even better use a ordinary electric furnace.
I agree. The main issue with doing it this way is that, assuming the crucible is made of pure graphite, there's no way it could possibly produce enough resistance. Graphite is a pretty good conductor.
I have no idea how the guy in the video managed to melt aluminium, perhaps he faked it. I did some rough calculations: based on a crucible with a 2cmx2cmx2cm cube-shaped interior giving a volume of 8cm^3 (which would fit 100g of gold with about 7mm height left at the top) the resistance from one side to the other, or from top to bottom, would be in the order of less than a milliohm, when empty. To achieve even 0.5ohm you'd need walls thinner than paper. And it gets even worse when you fill it with gold, a highly efficient conductor of current!
Perhaps if it were some kind of highly resistive graphite clay...
Or, as you say, simply use a long thin heating coil wrapped many times around a non-conductive crucible, with lots of insulation. Trying to reinvent the wheel is fun but alas there's always a reason why it hasn't been done before.
@Amol Gupta :
Here are some of the calculations I started on but I abandoned them when I started calculating the resistance of the crucible and realized it wouldn't work. Maybe you will find something useful here for your calculations since I spent time on it:
Using the UK supply for example purposes- we have 240V supply and for the sake of argument we can assume it's fused at 13A as per normal (it's possible to get up to 16A if you wire in directly but that's illegal unless you're an electrician).
Example:
Supply is 240V and can give max 13A
Assume a starting temperature of 20degrees Celcius
Gold melts at 1064 degrees Celcius
So our gold will need to be heated by 1044 degrees to reach melting point ("deltaT")
Gold has a specific heat capacity of 129 J/kg ("c")
Gold has a latent heat of fusion of 64500J/mol ("L")
We want to heat and melt 100g
so the mass of our gold =0.1kg ("m")
Gold has an atomic mass of 197g/mol
so the molar mass of our gold is 100/197 = 0.5076mol ("Moles")
Gold has a density of 19320kg/m^3
so the volume of our 100g of gold = 0.1 / 19320
= 5.18 x 10^6 m^3
= 5.18cm3 ("Vol")
Calculating the energy requirement:
Heating the gold to melting point:
Energy required = Mass x Specific heat capacity x Change in temperature
Q(heating) = m x c x deltaT
= 0.1 x 129 x (1064 - 20)
= 13442J
Melting the gold:
Energy required = Molar mass x Latent heat of fusion
Q(melting) = Moles x L
= 0.5076 x 64500
=32740.2J
Total energy requirement = Q(heating) + Q(melting)
=46182.2J
Resistance of crucible:
Abandoned