Scott is an intelligent boy who, among other things, is fully au fait with basic theories of Physics. His younger brother Gavin, however is vain and idle, who whiles away his time practising his fake magical powers. Gavin also believes himself superior to Scott in intelligence.
Accordingly, Gavin challenges Scott to a little competition whereby, the first to get 5 ounces of water to freeze will be declared the most intelligent guy at their residence. They set up some rules as follows:
- Each of them can only use normal water that comes out of their stainless steel faucet.
- They both must use identical containers.
- They both must use the same freezer at the same time.
Now, it is a do-or-die situation for Scott as his prowess in Physics has been called into question.
How will Scott have the best chance of winning over Gavin?
Scott could take advantage of freezing point depression. Whenever there is any contaminant dissolved pure water, such as salt or
even air, water must reach a colder temperature in order to freeze. Tap water itself contains dissolved air, and the maximum is put in by the aerator cap on most taps. As water warms, it can hold less dissolved air. Assuming the pipes in their house, running through the ground, deliver cooler water than their house temperature, simply by filling his container some time before Gavin fills his, Scott's water will warm longer (equilibrating with room temperature) and lose more air. For example, if the water warms from 60 to 70F (15 to 21C), at 1 atm (10 kPa) the
air in the water by volume drops from 3.6 to 3.5% While freezing subsequently will drive most of this dissolved air out of the water, especially if freezing is done from the bottom up allowing bubbles to rise, most freezers cannot complete the purge before the complete state change to solid is achieved, and that's why we see whiteish-toped ice cubes. Scott's cubes will have less white and freeze first, marginally.
Thinking further on this, I have the following concern: If Scott draws his water first, it will always be a little warmer than Gavan's, until they both reach the ambient temperature, which is a disadvantage for Scott. At the same time, Scott's water will have out-gassed more air, until they both reach the various atmospheric component's dissolved concentrations characteristic of the room temperature: an advantage for Scott. The out-gassing must lag the temperature rise, as the bubbles take time to rise or crawl up the walls. So, supposing there are imbalances both in temperature and degree of out-gassing: which is faster to freeze, the cooler or the flatter water? While I do not know the answer, I believe the answer is known, and if Scott knows it, it would inform him of whether to draw the first or the second sample.
Edited on April 11, 2022, 10:27 am
a marginal solution
