A tank of compressed helium for inflating balloons is advertised as containing helium at a pressure of 2374 psi, which, when allowed to expand at atmospheric pressure, will occupy a volume of 194 ft3. Assuming no temperature change takes place during the expansion, what is the volume of the tank in cubic feet?

P V = n R T

so
P1 V1 = P2 V2

2374 V1 = 14.7 * 194

To find the volume of the tank in cubic feet, we need to calculate the initial volume of the compressed helium.

Given:
Pressure of compressed helium (P1) = 2374 psi
Volume of expanded helium (V2) = 194 ft^3
Pressure of expanded helium (P2) = atmospheric pressure (~14.7 psi)

First, let's convert the pressure units to the same unit:
P1 = 2374 psi
P2 = 14.7 psi

We can use Boyle's Law, which states that the product of the initial pressure and volume is equal to the product of the final pressure and volume, as long as the temperature remains constant:

P1 * V1 = P2 * V2

Now, we can substitute the given values:

2374 psi * V1 = 14.7 psi * 194 ft^3

To find V1 (the initial volume of the compressed helium), we divide both sides of the equation by 2374 psi:

V1 = (14.7 psi * 194 ft^3) / 2374 psi

Simplifying the equation:

V1 ≈ 1.2 ft^3

Therefore, the volume of the tank in cubic feet is approximately 1.2 ft^3.