how the volume of air in a tank of compressed air would change if the volume of the tank doubled?
To determine how the volume of air in a tank of compressed air would change if the volume of the tank doubled, we need to understand the principles of ideal gas behavior and the relationship between volume and pressure.
According to Boyle's Law, which describes the inverse relationship between volume and pressure at constant temperature, we can use the equation:
P₁V₁ = P₂V₂
Where:
P₁ = Initial pressure
V₁ = Initial volume
P₂ = Final pressure
V₂ = Final volume
In the given scenario, the initial and final pressures are assumed to be constant because the volume change occurs without any change in external factors or temperature. Therefore, we can rewrite the equation as:
V₁/P₁ = V₂/P₂
Since the pressure remains constant, we can simplify the equation further:
V₁ = V₂/P₂
Given that the volume of the tank doubled, the initial volume (V₁) is equal to half the final volume (V₂). Substituting this information into the equation:
V₁ = (1/2)V₂/P₂
From this equation, we can conclude that if the volume of the tank doubles, the volume of air in the tank (V₂) would be reduced to half of its original value.