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?

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

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.