Answer:
The new volume of the balloon is 2.422 liters.
Explanation:
Let suppose that gas inside the balloon behaves ideally. From the Equation of State for Ideal Gases, we know that pressure ([tex]P[/tex]), in atmospheres, is inversely proportional to volume ([tex]V[/tex]), in liters, and directly proportional to temperature ([tex]T[/tex]), in Kelvin. Based on this fact, we construct the following relationship:
[tex]\frac{P_{1}\cdot V_{1}}{T_{1}} = \frac{P_{2}\cdot V_{2}}{T_{2}}[/tex] (1)
Where:
[tex]P_{1}, P_{2}[/tex] - Initial and final pressures, in atmospheres.
[tex]V_{1}, V_{2}[/tex] - Initial and final volumes, in liters.
[tex]T_{1}, T_{2}[/tex] - Initial and final temperatures, in Kelvin.
If we know that [tex]P_{1} = 1\,atm[/tex], [tex]V_{1} = 1.80\,L[/tex], [tex]T_{1} = 293.15\,K[/tex], [tex]P_{2} = 0.667\,atm[/tex], [tex]T_{2} = 263.15\,K[/tex], then the final pressure is:
[tex]V_{2} = V_{1} \cdot \left(\frac{P_{1}}{P_{2}} \right)\cdot \left(\frac{T_{2}}{T_{1}} \right)[/tex]
[tex]V_{2} = 2.422\,L[/tex]
The new volume of the balloon is 2.422 liters.
