Some helium at 20.0psi gauge pressure occupies 40.0ft^3. find its volume at 32.4 psi if the temperature remains constant.
use Boyle's Law,
p1V1=p2V2
To find the volume of helium at a different pressure while assuming constant temperature, you can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional at a constant temperature.
The equation can be written as: P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (20.0 psi)
V1 = Initial volume (40.0 ft^3)
P2 = Final pressure (32.4 psi) (what we want to find)
V2 = Final volume (what we want to find)
Let's now solve the equation for V2:
P1 * V1 = P2 * V2
Substituting the given values:
(20.0 psi) * (40.0 ft^3) = (32.4 psi) * V2
Now, solve for V2:
V2 = (20.0 psi * 40.0 ft^3) / 32.4 psi
V2 ≈ 24.69 ft^3
Therefore, the volume of helium at 32.4 psi gauge pressure, with the temperature remaining constant, is approximately 24.69 ft^3.