# A container with a volume of 12 L contains a gas with a temperature of 240^o C. If the temperature of the gas changes to 450 ^o K without any change in pressure, what must the container's new volume be?

Aug 13, 2016

$\text{The final volume is } 10.53 L$

#### Explanation:

$\text{The given data:}$
${V}_{i} : \text{Initial volume of gas ;} {V}_{i} = 12 L$
V_f:"Final volume of gas ;"V_f=?

${T}_{i} : \text{Initial temperature of gas ;} {T}_{i} = {240}^{o} C$
${T}_{i} = 240 + 273 = {513}^{o} K$

${T}_{f} : \text{Final temperature of gas ;} {T}_{f} = {450}^{o} K$

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

$\frac{12}{513} = {V}_{f} / 450$

${V}_{f} = \frac{12 \cdot 450}{513}$

${V}_{f} = \frac{5400}{450}$

${V}_{f} = 10.53 L \text{ rounded to two decimal place}$
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