A region of the galaxy where new stars are forming-contains a very tenuous gas with 100 atoms/cm^3/cm3. This gas is heated to 7500 K7500K by ultraviolet radiation from nearby stars. What is the Gas Pressure in ATM?

1 Answer
Cosmic Defect
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.

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