# A container with a volume of "16 L" contains a gas with a temperature of "100 K". If the temperature of the gas changes to "480 K" without any change in pressure, what must the container's new volume be?

May 20, 2016

The volume after the increase in temperature will be 77 L.

#### Explanation:

This is an example of Charles' law which states that at constant pressure, the volume of a gas varies directly with the temperature in Kelvins. This means that when the volume increases, so does the temperature and vice versa. The equation to use is ${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$.

${V}_{1} = \text{16 L}$
${T}_{1} = \text{100 K}$
${T}_{2} = \text{480 K}$
${V}_{2} = \textcolor{red}{\text{unknown}}$

Solution
Rearrange the equation to isolate ${V}_{2}$. Substitute the given 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=(16"L" * 480cancel"K")/(100cancel"K")="77 L" (rounded to two significant figures)