LightBulb
(photo of "GE reveal 100" filament light bulb goes here)
- No, I don't deploy filament bulbs any more, but they do make dandy test loads for 100 volt electronic power supplies.
- They ARE a better example for what follows (LED light bulbs are much heavier per watt consumed).
This 100 watt incandescent bulb weighs 28 grams, and and consumes 100 watts to produce 1260 lumens (about two watts of photons) and a LOT of heat. From here on, ignore the photon output.
100 watts is 100 joules per second, or 360 KJ per hour, or 8.64 MJ per day.
Earth "escape energy" is the amount of energy needed to lift a mass entirely out of the Earth's gravity well, or launch into solar orbit. That energy is the integral of μ/r² gravity. At the Earth's surface, radius Re=6370 km, μ/Re² = 9.8 m/s² so μ≈4e8 m³/s² .
The integral of μ/r² with respect to r is ... -μ/r. The energy to lift a mass m from Re to infinity is m[ μ/∞ - (-μ/Re) ] = mμ/Re = m Re * μ/Re² = m × g × Re = m × 62 MJ/kg (for m in kilograms).
The energy to lift a 28 gram = 0.028 kg light bulb from the Earth's surface to infinity is 1.8 MJ, about 20% of the energy burned by the bulb in a day.
The energy burned by a 100W light bulb is enough to lift it to infinity 5 times a day ... IF you have a magic 100% efficient levitation mechanism, or a magic launcher. A launch loop comes close to that.
A PERFECT space elevator does BETTER than that, because it torques the Earth a wee bit and slows it down. OTOH, a PERFECT space elevator requires a VAST investment, Unobtanium, and a huge number of rocket launches to move mEarth-manufactured tether into orbit. Also, climbers that must (somehow) gather a lot of lift motor energy from SOMEWHERE. A whole 'nother kettle of flying fish we won't go into here, beyond noting that many in the space elevator community conflate gossamer solar SAILS with rigid arrays of solar CELLS.
The current version of the launch loop involves ultra high efficiency linear motors - I won't argue the numbers here, but most of the losses are resistive "slip", a few meters per second relative to kilometers per second.
Rockets do much worse than that, because >98% of what they move is propellant out of a rocket nozzle, and a lot of empty propellant tank weight near the end of the rocket burn.
More Later ... I need to convert the above into readable prose.