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Which substances exist that are normally liquid and that will not freeze nor boil even at relatively low/high temperatures as compared to the freezing and boiling points of water? Or how can I identify such substances online?
If it is relatively non-reactive, non-toxic, cheap and has high thermal conductivity that is also a bonus!
Gallium melts at 30 °C but doesn't boil until 2200 °C. If 30 °C is a bit too warm to count as "room temperature" or "normally" for you, I found an old paper that recommends tetralkyl silanes such as tetradodecyl silane as lubricants that are liquid over very wide temperatures.
Dowtherm A is a eutectic mixture of biphenyl and diphenyl ether. According to its manufacturer:
These compounds have practically the same vapor pressures, so the mixture can be handled as if it were a single compound. DOWTHERM A fluid may be used in systems employing either liquid phase or vapor phase heating. Its normal application range is 60°F to 750°F (15°C to 400°C), and its pressure range is from atmospheric to 152.5 psig (10.6 bar).
[...]
The viscosity of DOWTHERM A fluid is low and changes only slightly between the melting point of the product and its top operating temperature.
The polar aprotic solvents (for example dimethylformamide, mp −61 °C, bp 153 °C, or hexamethylphosphoramide, mp 7 °C, bp 230–232 °C) would be a place to start. Silicone oil is often used in heating baths – one product in the Aldrich catalog is advertised as having a working range of −40 °C to +230 °C.
A good place for a general list is http://www.engineeringtoolbox.com/melting-boiling-temperatures-d_390.html
For high temperatures, here is a list of alloys https://en.wikipedia.org/wiki/Fusible_alloy Some of these have melting points below 0 °C and boiling points as high as you will ever need. Some are pretty expensive, though. Note that in general mixtures have a lower melting point than pure substances. The mixture whose percentage composition has the lowest melting point is called a Eutectic.
As a pure metal, tin is a good choice as it has low toxicity and a wide range. Hence it is used in the float glass process for window glass. Even though it is not particularly reactive, there is some potential for an explosive reaction of molten tin with water/steam if used in large quantities, partly due to the liberation of hydrogen.
The solar energy industry has used sodium and potassium nitrate (and previously sulfuric acid) but both are corrosive. Additionally, nitrates may be difficult to get hold of outside the agricultural industry in some countries as they are used in making explosives.
Then there are the organics. Silicone oil and Dowtherm A have been mentioned. Neither is particularly good for you. Cooking oil doesn’t have a bad range and is preferable to Diesel from both toxicity and flammability points of view. Among the alcohols, ethanol and methanol are probably too volatile for your use. The glycols (diols) are used as antifreeze additives with water. Ethylene glycol is quite toxic. Propylene glycol is much less toxic. Glycerol (a triol) is also nontoxic and higher boiling than propylene glycol, but it is highly viscous which will negatively impact its heat transfer properties.
It should be remembered that non-toxic organics can decompose into toxic ones, particularly when the heat flux applied to them is too high (as can happen with electric heating elements.)
Fun fact: Propylene glycol is much less toxic than ethylene glycol because the latter is metabolized to oxalic acid, whereas the former is metabolized to lactic acid, one of the most common substances in the body.
Galinstan is a substance similar to mercury in its basic properties, but has a liquid range at atmospheric pressure which is much larger than that of mercury's. It melts at −19 °C and boils at 1300 °C.
At the same time, it also has good thermal conductivity (16 W/(m K)) and is relatively non-toxic and unreactive.
From Wikipedia:
\begin{array}{c|c|c|c} \mathrm{Element} & \text{MP in K} & \text{BP in K} &\Delta T \text{ in K} \\\hline \mathrm{Neptunium} & 917 &4\,273 &3\,356\\ \mathrm{Uranium} & 1\,405 &4\,404 &2\,999\\ \mathrm{Thorium} & 2\,115& 5\,061& 2\,946\\ \mathrm{Cerium} & 1\,068& 3\,716& 2\,648\\ \mathrm{Plutonium} & 913& 3\,501& 2\,589\\ \mathrm{Praseodymium} &1\,208& 3\,793& 2\,585\\ \mathrm{Zirconium}& 2\,128& 4\,682& 2\,554\\ \mathrm{Lanthanum}& 1\,193& 3\,737& 2\,544\\ \mathrm{Protactinium}& 1\,841& 4\,300& 2\,459\\ \mathrm{Tantalum}& 3\,290& 5\,731& 2\,441 \end{array}
And that is just elements (top 10 delta).
