ASTR 498N            Homework #3               due in class Th 28 Feb

 

R   Please read O&C Ch. 9, Sec. 2 and Ch. 10, Secs. 3 and 4.

 

P    Estimate the central temperature of a star in which the dominant source of hydrostatic support is radiation pressure.  Is radiation pressure more important for high or low-mass stars?

 

P    Calculate the Jeans mass for interstellar neutral hydrogen characterized by  T = 100 K and ρ  = 10^–19 kg m^–3, and also for a cloud of molecular hydrogen characterized by  T = 20 K and ρ  = 10^–22 kg m^–3.  Comparing these Jeans mass with the typical masses of stars, speculate on how star-sized condensations form.

 

P    Define the interface between a stellar core and its envelope as the surface across which the chemical composition changes.  In equilibrium, pressure and temperature will be constant across this surface.  Show that a density discontinuity must result.  If the core is pure He and the envelope pure H, by what fraction must the density change?

 

P    Consider a particle near the center of the Sun.  Compare its kinetic energy with its Coulomb interaction energy (O&C §5.3) with the typical nearest particle.  Is gas at the center of the Sun a perfect gas to good approximation?

 

P    Show that P_gas = 2 u_gas / 3 for a perfect gas of non-relativistic particles and P_gas = u_gas / 3 for ultra-relativistic particles, where u_gas is the kinetic energy density.

 

P    Use the normalization condition  to derive an expression for the chemical potential ψ  of a classical gas of non-relativistic particles and show that the condition for a classical gas demands that the average separation of gas particles is large compared with their typical de Broglie wavelength.

P  O&C  problems:

9.11
10.4, 10.5