# A nebula's a region of the galaxy where new stars are forming contains a very tenuous gas with 128 a t o m s/cm^3. This gas is heated to 7459 K by ultraviolet radiation from nearby stars. What is the gas pressure?

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May 26, 2016

Pressure = $1.318 \setminus \times {10}^{- 11} \text{ Pa}$.

Use the Ieal Gas Law to get this answer.

#### Explanation:

For this purpose we render the Ideal Gas Law on an atomic basis instead of the usual molar basis:

(Pressure)$\setminus \times$(Volume)
= (Boltzmann's constant)$\setminus \times$(No. of atoms)$\setminus \times$(Absolute temprerature)

Volume = $1 \setminus \times {10}^{- 6} {\text{ m}}^{3}$

Boltzmann's constant = $1.3806 \setminus \times {10}^{- 23} \text{ J/K}$

No. of atoms = $128$

Absolute temperature = $7459 \text{ K}$

So

(Pressure)\times(1\times10^{-6}" m"^3) = (1.3806\times10^{-23}" J/K")\times(128)\times(7459" K")

Pressure = $1.318 \setminus \times {10}^{- 11} \text{ J/m"^3=1.318\times10^{-11}" Pa}$

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