what happens to liquid water at 1 atmosphere at each end of the range.
At 20C the partial pressure of water vapour is about 0.025 atmospheres and rises to just under 0.7 atmospheres at 90C. This means that at the higher temperature the very large amount of water vapour that has been produced has ejected nearly 70% of that 80% of air that remained after thermal expansion.
So when the flask is closed only about 25% of the original air is still in there and when the water vapour has condensed after cooling the pressure will have fallen to 0.25 atmospheres, perhaps a third of what would have happened with air alone.
Of course because the pressure is now below 1 atmosphere not all of the water vapour will have condensed, but I have been unable to find any figures to use there.
If a lower temperature is chosen, say 70C, the thermal expansion of the air alone would produce a pressure drop to 0.85 atmospheres after sealing and cooling, and with water in the flask a drop to 0.6 atmospheres.