# A container with a volume of 18 L contains a gas with a temperature of 220^o C. If the temperature of the gas changes to 320 ^o K without any change in pressure, what must the container's new volume be?

Oct 6, 2016

The new volume will be $\text{12 L}$ rounded to two significant figures.

#### Explanation:

This is an example of Charles' law, which states that the volume of a given amount of gas that is held at a constant pressure, is directly proportional to its temperature in Kelvins. This means that as the temperature increases, so does the volume and vice versa. The equation below represents Charles' law when volume or temperature changes.

The following are the known and unknown variables for this question.

Known
${V}_{1} = \text{18 L}$
${T}_{1} = \text{220"^@"C"+"273.15"="493 K}$
${T}_{2} = \text{320 K}$

Unknown
${V}_{2}$

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

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

V_2=(18"L"xx320cancel"K")/(493cancel"K")="12 L" rounded to two significant figures