 
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 .
PV = nRT ! PV = NkT ! P =
N
V
"
#$
%
&' kT =
Nm
V
"
#$
