I'm currently writing a story, but however I'm having trouble with one part. The hero is faced with a situation where he has to create a fire strong enough melt 5 kg of copper, and he only has a match box, 2 four foot long wooden planks, and 3 boxes of crackers (which have 70 kCal per serving, and there are 16 servings per box). Would setting fire to the crackers be enough to reach these temperatures, with aid from the wood?
The short answer is no.
A more full answer is that the melting point of copper is 1084C. A fire cannot reach this temperature on the air it draws in naturally, you need bellows to force more air in and increase the temperature of combustion.
Also you're going to need a lot more fuel, using the data from Wikipedia (https://en.wikipedia.org/wiki/Copper) We know that molar mass = 63.546 g/mol, heat capacity = 24.440 J/(mol·K), and heat of fusion = 13260 J/mol, and assuming ambient temp it 20C we get: $$ mol = mass/gmol=5000/63.546=78.683 $$ $$ E = (1064*78.683*24.440)+(78.683*13269)=3090130.048J $$ $$ E=3MJ $$ So allowing for inefficiencies in transfer you'd need somewhere in excess of 3 MJ of energy to melt the metal. Since we have no way of knowing the efficiency of this combustion along with the efficiency of the heat transfer without testing under this situation, I'm going to take the the low ballpark efficiency of a fireplace (http://www.engineeringtoolbox.com/combustion-process-efficiency-d_1025.html) and and halve it giving an efficiency of 5%. So given one serve of crackers is 292.88kJ: $$ NumberCrackerServes = 3090/(292.88*0.05)=211 $$ Basically if you were going on crackers alone you'd need about 200+ servings assuming 5% overall efficiency in burn and energy transfer.
If you give your hero some sort of impermeable material like leather and something tubular that won't melt in the heat he would likely be able to fashion some crude bellows. By increasing the airflow you can increase the efficiency. Also have him dig a hole, put the copper in it, then cover it up as much as possible leaving space only for the bellows, being enclosed will reflect some of the heat and increase the efficiency again. Finally give your hero more wood, it's a much better energy source; even better would be charcoal or coal.
Your hero can better try to harvest more wood than wasting those crackers.
Copper melts at 1357 K (1084 C), it has a specific heat of 385 J/kg K and a melting heat of 13.05 kJ/mol. 5 kg of Copper are about 79 mol.
In order to melt 5 Kg of Copper you need:
- warm it up from room temperature (20 C, 293 K) to the melting point. This requires (assuming you have no heat dissipation, which is far from real) $385*5*(1357-293) = 2048 kJ = 2.0 MJ$
- provide the melting heat to have it smelted, which account for additional $79*13.05 = 1035 kJ = 1.0 MJ$, again assuming no heat is dissipated.
Total = $3 083 kJ = 3.1 MJ$
Dry wood has an average heat of combustion of $17 MJ/kg$, which tells you that burning 1/6 kilogram of wood in ideal conditions (perfect oxygenation, no heat loss) you can get roughly that amount of heat.
1 kCal is 4.1 kJ, but your hero can probably make better use of the $70*16*3*4.1 = 13 776 kJ = 13.8 MJ$ provided the crackers, by giving him energy to chop some more wood.
If your hero is MacGyver, have him turn the planks and crackers into a laser. It will be much better at directing heat into the metal.
If your hero is not MacGyver, then no, it won't work. You can try this at home. Build a campfire (with or without crackers) from 2 planks of wood, and put a pot on it. Does it melt? Usually, it will only get hot enough to cook food - i.e. about 200*C.
Others have done the math. This is a no-sell.
But he probably could do it with two bags of grill charcoal and a large clay flowerpot.
To melt mid-melting metals like copper, brass, and silver with natural solid fuel, one needs to contain it somehow (usually in an appropriate clay pot) which will insulate heat, bury the metal in the charcoal, and blow air into it through a hole. The volume of fuel will be much more than that of the metal, and the air blast will need more than lung power. You can find out plenty about flowerpot furnaces on backyard foundry sites.