The pressure of a given volume of gas is 50N/m², when volume is 200m³ the pressure is 30N/m²
Find the initial volume
Let's set up a proportion to solve for the initial volume.
The relationship between pressure and volume is described by Boyle's Law, which states that the pressure of a given amount of gas is inversely proportional to its volume when temperature is held constant.
Let V₁ be the initial volume and P₁ be the initial pressure.
We can set up the proportion as follows:
P₁/V₁ = P₂/V₂
where P₂ = 30 N/m² (pressure at volume 200 m³) and V₂ = 200 m³.
Substituting the given values into the equation, we have:
P₁/V₁ = 30 N/m² / 200 m³
Now, we can solve for V₁:
P₁/V₁ = 0.15 N/m²/m³ (simplifying the right side of the equation)
To isolate V₁, we can rearrange the equation as:
V₁ = P₁ / (0.15 N/m²/m³)
Since P₁ = 50 N/m², we can substitute the value into the equation:
V₁ = 50 N/m² / (0.15 N/m²/m³)
V₁ ≈ 333.33 m³
Therefore, the initial volume is approximately 333.33 m³.