That depends on how long you want to sustain the extraction of power. Perhaps you meant to ask how many joules of thermal energy there are in the Earth? Apparen

That depends on how long you want to sustain the extraction of power. Perhaps you meant to ask how many joules of thermal energy there are in the Earth? Apparently about 2*10^31 joules[1]. So at an extraction rate of 1 terawatt (=10^12 joules/second), that would last 2*10^19 seconds = 600 billion years. But the natural rate at which the Earth already loses this thermal energy has been estimated to be about 7 terawatts[2]. This rate would slow down as the Earth cools. On the other hand, the expanding sun may swallow the Earth somewhere in the next 10 billion years, so that should help to keep the Earth warm. [1] https://physics.stackexchange.com/questions/51920/amount-of-thermal-energy-in-the-earth https://physics.stackexchange.com/questions/51920/amount-of-... [2] https://www.sciencedirect.com/science/article/abs/pii/0031920180900497 https://www.sciencedirect.com/science/article/abs/pii/003192...