Final answer:
To determine the final temperature and pressure of the air, you can use the ideal gas law and equate the initial and final pressures.
Step-by-step explanation:
The final temperature of the air can be determined using the ideal gas law, which states that PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Since the piston is experiencing no change of state, the final volume of the air on both sides of the piston remains the same. Therefore, we can equate the initial and final pressures:
P1V1=P2V2
where P1 and P2 are the initial and final pressures, and V1 and V2 are the initial and final volumes, respectively. Plugging in the given values:
(3 bar)(1.0 m3)=(1.5 bar)(1.0 m3)
Simplifying this equation will give you the final pressure.