A large scuba tank (Figure 9.16 ) with a volume of 18 L is...

A large scuba tank (Figure 9.16 ) with a volume of 18 L is rated for a pressure of 220 bar. The tank is filled at $20^{\circ} \mathrm{C}$ and contains enough air to supply $1860 \mathrm{L}$ of air to a diver at a pressure of 2.37 atm (a depth of 45 feet). Was the tank filled to capacity at $20^{\circ} \mathrm{C}$ ?

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Key Concepts

Temperature Effects and Unit Conversion

In gas calculations, temperature must be measured in Kelvin to accurately apply the ideal gas law. Recognizing the impact of temperature helps ensure that comparisons made between conditions, such as the temperature at which the tank was filled and the conditions of use, remain valid.

Ideal Gas Law

The ideal gas law (pV = nRT) provides a fundamental relationship among pressure, volume, temperature, and the number of moles of a gas. It is essential in evaluating how much gas is contained in a tank under given conditions and in predicting how that gas will behave when the pressure or temperature changes.

Pressure Units and Conversions

Working with pressures in different units, such as bar versus atmospheres, is crucial. Converting between these units ensures accuracy in calculations when comparing the rated pressure in a tank to the operating or ambient pressures, which is a common requirement in diverse applications including scuba diving.

Boyle's Law

Boyle's Law, a principle derived from the ideal gas law under isothermal conditions, shows that the pressure of a gas is inversely proportional to its volume. This concept is valuable when assessing how the air in a high-pressure scuba tank expands to a larger volume at a lower ambient pressure during use.

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