Final answer:
The gas is classified as polyatomic based on the value of y obtained in the adiabatic process equation.
Step-by-step explanation:
The gas can be classified as monatomic, diatomic, or polyatomic based on the number of atoms in its molecule. Monatomic gases consist of single atoms, diatomic gases consist of two atoms, and polyatomic gases consist of three or more atoms. To determine if the gas in question is monatomic, diatomic, or polyatomic, we need to know the degrees of freedom (y) of the gas molecules.
The relation between the pressure (P), volume (V), and number of moles (n) of an ideal gas is given by the ideal gas law: PV = nRT. For adiabatic processes, the relation between the pressure and volume is given by P1V1^y = P2V2^y, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the initial pressure (P1) is 0.50 atm and the initial volume (V1) is 10 L, while the final pressure (P2) is 3.0 atm and the final volume (V2) is 2.8 L. By rearranging the adiabatic equation, we can determine the value of y, which will help us classify the gas.
Using the given values:
P1V1^y = P2V2^y
(0.50 atm)(10 L)^y = (3.0 atm)(2.8 L)^y
By solving for y, we can determine the value of y, which will help us classify the gas.
By solving the equation, we find that the value of y is approximately 1.47. Since y is less than 1.5, the gas is considered polyatomic.