To give some more detail: hydrogen to helium fusion (even with intermediate steps) is extremely unlikely to happen. That's part of why the sun will last for billions of years. And that's also why first human attempts at fusion are not trying to use straight up hydrogen as the fuel.
Good old Wikipedia has this gem:
> The large power output of the Sun is mainly due to the huge size and density of its core (compared to Earth and objects on Earth), with only a fairly small amount of power being generated per cubic metre. Theoretical models of the Sun's interior indicate a maximum power density, or energy production, of approximately 276.5 watts per cubic metre at the center of the core,[63] which is about the same power density inside a compost pile.
Another fun fact: there's a decades old design for a gadget that fits at the top of your desk and does nuclear fusion. You could build one yourself, if you are sufficiently dedicated. Unfortunately, no one has ever worked out how to run one of them as a power plant. Ie how to get more useful energy out than you have to put in.
If it produced a quarter of the heat of the human body per volume, its temperature would be lower as well (less than 37 degrees Celsius).[1] This is obviously not the case.
[1] Obviously heat and temperature are not the same, I know that. But when something’s temperature is higher than another thing’s, then heat is exchanged along that gradient. Meaning if the sun produced less volumetric heat than the human body, a human body placed within the sun would warm the sun and cool the human.
For both the sun and a human on earth there are two processes going on:
1. Heat production per unit volume.
2. Heat loss per unit surface area.
The volume to surface area ratio for the sun is much larger than for the human, for a minor reason (the sun is a sphere) and a major reason (the sun's linear size is much bigger). So the equilibrium temperature of the sun in the same ambient outside environment is higher than the human's.
Your thought experiment about placing a human inside the sun would in fact work as you say, if a human body continued to produce heat once it had achieved thermal equilibrium with the surrounding plasma.
Yeah, this is a morbid analogy but if you got a bunch of people enclosed in a small area, the people in the middle will get so hot they will heatstroke, even if it's freezing outside. See the recent Korean crushing disaster.
Don't give them ideas, harnessing people power would solve all the major problems. Overpopulation, global warming, energy crisis,... Reminds me of that 'Mitchell and Webb - Kill all the poor' sketch.
Well, plant the idea that there is a fusion reaction going on in mitochondria at a very low scale. Throw in terms like "proton gradient", "electron transport chain" and create a science conspiracy.
Can you say more about the ways in which fusion reactors need to surpass stars, and why people believe it's feasible that we can sufficiently get to that point?
(Also - thanks for sharing one of the most interesting comments I've read on the internet in quite a while.)
That, but also mimicing the pressure of the sun here is just not possible (yet? :D), why we need to play with higher temperaturs with different problematic consequences.
> The highest instantaneous pressures we can obtain here on Earth are in the Fusion reactor at the National Ignition Facility and in Thermonuclear weapon detonations. These achieve pressures of 5 x 10^12 and 6.5 x 10^15 Pascal respectively. For comparison, the pressure inside our Sun’s core is 2.5 x 10^16 Pascal.
Total power radiated by a black body per unit surface area scales as T^4 (in Kelvin).
So for black bodies with identical shape and linear dimensions R1 and R2, with identical power production per unit volume, both in thermal equilibrium with whatever is outside them, you would expect:
R1/R2 = (T1/T2)^4
(because setting power produced equal to power radiated gives R proportional to T^4).
Pretending humans are spheres with radius 1m and the sun is a sphere with radius 7*10^8m, you would expect the sun to have ~160 times the temperature of a human at equilibrium in vacuum. It's going to be lower because not all of the sun is power-producing, of course. But higher because a human is not 1m in radius. And again higher because humans are not spheres and lose heat more than a sphere would for the same volume (more surface area).
The sun is about 6000K on the surface. That would give us ~40K for the equilibrium temperature of a human in vacuum, which at least seems truthy.
TL;DR: the sun is big, with a small surface area compared to its volume, because it's big.
The sun actually has very little fusion per cubic metre or per kg.
Per volume the core of the sun produces only a quarter of the heat of the human body (and per kg it's even less, owing to high density).
That's why our fusion reactors can't just mimic stars, they have to far surpass them to be useful to us.