Summary: Physics 314 (Survey of Astronomy) Exam 3
Please show all significant steps clearly in all problems.
Please give clear, legible, and reasonably complete (although brief) responses to qualitative questions.
See the last page for values of constants.
1. Jeans' criterion for gravitational collapse
Consider a spherical cloud of gas with temperature T and mass density !m (near the center), and with radius
L . The cloud is composed of a single molecular species with molecular mass m .
(a) (5) Using the ideal gas law, obtain the outward pressure P in this gas (near the center) in terms of T ,
!m , m , and the Boltzmann constant k .
(b) (5) There is also an inward pressure due to the gravitational force on a column of gas of height L and
cross-sectional area A . If the density is approximated as !m for the entire height of this column, what is the
mass of the gas in the column, Mcolumn , in terms of !m , L , and A ?
(c)(5) Now suppose that the gravitational force on the gas in this column is estimated by
Obtain the corresponding estimate for LJ , the minimum size of a cloud that will undergo gravitational
collapse at temperature T , and mass density !m , if the molecular mass is m .
(d) (5) Estimate the value of LJ in light years if the temperature is 4000 K, the mass density is 10!18