Question

A container with a volume of `25 L` contains a gas with a temperature of `150^o K`. If the temperature of the gas changes to `120 ^o K` without any change in pressure, what must the container's new volume be?

Answer 1

The new gas volume would have decreased to 20 L.

Explanation:

Apply Charles's law which states that the volume of an ideal gas is directly proportional to its absolute (Kelvin) temperature.

In equation form: V = k T

Your question requires that we write this in the form of a proportion

`V_1/T_1 = V_2/T_2`

(Note that these ratios are equal, because both would equal the constant, k.)

Now, we are ready:

`V_1` and `T_1` are the initial conditions - 25 L and 150 K.

`T_2` is the new (changed) temperature - 120 K

`25/150 = V_2/120`

Solving for `V_2`, we get `V_2` = `(25 xx 120) / 150` = 20 L

A reduction in temperature has resulted in a reduction in volume.