# A container with a volume of 15 L contains a gas with a temperature of 290^o K. If the temperature of the gas changes to 350 ^o K without any change in pressure, what must the container's new volume be?

$\approx 18.1 L$.

#### Explanation:

According to ideal gas law,

$P \cdot V = n \cdot R \cdot T$

Since,
$P , n , R$ are constant throughout the process,

$\frac{V}{T} = \frac{n \cdot R}{P} = c o n s \tan t$

Therefore,

$V \propto T$

${V}_{\text{initial"/T_"initial"=V_"final"/T_"final}}$

So,
${V}_{\text{final"=(V_"initial"*T_"final")/T_"initial}} = \frac{15 \cdot 350}{290} \approx 18.1 L$

The answer is $18.1 L$

May 15, 2016

${V}_{2} = 18.1 L$

#### Explanation:

$P = \text{constant}$
${V}_{1} = 15 L$
${T}_{1} = {290}^{o} K$

${T}_{2} = {350}^{o} K$
V_2=?

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

$\frac{15}{290} = {V}_{2} / 350$

${V}_{2} = \frac{15 \cdot 350}{290}$

${V}_{2} = 18.1 L$