Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30
PV = NkTwhere P is the gas pressure, V is the volume occupied by the gas, N is the number of gas particles, T is the gas temperature, and k is the Boltzmann Constant. This can be rewritten as
P = nkTwhere I have substituted in n=N/V, which is the number density of gas particles (the number of particles per unit volume). This latter form lets me state the pressure in terms of density and temperature, as done in the notes.
Kelvin's age estimate was based on a calculation of how long it would take for a molten Earth to cool to its present temperature, which gave a range of ages between 24 and 400Myr. Because of the general agreement between the solar contraction age (Helmholtz) and earth cooling age (Kelvin), the initial response of many scientists of the late 19th century was that these two essentially independent estimates being in agreement was confirmation of this age of 20-30Myr for the Sun. Both estimates are flawed (Helmholtz and others didn't know about nuclear fusion as a stellar energy source, and Kelvin's estimates did not take into account then then-unknown additional heating due to natural radioactivity), so their apparent agreement is coincidental. Both estimates were at great odds with even conservative estimates of the age of the Earth being done by geologists, and so were not much accepted outside of physics and astrophysics circles.
3He + 4He -> 7Be + photon 7Be + e- -> 7Li + neutrino 7Li + 1H -> 4He + 4HeNote that the 4He nucleus that enters at the top of the PPII chain exits at the bottom (the net result is production of a new 4He from 4 protons).
3He + 4He -> 7Be + photon 7Be + 1H -> 8B + photon 8B -> 8Be + e+ + neutrino 8Be -> 4He + 4HeAs with PPII, the 4He nucleus that enters at the top of the chain exits at the bottom with a new 4He produced from 4 protons inserted in the previous steps. The so-called "Boron-8 neutrino" produced in the 3rd line above is important for studies of solar neutrino production.
15N + 1H -> 16O + photon 16O + 1H -> 17F + photon 17F -> 17O + e+ + neutrino 17O + 1H -> 14N + 4HeNote that the first step above is an alternative branch of the last step in the main CNO cycle:
15N + 1H -> 12C + 4HeThe 15N proton capture reaction that produces 16O and starts the second subcycle is very rare: it only occurs ~0.04% of the time, or on average once every 2500 reactions. The 14N created by the last step of the second cycle feeds back into the main CNO cycle in the middle. The net result is that over time C and N are slowly turned into 16O, which itself gets transformed into 14N and injected back into the main CNO cycle. Yeah, it is complicated.