# A container with a volume of 7 L contains a gas with a temperature of 120^o K. If the temperature of the gas changes to 360 ^o K without any change in pressure, what must the container's new volume be?

Jun 12, 2016

The new volume, ${V}_{2}$, is $\textcolor{b l u e}{\text{21 L}}$.

#### Explanation:

This is an example of Charles' law, which states that the volume of a given amount of a gas kept at constant pressure varies directly with the temperature in Kelvins. This means that if the volume increases, so will the temperature, and vice versa. The equation used to solve Boyle's law problems is ${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$.

Known
${V}_{1} = \text{7 L}$
${T}_{1} = \text{120 K}$
${T}_{2} = \text{360 K}$

Unknown
${V}_{2} = \text{?}$

Solution
Rearrange the equation to isolate ${V}_{2}$. Substitute the known values into the equation and solve.

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

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

${V}_{2} = \left(7 \text{L"*360cancel"K")/(120cancel"K}\right)$

${V}_{2} = \textcolor{b l u e}{\text{21 L}}$