Final answer:
Using Boyle's Law, P₁V₁ = P₂V₂, with initial conditions of 500 m² pressure and 2 m² volume, we find the pressure to be 200 m² when the volume changes to 5 m².
Step-by-step explanation:
To solve for the new pressure when the volume changes from 2 m² to 5 m², we will use Boyle's Law, which states that for a given mass of gas at a constant temperature, the pressure and volume are inversely proportional. In mathematical terms, Boyle's Law is given by the equation P₁ × V₁ = P₂ × V₂, where P₁ is the initial pressure, V₁ is the initial volume, P₂ is the final pressure, and V₂ is the final volume.
Given that the initial pressure (P₁) is 500 m² and the initial volume (V₁) is 2 m², we rearrange the equation to solve for the final pressure (P₂) when the final volume (V₂) is 5 m²:
P₂ = (P₁ × V₁) / V₂P₂ = (500 m² × 2 m²) / 5 m²P₂ = 1000 m´ / 5 m²P₂ = 200 m²
Thus, the new pressure when the volume is 5 m² will be 200 m².