A container with a volume of 6 L contains a gas with a temperature of 650 K. If the temperature of the gas changes to 350 K without any change in pressure, what must the container's new volume be?

May 8, 2018

You can use Charles' Law for this:

${V}_{1} \left({T}_{2}\right) = {V}_{2} \left({T}_{1}\right)$

${V}_{1}$ = $6$ liters
${V}_{2}$ = ?
${T}_{1}$ = $650$ K
${T}_{2}$ = $350$ K

and plug them in:

$6 \left(350\right) = {V}_{2} \left(650\right)$

Multiply $6$ and $350$ to get $2100$, which gets you to

$2100 = {V}_{2} \left(650\right)$

Divide both sides by $650$ to get ${V}_{2}$ by itself:

$\frac{2100}{650} = \textcolor{red}{3.2308}$

And that's your final answer. The container's new volume must be $3.2308$ liters.

Note that if the temperature were in Fahrenheit or Celsius you would have to convert to Rankine or Kelvin, respectively - as Charles' Law only works with an absolute temperature scale. However, since the given temperatures were in Kelvin, no such conversion is necessary.