Question

A scuba diver takes a tank of air on a deep dive. The tank's volume is...

A scuba diver takes a tank of air on a deep dive. The tank's volume is 10 L and it is completely filled with air at an absolute pressure of 237 atm at the start of the dive. The air temperature at the surface is 85 ?F and the diver ends up in deep water at 60 ?F.

Assuming thermal equilibrium and neglecting air loss, determine the absolute internal pressure of the air when it is cold.

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Answer #1

The pressure P1 = 237 atm

The temperature T1 = 85 F or 29.44 deg = 302.44 K

and the temperature T2 = 60 F or 15.56 deg = 288.56 K

From Ideal gas equation

        P1 V1 / T1 = P2 V2/T2

then

P1/T1 = P2 /T2 (when it is in equilibrium)

Therefore the pressure

        P2 = (T2/T1) P1

             = (288.56/302.44) (237)

              = 226.12 atm

the absolute internal pressure of the air when it is cold is 226.12 atm

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