Final answer:
We find that the minimum pressure required to compress the air is 2.5 bar. The minimum pressure required can be found using Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is kept constant.
Step-by-step explanation:
To find the minimum pressure required to compress the air, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is kept constant.
The initial pressure and volume are given as 1 bar and 500 dm³, respectively, and the final volume is given as 200 dm³. So, we can set up the equation:
Pi * Vi = Pf * Vf
Solving for Pf, we get:
Pf = (Pi * Vi) / Vf
Substituting the given values, we have:
Pf = (1 bar * 500 dm³) / 200 dm³ = 2.5 bar
Therefore, the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ while keeping the temperature constant is 2.5 bar.