# 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?

Dec 18, 2016

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.)

${V}_{1}$ and ${T}_{1}$ are the initial conditions - 25 L and 150 K.
${T}_{2}$ is the new (changed) temperature - 120 K
$\frac{25}{150} = {V}_{2} / 120$
Solving for ${V}_{2}$, we get ${V}_{2}$ = $\frac{25 \times 120}{150}$ = 20 L