Maxwell's Demon — the thought experiment where a tiny gatekeeper sorts fast molecules from slow ones, creating a temperature gradient from nothing — is famously forbidden by the Second Law of Thermodynamics. But what if we built a 1-kilometer tower that exploited a real physical sorter: gravity itself? In a tall column of gas, molecules moving upward lose kinetic energy to potential energy. Could a skyscraper-sized atmospheric column generate a usable temperature gradient — and harvest it?

The physics is real but cruel. The dry adiabatic lapse rate for air is g/c_p ≈ 9.8/1005 ≈ 9.75 K/km. A parcel of air rising 1 km cools by about 9.75°C without any heat exchange. So at the top of our tower, air is roughly 10°C colder than at the base. Free temperature difference!

Except — and here's where Maxwell's ghost laughs — this gradient is the equilibrium state. An isolated gas column in gravity reaches isothermal equilibrium (Boltzmann's result), not adiabatic. The lapse rate exists in the real atmosphere only because convection constantly stirs it. You cannot run a heat engine between the top and bottom of a static gas column at equilibrium. If you could, you'd have a perpetual motion machine of the second kind.

But our tower isn't static. The real atmosphere is turbulently mixed, so the 10 K/km gradient is genuinely available. Let's build it.

The design: A 1 km hollow tower, 100 m diameter, open at top and bottom. Inside: a giant heat-pipe loop. Working fluid (ammonia, boiling at ~-33°C) evaporates at the warm base, vapor rises, condenses at the cold top, liquid returns by gravity. The phase-change loop drives turbines.

Back-of-envelope power: Carnot efficiency between T_hot = 293 K (20°C base) and T_cold = 283 K (10°C top) is 1 - 283/293 = 3.4%. Real heat-pipe systems achieve maybe 30% of Carnot, so call it 1%.

Heat flux available equals the mass flow of air × c_p × ΔT. With a 100 m diameter tower and natural draft velocity ~2 m/s:

• Cross-section: π × 50² ≈ 7,850 m²
• Mass flow: 7,850 × 2 × 1.2 = 18,800 kg/s
• Thermal power: 18,800 × 1005 × 10 = 189 MW
• Electrical at 1%: ~1.9 MW

Powers about 1,500 homes. For a 1-kilometer megastructure costing perhaps $5 billion in steel and concrete, that's $2,600 per watt — roughly 1000× worse than rooftop solar.

The deeper problem: we're not really exploiting gravity. We're a clumsy solar updraft tower. The 10 K gradient is maintained by sunlight heating the ground; our "demon" is just stealing convective enthalpy that the atmosphere would dissipate anyway. Remove the sun and the gradient vanishes within hours as conduction equilibrates the column.

The honest version of this idea already exists: solar updraft towers (Manzanares prototype, 1982). They work, badly. The Maxwell's Demon framing was a fantasy — gravity sorts potential energy, not temperature, and the universe charges full price for the conversion.