# A container with a volume of 4 L contains a gas with a temperature of 720^o K. If the temperature of the gas changes to 420^o K without any change in pressure, what must the container's new volume be?

##### 1 Answer
Nov 15, 2016

$\text{The final volume of gas is 2.33 Liters.}$

#### Explanation:

${V}_{i} : \text{initial volume } {v}_{i} = 4 L$

${T}_{i} : \text{initial temperature } {T}_{i} = {720}^{o} K$

${T}_{f} : \text{final temperature } {T}_{f} = {420}^{o} K$

V_f:"final volume "V_f=?

${V}_{i} / {T}_{i} = {V}_{f} / {T}_{f}$

$\frac{4}{720} = {V}_{f} / 420$

${V}_{f} \cdot 720 = 4 \cdot 420$

${V}_{f} = \frac{4 \cdot 420}{720}$

${V}_{f} = \frac{1680}{720} = \frac{168}{72}$

${V}_{f} = 2.33 L$