Final answer:
The question is about finding the final pressure of a diatomic ideal gas after adiabatic compression. The pressure, volume, and the specific heat ratio are used in the P1V1^y = P2V2^y equation to determine the final pressure, which can be calculated using the given initial conditions and the property that the process is adiabatic.
Step-by-step explanation:
The question concerns a diatomic ideal gas undergoing adiabatic compression, and we're asked to find the final pressure after this process. In an adiabatic process, no heat is exchanged with the surroundings, and the relationship between pressure (P), volume (V), and the specific heat ratio (γ, gamma) is given by PV^γ = constant.
For a diatomic ideal gas, we typically use γ = 7/5 or 1.4. Using the initial conditions of pressure P1 = 64 kPa and volume V1 = 2.3 m^3, and the final volume V2 = 1.3 m^3, we can set up the equation like this:
P1 * V1^γ = P2 * V2^γ
Solving for P2, we get:
P2 = P1 * (V1/V2)^γ
Plugging in the numbers and calculating the final pressure (P2) we find the final pressure of the gas after compression.