Question

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?

Answer 1

`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`.