Question

A large scuba tank with a volume of 18 L is rated for a pressure of 220 bar. The tank is filled at 20 °C and contains enough air to supply 1860 L of air to a diver at a pressure of 2.37 atm (a depth of 45 feet). Was the tank filled to capacity at 20 °C?

Answer 1

To determine if the scuba tank was filled to capacity at 20 °C and a depth of 45 feet, we can use the combined gas law. By plugging in the given values and solving for the final pressure, we can compare it to the rated pressure of the tank to determine if it is filled to capacity.

Step-by-step explanation:

To determine if the scuba tank was filled to capacity at 20 °C, we can use the combined gas law. The combined gas law states that the product of the pressure and volume of a gas is directly proportional to the product of its temperature and the number of moles. We can set up the equation:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where P1 and V1 are the initial pressure and volume, T1 is the initial temperature, P2 and V2 are the final pressure and volume, and T2 is the final temperature. Since the tank is filled at 20 °C and the diver is at a depth of 45 feet, we can assume that the final temperature is also 20 °C. We know the initial volume of the tank is 18 L, and the final volume required for the diver is 1860 L. Plugging in the given values:

(220 bar * 18 L) / (20 °C + 273) = (2.37 atm * 1860 L) / (20 °C + 273)

Simplifying this equation, we can find the final pressure in bars. If the final pressure is equal to the rated pressure of the tank (220 bar), then the tank is filled to capacity at 20 °C.

Answer 2

Yes, at 20 °C the tank was filled to full capacity

Step-by-step explanation:

Given;

let initial pressure, P₁ = 2.37 atm

let initial volume, V₁ = 1860 L

let final pressure, P₂ = 220 bar = 217.123 atm

let final volume, V₂ = ?

Subject the air volume (1860 L ) at 2.37 atm to the tank rating (220 bar)

Ideal law is given by;

PV = nRT

At a fixed mole and gas temperature, the equation becomes;

P₁V₁ = P₂V₂

V₂ = (P₁V₁) / P₂

V₂ = (2.37 x 1860) / 217.123

V₂ = 20.3 L

After subjecting the air volume to tank rating, the volume of the air at 220 bar is 20.3 L which is greater than tank volume (18 L).

The extra 2.3 L can be assumed to be compressed gas volume due to the given (lower) temperature.

Thus, at 20 °C the tank was filled to full capacity.