Visited on a chilly day in December, the area around the top of the mine, the “collar” in mining terms, doesn’t look inviting. Steam clouds pour from the mouth of No. 9. It’s the hot air being drawn from the cave dug at the bottom of No. 10. That far down, rocks formed billions of years ago still carry heat from the molten core of the earth. Without the elaborate refrigeration system that pumps chilled air down No. 10, the bottom of the mine would be 180F, far too hot for a human to withstand. ... a venture between the two largest mining companies in the world, Rio Tinto and BHP Billiton. Together they’ve spent more than $1 billion, including $350 million sinking the No. 10 mine shaft, in hopes of tapping nearly 2 billion metric tons of ore. Less than 2 percent of it is believed to be copper. It might not sound like much, but that’s considered dense, making it the fourth-largest undeveloped copper deposit in the world. ... Resolution Copper plans to dig four more shafts over the next 15 years. At peak production, this will be the biggest copper mine in the U.S., producing 100,000 tons of rock a day, and enough copper to meet a quarter of the country’s demand. It could also end up being a financial problem for its owners. The price of copper, along with lots of other commodities, has crashed as China’s economy has slowed. The Resolution mine is essentially an enormous bet that the third-most-used metal in the world is oversold and that prices will rebound by the time the mine opens in several years. ... Steaming hot water pours off the rocks; during construction, workers bored into an ancient lake trapped thousands of feet underground by impermeable rock, and it’s leaking into the mine. It’s like standing in a tropical rainstorm. A digital hydrometer on the wall registers 100 percent humidity. Overhead, cooled air gushes out of a metal duct, blowing the rain sideways and keeping the temperature in the mid-70s.