D&D has always stipulated that 50 coins equate to 1 pound. But mithral/adamantine do have different wieghts, so we can assume that 50 adam. coins weighs much more than 50 copper coins.
So the whole thing is flawed.
Now, as to Mithral... I've assumed it's just another name for platinum myself...
I don't think it was intended to be any real metal, but its described properties make it closer to Titanium.
Mithral is a very rare silvery, glistening metal that is lighter than iron but just as hard. When worked like steel, it becomes a wonderful material from which to create armor and is occasionally used for other items as well. Most mithral armors are one category lighter than normal for purposes of movement and other limitations. Heavy armors are treated as medium, and medium armors are treated as light, but light armors are still treated as light. Spell failure chances for armors and shields made from mithral are decreased by 10%, maximum Dexterity bonus is increased by 2, and armor check penalties are lessened by 3 (to a minimum of 0).
An item made from mithral weighs half as much as the same item made from other metals. In the case of weapons, this lighter weight does not change a weapon’s size category or the ease with which it can be wielded (whether it is light, one-handed, or two-handed). Items not primarily of metal are not meaningfully affected by being partially made of mithral. (A longsword can be a mithral weapon, while a scythe cannot be.)
Weapons or armors fashioned from mithral are always masterwork items as well; the masterwork cost is included in the prices given below.
Mithral has 30 hit points per inch of thickness and hardness 15.
One other thing to keep in mind is that if there is this mine with tons of mithral here, the huge influx of mithral will cause the market price of it to plummet. IMHO I think the market price of mithral within a region around this mine would actually be lower than gold. However this could vary wildly so you could use this to justify any price lower than normal near the cave.
Is that with or without smoke breaks?In my scenario the Phandelver mine's been running for hundreds of years with skeletal miners. I did the math using the 1e DMG mining table and even if there's just a trace of mithral in the host rock (0.001% if memory serves) it works out to a 60' cube stack of smelted mithral after 500 years of three shifts of 10 skeletons digging.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.