Question

A container with a volume of `12 L` contains a gas with a temperature of `230^o C`. If the temperature of the gas changes to `420 ^o K` without any change in pressure, what must the container's new volume be?

Answer 1

I get approximately `10 \ "L"`.

Explanation:

We first convert `230^@"C"` into `"K"`, and we have:

`230^@"C"=(273.15+230) \ "K"` (since `"K"=""^@"C"+273.15`)

`=503.15 \ "K"`

If there is no change in pressure and the number of moles, we may use Charles's law, which states that

`VpropT`

or

`V_1/T_1=V_2/T_2`

We need to solve for the new volume, so we rearrange the equation in terms of `V_2`, and we get:

`V_2=V_1/T_1*T_2`

Plugging in the given values, we find that

`V_2=(12 \ "L")/(503.15color(red)cancelcolor(black)"K")*420color(red)cancelcolor(black)"K"`

`~~10 \ "L"` to the nearest whole number.