# The gas inside of a container exerts 6 Pa of pressure and is at a temperature of 360 ^o K. If the pressure in the container changes to 42 Pa with no change in the container's volume, what is the new temperature of the gas?

Jun 14, 2017

$3000$ $\text{K}$

#### Explanation:

To solve this problem, we can use the pressure-temperature relationship of gases, illustrated by Charles's law:

$\frac{{P}_{1}}{{T}_{1}} = \frac{{P}_{2}}{{T}_{2}}$

Our known quantities are

• ${P}_{1} = 6$ $\text{Pa}$

• ${T}_{1} = 360$ $\text{K}$

• ${P}_{2} = 42$ $\text{Pa}$

Since we're trying to find the final temperature, let's rearrange this equation to solve for ${T}_{2}$:

${T}_{2} = \frac{{P}_{2} {T}_{1}}{{P}_{1}}$

Plugging in the known quantities, we have

T_2 = ((42cancel("Pa"))(360"K"))/(6cancel("Pa")) = color(red)(3000 color(red)("K"

rounded to color(blue)(1 significant figure, the lowest amount given in the problem.