The diver uses compressed air to breathe under water. 1700 litres of air from the atmosphere is compressed into a 12-litre gas cylinder. The compressed air quickly cools to its original temperature. Calculate the pressure of the air in the cylinder.

The answer is below

Explanation:

A diver works in the sea on a day when the atmospheric pressure is 101 kPa. The diver uses compressed air to breathe under water. 1700 litres of air from the atmosphere is compressed into a 12-litre gas cylinder. The compressed air quickly cools to its original temperature. Calculate the pressure of the air in the cylinder.

Solution:

Boyles law states that the volume of a given gas is inversely proportional to the pressure exerted by the gas, provided that the temperature is constant.

That is:

P ∝ 1/V;   PV = constant

P₁V₁ = P₂V₂

Given that P₁ = initial pressure = 101 kPa, V₁ = initial volume = 1700 L, P₂ = cylinder pressure, V₂ = cylinder volume = 12 L. Hence:

P₁V₁ = P₂V₂

100 kPa * 1700 L = P₂ * 12 L

P₂ = (100 kPa * 1700 L) / 12 L

P₂ = 14308 kPa

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