# A container with a volume of 32 L contains a gas with a temperature of 240^o K. If the temperature of the gas changes to 160 ^o K without any change in pressure, what must the container's new volume be?

Feb 16, 2016

New volume is $21.33 L$.

#### Explanation:

If $P$ is pressure, $V$ is volume and $T$ is temperature (in Kelvin), $P \frac{V}{T}$ is constant. As pressure $P$ is constant, in above case $\frac{V}{T}$ will be constant i.e. $\left({V}_{1} / {T}_{1}\right) = \left({V}_{2} / {T}_{2}\right)$.

Applying this we have $\frac{32}{240} = {V}_{2} / 160$

Hence ${V}_{2} = \left(\frac{32}{240}\right) \cdot 160$ or #V_2=64/3) or

New volume is $21.33 L$.