I just ran into this recently. Drat. My memory is no good these days.

Say a candle is about a watt and burns for 2 hours. Okay, I'll look it up! 80W. Wow; I was off by almost a magnitude.

Anyhoo, that means we are putting 80,000 kW out.

Typical sizing for a room heater is 10W/ square foot. Garage heater gets up to 5,000 W. This is quite a bit lower than our million candles!

But brings up the question; how big is the room? Model a candle as a rectangular solid 1" x 1" by 6" long or 6 CU. 6 million CU is 42,000 square feet. That's about the size of a Wallmart store, or a typical warehouse. Not including space for air circulation!

But let's assume that somehow, through some TARDIS-like trick of candle-ry, we've got them all crammed into a typical room of 150 square feet. And putting out the same power as a Eurorail locomotive hauling a train across the Swiss Alps! (Or, about 1/10 the typical output of a municipal power plant).

The rule of thumb for heating air at standard conditions is 0.0012 joules per cm^3 per degree Celsius. Or 32 joules to raise the temperature of one square foot by 1 degree.

We have 150 square feet of room air, but 80 megajoules every second being output by those million candles. All else being equal (which it very much is NOT) you'd raise the temperature of the air 16,000 degrees every second.

Fortunately heat only flows from hot to cool, so when equilibrium is reached between the air and room contents, and the candles, assuming the chemistry of a candle still works at an extremely high ambient temperature (NOT a good assumption), we could be at 1,400 C. (2,500 F, for those that don't speak Continental).

Which means, theoretically, within the burning time of those million candles the local temperature would be over the melting point of steel.



However, Randal Munroe style, I'm more intrigued by the ventilation problem.

A candle burns at .1 gm/minute. Assume that for this to happen, it has to combine with an equal mass of atmospheric oxygen, and as a candle will go out when the partial pressure drops to 8%, we need to supply roughly twice that volume as replacement.

Dry air has a density of about a kilogram per square meter. If I didn't just slip a decimal place, we need to move 16 kg or 16 square meters per second. Usual rating of fans is in CFM; we get 34,000 CFM when we convert.

Which is about the flow rate of this fan: [link to www.industrialfansdirect.com]

Those a five FOOT long fan blades, by the by. So you've got one of those things going full-out in the room with you and the candles.