Answer:
The final volume of the sample of gas is 36.287 liters.
Explanation:
Let suppose that sample of gas is a closed system, that is, a system with no mass interactions with surroundings, and gas is represented by the equation of state for ideal gases, which is described below:
[tex]P\cdot V = n\cdot R_{u}\cdot T[/tex] (1)
Where:
[tex]P[/tex] - Pressure, in atmospheres.
[tex]V[/tex] - Volume, in liters.
[tex]n[/tex] - Molar quantity, in moles.
[tex]T[/tex] - Temperature, in Kelvin.
[tex]R_{u}[/tex] - Ideal gas constant, in atmosphere-liters per mole-Kelvin.
As we know that sample of gas experiments an isobaric process, we can determine the final volume by the following relationship:
[tex]\frac{T_{1}}{V_{1}} = \frac{T_{2}}{V_{2}}[/tex] (2)
Where:
[tex]V_{1}[/tex] - Initial volume, in liters.
[tex]V_{2}[/tex] - Final volume, in liters.
[tex]T_{1}[/tex] - Initial temperature, in Kelvin.
[tex]T_{2}[/tex] - Final temperature, in Kelvin.
If we know that [tex]V_{1} = 33\,L[/tex], [tex]T_{1} = 291.15\,K[/tex] and [tex]T_{2} = 320.15\,K[/tex], then the final volume of the gas is:
[tex]V_{2} = V_{1}\cdot \left(\frac{T_{2}}{T_{1}} \right)[/tex]
[tex]V_{2} = 33\,L \times \frac{320.15\,K}{291.15\,K}[/tex]
[tex]V_{2} = 36.287\,L[/tex]
The final volume of the sample of gas is 36.287 liters.
