The volume of a gas is inversely proportional to the pressure. If a pressure of
30 pounds per square inch corresponds to a volume of 48 cubic feet, what pressure is needed to produce a volume of 60 cubic feet?
since PV = k, a constant, you want P such that
60P = 48*30
or, since the volume is multiplied by 5/4, the pressure is multiplied by 4/5
To find the pressure needed to produce a volume of 60 cubic feet, we can start by writing an equation using the inverse proportionality relationship between volume and pressure.
According to the given information, we have:
Volume 1 (V1) = 48 cubic feet
Pressure 1 (P1) = 30 pounds per square inch
We can express the relationship as:
V1 * P1 = V2 * P2
where V2 is the desired volume of 60 cubic feet, and P2 is the pressure we need to find.
Plugging in the given values, the equation becomes:
48 * 30 = 60 * P2
Simplifying, we have:
1440 = 60 * P2
To solve for P2, divide both sides of the equation by 60:
P2 = 1440 / 60 = 24 pounds per square inch
Therefore, a pressure of 24 pounds per square inch is needed to produce a volume of 60 cubic feet.