Imagine a giant dry-cleaner’s bag full of air at a tem- perature of −35°C floating like a balloon with a string hanging from it 10 km above the ground. Estimate what its temperature would be if you were able to yank it sud- denly back to Earth’s surface.

You are making beer. the first step is filling the glass carboy with the liquid wort. the internal diameter of the carboy is 15 in., and you wish to fill it up to a depth of 2 ft. if your wort is drawn from the kettle using a siphon process that flows at 3 gpm, how long will it take to fill?