Well, “invested” seems to be interpreted weirdly by magic. Sunlight is stored in acorns in the form of chemical energy, and the light you could get from a few acorns is about the same amount you’d get by burning them thoroughly (say, in oxygen flux). The effects of Harry’s potion seemed to be much more powerful than that, I’d say of the level of the light absorbed by the entire oak for a year or more.
So it seems like you can get something like “the entire effort” spent to produce something (grow a tree for a year) from just some of the results (nothing indicates they got all or even most acorns from a single tree).
Actually, I don’t find the amount of light released to be far from the mark. Burning several pounds of acorns and converting all the released energy into light would be ridiculous—consider that even at a MJ per kilo, you’re looking at a million watts worth of incandescent bulbs for 50-100 seconds (incandescents are only 1-2% efficient IIRC.)
Actually, you might be right. I was thinking in terms of a pound or so of gasoline deflagrating, which would be bright if it happened really quickly but doesn’t seem blinding when stretched over more than ten seconds (intuitions based on fires and movie explosions being much brighter than the real stuff). But I was ignoring the spectral focus and the lack of kinetic energy released.
Lets’s see: Wikipedia gives wood (red oak!) 14.89 MJ per kilogram. Spent over 60 seconds (the Chaos-Dragon battle is said to have lasted “a lot longer” than “very quickly”) that would generate 248 kW.
Direct sunlight is quoted at reaching 130,000 lux, but even with an albedo near 1 (conservativ, snow reaches .9) that’s not bright enough to make you unable to see by shielding your eyes with an arm (based on recent experience of noon sun while skiing). So I’d guess the cauldrons would have to generate more than 1M lux for the effects described (maybe significantly more, brightness is nonlinear).
Assuming conservatively that the illuminated surfaces in a battle to be a square at least twenty meters on the side, that’s 400 square meters and 400M lumens. With pure green light (the brightest kind) you get 683 lumens/W. But the cauldrons gave everything except green, so let’s say 400 lumens per W.
So you’d need about 1MW of power to light a square of snow 20m on the side to ten times brightest daylight during one minute, or about four kilograms of red oak.
Given that the illuminated area is probably much larger (including light lost to the sky), it’s surface has much lower albedo (grass: .25, bare soil: .17, deciduous trees: .15 to .18), acorns probably take more than a gallon per four kilos (and I doubt they had time to gather ten kilos of acorns for both cauldrons), and that the quoted figures for oak involve burning with oxygen, I’d say that the energy in the acorns themselves falls short by at least an order of magnitude.
But then again my errors are likely more than an order of magnitude, and we’re talking magic here, so it’s surprisingly close.
Well, “invested” seems to be interpreted weirdly by magic. Sunlight is stored in acorns in the form of chemical energy, and the light you could get from a few acorns is about the same amount you’d get by burning them thoroughly (say, in oxygen flux). The effects of Harry’s potion seemed to be much more powerful than that, I’d say of the level of the light absorbed by the entire oak for a year or more.
So it seems like you can get something like “the entire effort” spent to produce something (grow a tree for a year) from just some of the results (nothing indicates they got all or even most acorns from a single tree).
Actually, I don’t find the amount of light released to be far from the mark. Burning several pounds of acorns and converting all the released energy into light would be ridiculous—consider that even at a MJ per kilo, you’re looking at a million watts worth of incandescent bulbs for 50-100 seconds (incandescents are only 1-2% efficient IIRC.)
Actually, you might be right. I was thinking in terms of a pound or so of gasoline deflagrating, which would be bright if it happened really quickly but doesn’t seem blinding when stretched over more than ten seconds (intuitions based on fires and movie explosions being much brighter than the real stuff). But I was ignoring the spectral focus and the lack of kinetic energy released.
Lets’s see: Wikipedia gives wood (red oak!) 14.89 MJ per kilogram. Spent over 60 seconds (the Chaos-Dragon battle is said to have lasted “a lot longer” than “very quickly”) that would generate 248 kW.
Direct sunlight is quoted at reaching 130,000 lux, but even with an albedo near 1 (conservativ, snow reaches .9) that’s not bright enough to make you unable to see by shielding your eyes with an arm (based on recent experience of noon sun while skiing). So I’d guess the cauldrons would have to generate more than 1M lux for the effects described (maybe significantly more, brightness is nonlinear).
Assuming conservatively that the illuminated surfaces in a battle to be a square at least twenty meters on the side, that’s 400 square meters and 400M lumens. With pure green light (the brightest kind) you get 683 lumens/W. But the cauldrons gave everything except green, so let’s say 400 lumens per W.
So you’d need about 1MW of power to light a square of snow 20m on the side to ten times brightest daylight during one minute, or about four kilograms of red oak.
Given that the illuminated area is probably much larger (including light lost to the sky), it’s surface has much lower albedo (grass: .25, bare soil: .17, deciduous trees: .15 to .18), acorns probably take more than a gallon per four kilos (and I doubt they had time to gather ten kilos of acorns for both cauldrons), and that the quoted figures for oak involve burning with oxygen, I’d say that the energy in the acorns themselves falls short by at least an order of magnitude.
But then again my errors are likely more than an order of magnitude, and we’re talking magic here, so it’s surprisingly close.
(See http://en.wikipedia.org/wiki/Wood_fuel#Energy_content http://en.wikipedia.org/wiki/Lux http://en.wikipedia.org/wiki/Albedo for the numbers.)
Damn, I think I just killed a catgirl.