How to increase the temperature of my double boiler?
I have a double boiler that I wish to use to prepare a batch of fudge. The recipe I am using calls for heating to 240°F (=116°C), but a double boiler is limited to the boiling point of the working fluid used, so plain water, boiling at only 100°C, won't work.
I know that one can increase the boiling point of a liquid by dissolving material in it, governed by ?T = Kb m, where Kb is the boiling point elevation coefficient and m is the molal concentration of solute.
Using this, to get the boiling point of water to 116°C requires a ?T=16 K, and Kb = 0.512 K / m, so that would require a 31.25 molal solution. Using NaCl, that would mean about 1.8 kg of salt per kg of water, which is around 5 times as much salt as will even dissolve at all.
What can I do to increase the temperature of my double boiler?
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While I personally appreciate your scientific approach to this, I think this concept is fraught with peril. :)
For the acute application of a double-boiler to fudge: don't. Fudge is sugarwork/candy! Managing the heat and temperature over direct heat is part of the fun and peril of sugarwork in general! logophobe's "why" is on-point. You want to boil-off a fair amount of water in making fudge; indirect heat like a double-boiler probably isn't a good choice for that.
If you're interested in another take on the science of fudge, I recommend the fudge episode of Good Eats.
For the actual question of making a double-boiler work at much higher temperatures: I think you'll want a different (non-water) substrate. But unless you've got something with exactly the right boiling point, it's not going to automatically regulate the temperature any better than direct heat, and that entirely defeats the purpose of a double-boiler. You could try regulating something like vegetable oil at the correct temperature; perhaps there's an electronically-regulated temperature-controlled deep fryer or something that has a temperature setting in the low-100C/200F range, but most frying is in the 175C+/350F+ range.
As an aside: As pertains to Wayfaring's recommendation from comments to use sucrose syrup: Keep in mind that fudge is in fact itself candy / sugarwork at soft ball stage. Unless I misunderstand, I strongly believe that you do not want to use sugar syrup in the bottom vessel of a double-boiler. While clever, this solution will soon exceed the temperature you want to achieve, then in the worst case boil-off all the water and burn. Wayfaring's link is a good one and does contain percentages: sugar temperature chart; another from FAO has a more concise percentage chart by weight. Kb for water is 0.512°C/m ; more here. For any substance in the bottom of a double-boiler, you're going to be boiling-off some of the water, making higher concentration of whatever solute. That is, your boiling point is going to keep creeping up.
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