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How much energy is thermodynamically required to concentrate $CO_2$ from one liter of air? $CO_2$ concentration is 400ppm, or 0.4%. 1l of air is 1/22.4 or 44mMol. From wikipedia, the entropy of mixing is: $\Delta_{mix} S = n R (x_1 ln(x_1) + x_2 ln(x_2))$ where $x_1$ and $x_2$ are the fraction of air and $CO_2$ (0.996 and 0.004) This works out to $9.5e3 J/K$ . At STP, 300K, this means you need only about $2.9 J$ to extract the carbon dioxide. A car driving 1 km emits about 150g carbon dioxide. This is 3.4 moles, which will diffuse into 852 moles of air, or 19e3 liters of air (19 cubic meters). To pull this back out of the air then you'd need at minimum 55.3 kJ. This is not much at all  a car produces 100kW mechanical power, or 100kJ every second, and presumably it takes a minute to drive that 1km. But such perfectly efficient purification is not possible.  
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From the New Yorker, Feb 25:
