A container with a volume of 42 L contains a gas with a temperature of 150^o K. If the temperature of the gas changes to 75 ^o K without any change in pressure, what must the container's new volume be?

Aug 14, 2017

${V}_{2} = 21$ $\text{L}$

Explanation:

We're asked to find the final volume of a gas, given information about the temperature and volume.

To do this, we can use the temperature-volume relationship of gases, illustrated by Charles's law:

$\underline{\overline{| \stackrel{\text{ ")(" "(T_1)/(V_1) = (T_2)/(V_2)" }}{|}}}$

where

• ${T}_{1}$ and ${T}_{2}$ are the initial and final absolute temperatures of the gas system (which must be in units of Kelvin)

• ${V}_{1}$ and ${V}_{2}$ are the initial and final volumes of the gas

We know:

• ${V}_{1} = 42$ $\text{L}$

• ${T}_{1} = 150$ $\text{K}$

• V_2 = ?

• ${T}_{2} = 75$ $\text{K}$

Let's rearrange the equation to solve for the final volume*, ${V}_{2}$:

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

Plugging in known values:

V_2 = ((75cancel("K"))(42color(white)(l)"L"))/(150cancel("K")) = color(red)(ulbar(|stackrel(" ")(" "21color(white)(l)"L"" ")|)

The final volume of the gas container is thus color(red)(21color(white)(l)"liters".