Question

Hank's Garage has an air compressor with a holding tank that contains 200L of compressed air at 5200 torr. One day a hose ruptured and all the compressed air was released. What volume of air was released? (Disregard any air that might have remained in the tank after the pressure reached atmospheric pressure).

Answer 1

Hank's Garage has an air compressor with a holding tank that contains 200L of compressed air at 5200 torr. One day a hose ruptured and all the compressed air was released to a volume of 1370 L at atmospheric pressure.

Hank's Garage has an air compressor with a holding tank that contains a volume of 200L (V₁) of compressed air at a pressure of 5200 torr (P₁).

One day a hose ruptured and all the compressed air was released. The final pressure was the atmospheric pressure (1 atm = 760 torr) (P₂).

We can calculate the new volume (V₂) in these conditions using Boyle's law, which states there is an inverse relationship between the volume and the pressure of an ideal gas.

$P_1 \times V_1 = P_2 \times V_2\\\\V_2 = \frac{P_1 \times V_1}{P_2} = \frac{5200 torr \times 200L}{760torr} = 1370 L$

Hank's Garage has an air compressor with a holding tank that contains 200L of compressed air at 5200 torr. One day a hose ruptured and all the compressed air was released to a volume of 1370 L at atmospheric pressure.

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