# 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?

Mar 9, 2016

$P = \left(\frac{N}{V}\right) {k}_{B} T = 1.0252 \setminus \times {10}^{30} \setminus \quad A t m s$.

#### Explanation:

Ideal Gas Equation of State: $P V = N {k}_{B} T$

$P$ - gas pressure in Pascals ($P a$),
$V$ - gas volume in cubic meters (${m}^{3}$),
$N$ - Number of atoms/molecules,
$T$ - gas temperature in Kelvins ($K$),
${k}_{B} = 1.3806 \setminus \times {10}^{23} \setminus \quad \frac{J}{K}$

Rearrange the equation and write it as follows :

$P = \left(\frac{N}{V}\right) {k}_{B} T$

$\left(\frac{N}{V}\right) = 100 \setminus \quad c {m}^{- 3} = {10}^{8} \setminus \quad {m}^{3}$
$P = \left({10}^{8} \setminus \quad {m}^{- 3}\right) \left(1.3806 \setminus \times {10}^{23} \setminus \quad \frac{J}{K}\right) \left(7500 \setminus \quad K\right)$
$\setminus q \quad = 1.035 \setminus \times {10}^{35} \setminus \quad P a$

$1 \setminus \quad A t m s = 101 \setminus \quad k P a = 1.01 \setminus \times {10}^{5} \setminus \quad P a$

$P = 1.035 \setminus \times {10}^{35} \setminus \quad P a = 1.0252 \setminus \times {10}^{30} \setminus \quad A t m s$.