Answer:
The new volume of the gas is 9.086 liters.
Explanation:
Let suppose that nitrogen has a behavior of ideal gas, the equation of state for ideal gases is:
[tex]P\cdot V = n \cdot R_{u}\cdot T[/tex] (1)
Where:
[tex]P[/tex] - Pressure, measured in atmospheres.
[tex]V[/tex] - Volumen, measured in liters.
[tex]n[/tex] - Molar amount, measured in moles.
[tex]T[/tex] - Temperature, measured in Kelvin.
[tex]R_{u}[/tex] - Ideal gas constant, measured in atmosphere-liters per mole-Kelvin.
If pressure and molar amount of the gas remain constant, then we construct the following relationship:
[tex]\frac{T_{1}}{V_{1}} = \frac{T_{2}}{V_{2}}[/tex] (2)
If we know that [tex]T_{1} = 290.15\,K[/tex], [tex]P_{1} = 8.5\,L[/tex] and [tex]T_{2} = 310.15\,K[/tex], then the new volume of the gas is:
[tex]V_{2} = \left(\frac{T_{2}}{T_{1}}\right)\cdot V_{1}[/tex]
[tex]V_{2} = \left(\frac{310.15\,K}{290.15\,K} \right)\cdot (8.5\,L)[/tex]
[tex]V_{2} = 9.086\,L[/tex]
The new volume of the gas is 9.086 liters.
