PHYS 3022 Lecture 12 (Wise)

Pressure Integral

What does hydrostatic equilibrium describe?

Gravity is balanced by pressure.

What does mass conservation track in a star?

How enclosed mass changes with radius.

What does an equation of state relate?

Pressure to the physical state and properties of gas.

What is gas pressure microscopically caused by?

Particles transferring momentum through collisions.

What is the pressure integral used for?

Calculating pressure from a particle momentum distribution.

What does particle number density mean?

Number of particles per unit volume.

What distribution is used to derive ideal gas pressure for massive particles?

The Maxwell–Boltzmann velocity distribution.

What is the ideal gas law's conceptual message?

Gas pressure depends on particle density and temperature.

What is mean molecular weight (μ)?

Average mass per gas particle, measured relative to hydrogen mass.

What influences a gas's mean molecular weight?

Its chemical composition and ionization state.

How is a completely neutral gas's particle count characterized?

Atoms contribute particles; there are no free electrons from ionization.

Why does ionization change mean molecular weight?

Free electrons increase the total number of particles.

For an ionized atom, what particles are counted?

Its nucleus/ion and its free electrons.

What is a mass fraction?

The fraction of total gas mass contributed by a species.

What do X, Y, and Z represent in stellar composition?

Mass fractions of hydrogen, helium, and metals, respectively.

What does the metal fraction Z mean in stellar astrophysics?

The mass fraction in elements heavier than helium.

What does the weighted metal-composition average account for?

The relative abundances and atomic weights of metals.

How does ionization generally affect particle number per unit mass?

It increases the number of particles per unit mass.

What is the typical young-star composition used in lecture?

Hydrogen 0.70, helium 0.28, metals 0.02 by mass.

For that young-star example, how do neutral and ionized μ compare?

Neutral μ ≈ 1.3; ionized μ ≈ 0.62.

What is the average kinetic energy per particle in a Maxwellian gas?

It increases in proportion to absolute temperature.

What is radiation pressure associated with?

Momentum carried by photons.

What sets radiation energy density in thermal equilibrium?

Temperature; it scales as the fourth power of temperature.

What are the two contributions to total pressure in the lecture?

Gas pressure and radiation pressure.

Which pressure dominates in the Sun's core example?

Gas pressure; radiation pressure is only about 0.065% of gas pressure.

Why is radiation pressure small in the cited solar-core example?

Its calculated value is much smaller than gas pressure.