>violate the second law of thermodynamics This is directionally correct, in that coal emissions sequestration is unlikely to be economical, but with two caveat

>violate the second law of thermodynamics This is directionally correct, in that coal emissions sequestration is unlikely to be economical, but with two caveats: 1) Most coals are not actually pure carbon, they do contain a small percentage of hydrogen. If you don't capture the resulting water vapor† then that gives you some combustion energy for free. 2) If you had to spend energy to split the carbon off CO2 and sequester the carbon, then yes, it would be a pointless round trip. Which is why most "clean coal" schemes just compress the CO2 and sequester it underground. --- †: Water vapor is itself a powerful greenhouse gas, but it varies between 4,000 and 25,000 ppm, so clean coal, which is intended to be a short term stopgap measure operated only for a few decades until the global PV solar infrastructure is built out, shouldn't have time to affect global gas balances.