Question

A container with a volume of `6 L` contains a gas with a temperature of `650 K`. If the temperature of the gas changes to `350 K` without any change in pressure, what must the container's new volume be?

Answer 1

You can use Charles' Law for this:

`V_1(T_2) = V_2(T_1)`

Find your values:

`V_1` = `6` liters
`V_2` = `?`
`T_1` = `650` K
`T_2` = `350` K

and plug them in:

`6(350) = V_2(650)`

Multiply `6` and `350` to get `2100`, which gets you to

`2100 = V_2(650)`

Divide both sides by `650` to get `V_2` by itself:

`2100/650 = color(red)(3.2308)`

And that's your final answer. The container's new volume must be `3.2308` liters.

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Note that if the temperature were in Fahrenheit or Celsius you would have to convert to Rankine or Kelvin, respectively - as Charles' Law only works with an absolute temperature scale. However, since the given temperatures were in Kelvin, no such conversion is necessary.