 
Summary: ASTR 3830: Problem Set 7
(due in class Wednesday April 11th)
1. Assume that gas in a cluster of galaxies is distributed spherically symmetrically, with
density (r) at distance r from the center. The pressure of the gas is given by the ideal gas
law,
!
P =
"kT
µmH
where µ is the mean molecular weight (assume this to be constant), mH is the mass of a
hydrogen atom, and k is Boltzmann's constant. If the mass interior to radius r is M(r),
show that the combination of the ideal gas law with the equation for hydrostatic
equilibrium gives,
!
M(r) = "
kTr
µmHG
dln#
dlnr
+
