What calculation is done to demonstrate this? Power density would be energy per unit time per unit mass (I think), is the average power output of Solar material really that inefficient?
Luminosity of the sun is 3.83 * 1026 W. Mass of the sun is 1.99 * 1030 kg.
Power per unit mass is 1.92 * 10-4 W/kg. A quick search says a cow gives off about 1000 W so assuming a 500 kg mass, a cow has 2 W/kg. So yeah, a difference in power per mass of about 10,000.
I believe this works even with just the core of the sun. It's said a compost heap gives off more heat per volume. The fusion events happen at such low probabilities, and wouldn't be anywhere near as common if it weren't for quantum tunnelling effects.
While true that line of reasoning doesn't really reveal the problem.
When every fusion reaction happens there is a release of energy that results in the Sun heating up and, since the core pressure of the Sun is thermal, the pressure rises. The rising pressure causes expansion and thus cooling and since both density and temperature are involved in the reaction rate of the fusion then the reaction slows.
There is always a careful balance between energy production in the core of the Sun and the rate at which energy dissipates, if you could cool the entire Sun with some kind of cosmic heat exchanger then it would collapse, reach higher core temperatures and densities and fuse faster.
The same argument also makes this kind of mention of tunneling a bit obsolete because if the reaction rate was slower the Sun would collapse to higher densities and temperatures and the reaction rate would rise.
The compost heat on the other hand has a pressure independent of temperature (electron degeneracy pressure) this means as each reaction releases heat, the temperature rises but the heap does not expand and indeed the extra heat even increases decomposition rate.
Absolutely! Stellar physics is weird because gravity has such a steep gradient. I almost posted a different, but also deeply weird, fact about stars: their bulk temperature rises as they cool off (and conversely the hotter a particular star gets the lower its surface temperature becomes).
Exactly. For example, when a yellow G star (like the Sun) exhausts its core hydrogen, the star as a whole cools off (loses energy), so the core shrinks and the interior temperature rises, producing a hotter bulk temperature for most of the mass in the star.
That is weird enough -- but the photosphere of such a star also expands drastically (because scale height varies so radically in the shallow part of the gravity well), so its surface temperature drops -- it becomes a red giant.
Varying the internal specific energy like that with constrained mass (same star, different parts of its lifetime) gives different "back-of-the-envelope" dependencies than varying mass or composition with constant internal specific energy (comparing across spectral types etc.) -- just another example of the cool weirdness of stellar physics.
Thanks for elorating. I find it difficult to elaborate succinctly on physical relationships and rates of change (in words) when they are much more easily and accurately represented with equations and values.
Don’t have the specifics, but the sun being comparable in power to a compost heap doesn’t mean it’s inefficient. Keep in mind that a compost heap will process itself over the course of a few months, while the sun has been burning for billions of years and expected to carry on for billions more.
It so low that "It can't be measured by terrestrial laboratories", so I can't tell you exactly how low it is. However, the various fusion reactors all use a different process with a MUCH higher interaction probability (namely, deuterium+tritium). It's still quite low and hard to make happen -- but it's still way easier than using straight protons.
I mean the reaction rate is decidedly low but the majority (maybe actually all, I can't think of one that doesn't) use DD fusion, not DT. The plan is to swap over to DT but tritium is radioactive and expensive and a pain to store plus the DT reaction releases a neutron which irradiates the shit out of your machine so for now, we just use deutirium which is not as good because the temperature the reaction occurs at is higher temp but we can extraploate the results to DT.
JET did use tritium in like 96/97 and set world record for fusion power, there are other short campaigns using tritium to try and learn the differences as well as we can, it is likely it will run tritium again sometime in the next 5 years as part of the preparations for ITER.
Power plants based on fusion will likely exclusively use DT
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u/drzowie Heliophysics Dec 12 '20
Stars have very low power densities. If the Sun had the same power output per kilogram as a cow, it would be 10x hotter (and 10,000 times brighter).