# The gas inside of a container exerts 9 Pa of pressure and is at a temperature of 250 ^o K. If the pressure in the container changes to 5 Pa with no change in the container's volume, what is the new temperature of the gas?

May 9, 2018

Approximately $138.9$ kelvin.

#### Explanation:

For constant volume and number of moles, we can use Gay-Lussac's law, which states that,

$P \propto T$ or ${P}_{1} / {P}_{2} = {T}_{1} / {T}_{2}$.

So here, we get:

$\frac{9 \setminus \text{Pa")/(250 \ "K")=(5 \ "Pa}}{T} _ 2$

T_2=(250 \ "K")/(9color(red)cancelcolor(black)"Pa")*5color(red)cancelcolor(black)"Pa"

$\approx 138.9 \setminus \text{K}$