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Interesting problem ... basic engineering solution
1256 Posts
So, today's engineering problem goes like this.

Someone in our family is dying their hair. The chemical (probably a Chromate-based hair dye) must be mixed with 180 ml of water at between 40 and 50 °C - if the temperature is too low, mixing is very difficult, too high and the compound breaks down, and perhaps you might not get the hair colour you need.

Simples ... except we have no thermometer.

How was this quick and easy to resolve?

11 Replies
Simon Barker
769 Posts
Get some ice cubes from the freezer and put them into a measuring jug.  Make up to 90ml with cold water.  Stir until the ice cubes are more-or-less melted.  Boil up the kettle and add another 90ml boiling water.
1256 Posts
I'm not sure that would work with the volumes you stated, as I'm pretty sure the ice is not at 0 °C when it melts. So I think I'd be going for about 45 °C.

The real answer is a little easier, but still uses the rule for mixing volumes of liquid at different temperatures.

And the first step is the Engineering bit. Assume tap water is 10 °C +/- 5 °C (not a bad guess, given here it's been 10 °C or so for a few days and nights now).

Aim for 45 °C by ratio of volume (just in case our assumption is a couple of degrees out either way - another bit of Engineering):
  • 110 ml of cold tap water, and
  • 70 ml of water straight out of the kettle, that we know is 100 °C to about a degree or so
2663 Posts
at the moment the last ice cube melts the water and the ice are both at 0C, assuming well mixed and 1 atm pressure.

Another method would be to note that lard turns from solid to liquid over the same range, and a spot of that could be used as a gauge. (beef dripping  and suet are a few degrees higher, what you have to hand will depend on your kitchen)
(animal fats being a blend there is an all solid temp, say 35 degrees, and an all clearly liquid temp, say 45 degrees, and a slushy region in between)
I presume the hair dye is not for the engineer ?
1256 Posts
Agreed ... perhaps takes a lot of watching to get the point where the ice melts.

If the engineer is me, the hair dye would have to travel back in time to be useful ... perhaps another project.

Another bit of Engineering though - the test before mixing - "Feels warm" is just above body temperature, "feels hot, but doesn't burn" is probably less than 50 deg C.
18 Posts
I seem to have been doing this sort of thing wrongly for months.

To be clear I have no experience of hair dye.
Since the beginning of the pandemic emergency, I have been washing cloth facemasks after use by mixing certain approximate volumes of cold tap water and freshly boiled water to realise the optimum soapy water temperature (between 40°C & 60°C) that should kill germs without affecting the mask's stated operational lifespan.
All this time I had been assuming that my tap water was slightly colder than 20ºC, perhaps 17°C or 15°C and choosing the roughly measured water volumes accordingly.
Now that I have seen GKenyon's second post above, I realise that my cold tap water must nearer to 10°C so I've just reconsidered my rough and ready mental arithmetic of how many cups (physical rather than the Imperial measure).

Coming back to the actual hair dye problem, how critical is the temperature accuracy? Do hairdressers use thermometers for this purpose, or do they just guesstimate based on their experience?
1256 Posts
I don't think the tap water in the summer months would have been 10 degrees C, I think you're correct at 15 degrees C, certainly up to a few weeks ago ... of course the temperature when you first turn on the tap may well be warmer unless someone has just used a quantity of water in the premises.

When I did the calculation, I actually did separate sheet for cold winter (5 degrees), late autumn / early spring at 10 degrees, 15 degrees for the majority of warmer months, and 20 for the periods when it's consistently baking for a few days.

I never bothered checking too closely on how critical the temperature was - following the manufacturer's instructions for the temperature range required.

The idea of this post, was to illustrate some engineering principles, the sorts of things we do on a day-to-day basis at work to make things happen in novel ways due to constraints, and the basic difference between science and engineering being we're used to working with tolerances and unknowns, and fashioning these to bring the result in the acceptable range.
I can confirm Graham's thoughts about the cold water temperature in summer.

I had similar problems developing films (if anyone remembers cameras that don't plug into the computer or make phone calls.....) as the temperature of the chemicals for developing them had to be 20 degrees Celsius. If mixed and they were too warm it was a b***** to wait until they cooled down so the proportions of water from the cold and the hot tap were critical. The cold could be anywhere between about 5-10 degrees in winter (cold water tank in the attic still got that cold in winter despite the central heating in the main house) to very close to 20 degrees in the summer when adding any hot water could put the temperature too high.
2663 Posts
Ah wet film - I was trying to explain it to my kids and getting blank looks of the 'why would anyone do that ?' kind.
(to be fair most of what I did was black and white for PCB artworks, so large sheets of fine grain slow film, and red light safe, not photos to print - mostly I trusted that to the chemists shop in town  - i suspect the fact you can see it develop makes the temperature thing less critical for red light safe film.)
Then we talked through the steps to make an IC,  and how many levels of photo-resist , masking, re-alignment and exposure that involves -  wet photography of a kind is actually very much alive and well in the age of the 'chip, its just got smaller, and in some cases the 'light' has gone very short wavelength  .
18 Posts
I found your post to be a fun puzzle, and appreciate the useful educational motivation behind it, not least the distinction between how what we do in engineering differs from 'mere' science. (I shall now duck to avoid brickbats from any passing scientists.)
I agree with what you and Alasdair say about cold tap water temperatures. My lazy assumption of something like 15°C-17°C in my laundry arithmetic was inspired by the common assumption of 290K for ambient thermal temperature when doing noise calculations in radio work.

Aladair and Mapj,
I have to admit that I still use a 135 film camera and don't have a digital one yet, apart from an old smartphone - much to the perplexed hilarity of most people, but I've never tried developing film.
A much more relevant issue at the moment is mixing the water ready to fill one's hot water bottle! Can't have the heating on too often!

The Trick's us use the 'cup' markers on the side of the kettle...
Denis McMahon
301 Posts
I would not make assumptions about the temperature of tap water. I would suggest toss some ice cubes into a little water and leave in the fridge (not freezer) for a few hours. Then take off 90 ml of water from here, and add 90 ml of boiling water from the kettle. The result should be near enough 50 °C. Mix the dye before the mixture has had time to cool much.

Don't get any ice into the mixture, or the latent heat required to melt the ice will mess up the figures.


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