Question

A diverâs backup oxygen tank reads 900 mm Hg while on her boat, where the temperature is 27 degrees C. When she dives down to the bottom of an unexplored methane lake on a recently discovered moon of Neptune, the temperature will drop to -183 degrees C. What will the pressure in her backup tank be at that temperature?

Answer 1

Taking into account the Gay Lussac's law, the pressure in the backup tank at -183 °C is 270 mmHg.

Gay Lussac's law

Gay Lussac's law establishes the relationship between the temperature and pressure of a gas when the volume is constant.

This law says that the pressure of the gas is directly proportional to its temperature: when there is a constant volume, as the temperature increases, the pressure of the gas increases. And when the temperature is decreased, gas pressure decreases.

Mathematically, Gay-Lussac's law states that the ratio between pressure and temperature has the same value:

$\frac{P}{T} =k$

Studying an initial state 1 and a final state 2, it is fulfilled:

$\frac{P1}{T1} =\frac{P2}{T2}$

Pressure in the backup tank

In this case, you know:

• P1= 900 mmHg
• T1= 27 C= 300 K (being 0C= 273 K)
• P2= ?
• T2= -183 C= 90 K

Replacing in the Gay-Lussac's law:

$\frac{900 mH}{300 K} =\frac{P2}{90 K}$

Solving:

$P2=90K\frac{900 mH}{300 K}$

P2=270 mmHg

Finally, the pressure in the backup tank at -183 °C is 270 mmHg.

Learn more about the Gay-Lussac's law:

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