Question

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?

Answer 1

`3000` `"K"`

Explanation:

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

`(P_1)/(T_1) = (P_2)/(T_2)`

Our known quantities are

• `P_1 = 6` `"Pa"`

• `T_1 = 360` `"K"`

• `P_2 = 42` `"Pa"`

Since we're trying to find the final temperature, let's rearrange this equation to solve for `T_2`:

`T_2 = (P_2T_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.