(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the Sun to be a sphere of hydrogen gas of uniform density equal to its

average density (1440 kg/m3).

a) Integrate the equation of hydrostatic equilibrium for dP/dr from the Sun’s radius to the

core to estimate the central pressure in Pa and in atmospheres. Assume the pressure at the

surface is zero.

Consider a spherical volume of radius 1 meter at the very centre of the Sun. Assume that

this volume contains only H nuclei and enough electrons to keep the volume electrically

neutral at a temperature of 15 million K .

b) What is the number density of atoms and of electrons (free electrons obey the same gas

law as atoms or ionized nuclei!) required to provide enough pressure to match your

estimate of part a)?

c) Now consider that the H in the volume fuses instantly into helium, four H combining

to produce one He, via the mechanisms of the proton-proton chain. Assuming no particles

escape the volume, is the volume still electrically neutral? Why? [Hint: a positron is the

anti-matter version of an electron, and they will annihilate each other on contact, a

process which will occur quickly in the dense core of the Sun]

d) Assuming the final volume can be treated as a collection of He nuclei and electrons

with kinetic energy given by their original temperature plus the energy of fusion (all of

which goes into heat this central volume with no effect on any upper layers), what is the

new temperature of the gas? Assume 0.8% of the mass m of the original hydrogen nuclei

is converted into energy E in the process according to E = mc^2 , and that all positrons have

annihilated.[Hint: The temperature T of a gas is related to its energy per atom E through

E = 3/2kT independent of their mass where k is Boltzmann’s constant.]

e) What is its instantaneous pressure after the conversion?

2. Relevant equations

E = 3/2kT

E = mc^2

the equation of hydrostatic equilibrium

3. The attempt at a solution

my work is very messy, and took 20 mins before I realised I was going in circles. I think I won't actually need to use the ideal gas law 0_o

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# Homework Help: Sun Help

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