How much oxygen would be consumed on a 1 cm squared surface which is on fire?

Question

I'm trying to figure out how much oxygen the Human Torch produces when he is on fire. I figure if I knew how much oxygen on average (per second?) is consumed by a 1 cm squared surface which is producing flame ( rapid combustion) I would then be able to take the average surface area of a human and figure out his oxygen burn rate.

Answer 1

Let's suppose that the Human Torch produces heat by burning methane (maybe he eats a lot of chilli), and suppose he produces a total heat output of 10,000W - I pulled this figure out of the air so feel free to modify it up and down.

The enthalpy of combustion of methane is 882kJ/mol, so, to generate 10,000W, he needs to burn 0.011 moles of methane per second.

The equation for the combustion of methane is:

$$CH_4 + 2O_2 \to CO_2 + 2H_2O$$

so one mole of methane requires 2 moles of oxygen to burn. That means the Human Torch consumes 0.022 moles or 0.7 grams of oxygen per second. The area of skin per human is about 2m$^2$ or 20,000cm$^2$ so the Human Torch consumes about 1.1 x 10$^{-6}$ moles or 3.6 x 10$^{-5}$ grams of oxygen per cm$^2$ per second.

Later:

Let's revisit that power output of 10kW that I guessed at the start of the calculation. maybe it would be better to ask what the Human Torch's surface temperature is, and use this to calculate the power. Assume the Human Torch is a black body. This probably isn't a good approximation at ambient temperatures, but is probably OK when he's really hot. The power output of a black body is given by the Stefan–Boltzmann law:

$$j = \sigma T^4$$

where $\sigma$ is about 5.67 x 10$^{-8}$Js$^{-1}$m$^2$K$^4$. So what temperature would my guess of 10kW correspond to? Taking the area as 2m$^2$ we get:

$$T = \left(\frac{5000}{\sigma}\right)^{-4} = 545K = 272^o C$$

so not that hot really. Good if you want to make a cup of tea, but not great for burning through steel. Suppose the Human torch is really going for it and burns as hot as the surface of the Sun - 6000K to keep it a round number. The power is just:

$$j = 2 \times \sigma \times 6000^4 = 1.5 \times 10^8W$$

Using the working above he now consumes 340 moles or 10.9kg of oxygen per second or about 0.55g per cm$^2$ per second.

So you wouldn't want to be in the same room as him. Not only would you be roasted, you'd be suffocated too!