Dive Physics: Part 3 (Gay-Lussac's law)

This one sometimes stumps divemasters and instructors in the recreational sector. That the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant.

How many times have you heard instructors or divemasters say "don't store cylinders in your car or they'll explode". It probably compares to "chewing gum stays in your stomach for 7 years" it simply isn't true.

The misunderstanding comes from lazy instructors teaching that "if the temperature doubles, the pressure doubles". This is true, but the safety advice given by some people to "not store tanks in your car or they'll rupture" is nonsense for 2 reasons;

  1. Tanks are Hydrostatic checked at five thirds their working pressure (5/3). So a 232 bar cylinder would be brought to at least 386.67 Bar for a hydro check. Cylinders are capable of handling far more pressure than we put them under, simply for safety reasons.

  2. The formula for Gay-Lussac's law is Pressure (P) over Temperature (T) = Constant (k). Temperature is not measured in Celsius or Fahrenheit, it is measured in Kelvin.

Kelvin is not comparable to Celsius. For instance, a Tweed Heads dive shop probably has an average internal temperature of 25 Celsius. So all cylinders in there at 230 bar would be a gas at 25 Celsius.

After more than an hour in the sun on a 25 degree day, a standard car could easily reach a temperature of 50 Celsius. If I had a cylinder charged to 230 bar in the car, what would the new pressure be? Not 460 bar, it would be 249.29 bar. If we accept the Hydrostatic testing pressure (386 bar) to be the maximum, then we are still well within range.

For a cylinder to reach double the pressure being left in your car on a 25 degree day, the internal temperature of the car would need to be at least 323.15 Celsius.

P/T = k is the correct way to interpret Gay-Lussac's law, just remember that T refers to Kelvin and NO other unit of measurement.

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