Too Busy For Words - the PaulWay Blog

Wed 28th Mar, 2007

Warm water evades freezing

A little science problem came up today, and I post this in the hopes that either by talking about it I'll come up with the solution or that someone reading it will know the answer.

You see, in the lab we have an old tap system suitable for laboratories: it has four taps and three outlets - one hot and one cold tap have separate outlets with those 'serrated' nozzles suitable for attaching rubber tubing to, and the other two taps combine to control a central 'washing' water outlet. It's somewhat of an antique, especially so because they don't make them any more and you can't get the parts for them (or so the department technicians say, and who am I to argue?). So when the hot 'combined' tap stopped turning off completely and started jumping its threads (so that when you got it nearly off it would then jump down a level and allow a good stream of water again, quite the opposite of what clockwise turning is intended to do) this is an engineering problem of the first order.

For weeks we've been plagued with it dripping in the background. I can mostly drown it out with headphones (the lab's small enough that I can afford this cone-of-silence approach), but the others' sanity has been suffering. Finally, today a guy with a serious box of tools arrived and immediately started the task of working out where the 'off' tap was to the supply. This, too, was a harder task than one might think.

It turned out that the pipes wended their wily way through the innards of the building in such a manner as to completely elude the plumber. After watching him drag the ladder around our room and the adjacent corridors for some time, I found myself thinking of a trick that I'd heard plumbers use when they want to attach a new pipe or work on an existing fitting where a tap doesn't exist - say, between your house tap and the mains water supply. They dig a pit around the pipe 'upstream' of where they want to work, and fill it with liquid nitrogen. The water inside freezes solid, a state they can easily maintain until they've finished, and then they simply let it melt and the water's on again. No mess, no fuss.

I suggested this to the plumber, and he knew the trick, but he claimed that it was impossible to do on this line because the water was running. Anything above a very slow drip, he vouchsafed, would prevent the water from freezing up, especially as this was the 'hot' line. So they shut the hot water to the entire building off while they worked on our plumbing, having salvaged another replacement tap from Trellis knows where, and it now shuts off correctly, albeit with a fair amount of twisting that implies that this one, too, will fail in its own time.

However, this 'flowing water' excuse has puzzled me mightily since then. Liquid nitrogen boils at -195°C - more than enough to freeze the carbon dioxide in the air, let alone the water in the pipe. The only reason I can think up for the plumber's explanation is that liquid nitrogen is essentially working in a very hot environment - like trying to cool down molten iron with water - and that the amount of heat it absorbs in its boiling and heating up to our temperature isn't enough to cool the water down that much.

Water has a specific heat capacity of 4184 Joules per Kilogram Kelvin - in other words, one litre of water absorbs 4184 Joules to go up by one degree Centigrade. I don't have any data for the specific heat capacity of liquid nitrogen, but nitrogen gas has a specific energy of 29.124 Joules per Mole Kelvin which, at a molar weight of 28 grams per Mole for N2 works out to around 1.04 Joules per gram Kelvin or 1040.1 Joules per Kilogram Kelvin. And that's just to get a one kelvin degree change.

The water has to go from 25°C to 0°C. Thanks to metric measures, there's twenty millilitres of water in a pipe one centimetre in cross-sectional area and twenty centimetres long, which is slightly larger than normal (it'd be 1.13 centimeters in diameter). So, for twenty grams of water to freeze from room temperature requires 2092 Joules to be taken out of it, and that would be done by 10 grams of nitrogen going from -195°C to 0°C. Liquid nitrogen has a density of 0.807 g/ml means I'd need about 12 millilitres. Even if we assume that only one percent of the nitrogen absorbs heat from the water, it's still only about 1.2 litres of liquid nitrogen. Hardly a problem.

So the only other reason that I can think of is that ice is an insulator, and it becomes less dense as it freezes, so that might stop the water in the middle of the pipe from being frozen. But I can't really believe it's that good an insulator. Pykrete, maybe, ice by itself, no.

Please email me if you know the answer to this puzzle.

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