Question

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?

Answer 1

`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"`.