A region of the galaxy where new stars are forming-contains a very tenuous gas with 100 atoms#/cm^3#. This gas is heated to #7500 K# by ultraviolet radiation from nearby stars. What is the Gas Pressure in ATM?

1 Answer
Mar 9, 2016

#P=(N/V)k_BT = 1.0252\times10^{30}\quad Atms#.

Explanation:

Ideal Gas Equation of State: #PV = Nk_BT#

#P# - gas pressure in Pascals (#Pa#),
#V# - gas volume in cubic meters (#m^3#),
#N# - Number of atoms/molecules,
#T# - gas temperature in Kelvins (#K#),
#k_B=1.3806\times10^{23}\quad J/K#

Rearrange the equation and write it as follows :

#P = (N/V)k_BT#

#(N/V) = 100\quad cm^{-3} = 10^8 \quad m^3#
#P = (10^8\quad m^{-3})(1.3806\times10^{23}\quadJ/K)(7500\quad K)#
#\qquad = 1.035\times10^{35} \quad Pa#

#1 \quad Atms = 101 \quad kPa = 1.01\times10^5\quad Pa#

#P = 1.035\times10^{35}\quad Pa = 1.0252\times10^{30} \quad Atms#.