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?

1 Answer
Aug 14, 2017

V_2 = 21 "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:

ulbar(|stackrel(" ")(" "(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 "L"

  • T_1 = 150 "K"

  • V_2 = ?

  • T_2 = 75 "K"

Let's rearrange the equation to solve for the final volume*, V_2:

V_2 = (T_2V_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".