Charles’s law in diving: why your full tank reads lower in the water
In short
Charles’s law says that at constant pressure, a gas’s volume is proportional to its absolute temperature; in a rigid scuba tank, pressure follows absolute temperature the same way. Always use kelvin (°C + 273) or Rankine (°F + 460). A tank filled hot to 220 bar at 50 °C reads about 200 bar at 20 °C, with no leak.
On a sunny deck, your tank reads full. Five minutes into the dive, the needle sits lower because the gas has cooled in the water. Leave the same tank in a hot car and the needle climbs.
What is Charles’s law?
Charles’s law states that at constant pressure, the volume of a fixed amount of gas is proportional to its absolute temperature. NASA’s Glenn Research Center calls it Charles and Gay-Lussac’s law: Charles did the original work and Gay-Lussac verified it. Warm a gas and it expands; cool it and it contracts.
For divers, the version that matters most is the rigid tank. Its volume can’t change, so its pressure rises and falls with absolute temperature instead. Many dive courses call both versions Charles’s law (see the FAQ on names below).
What does Charles’s law mean for a diver?
Charles’s law means your tank pressure depends on temperature, not only on how much air the tank holds.
- A hot fill cools down. Compressing gas heats it, so a tank filled warm reads lower once it cools. Fill stations fill slowly, sometimes with tanks in cool water, and top up after cooling.
- Into the water. A tank warmed on a sunny deck cools in the water, and its pressure drops a little.
- In the sun or a closed car. Heat raises the pressure. The burst disc on the valve vents the gas before the pressure becomes dangerous, but it empties the tank. Keep tanks shaded and out of closed cars.
- Air spaces. Cold water shrinks the air in your BCD, dry suit or lift bag by a few percent, a small extra on top of buoyancy changes with depth.
What is the Charles’s law formula?
The Charles’s law formula is V1 ÷ T1 = V2 ÷ T2 at constant pressure, and P1 ÷ T1 = P2 ÷ T2 in a rigid tank, so P2 = P1 × T2 ÷ T1. Combined with Boyle’s law, it gives the general gas law: P1 × V1 ÷ T1 = P2 × V2 ÷ T2.
Temperatures must be absolute. Kelvin = °C + 273 (NIST defines 0 °C as 273.15 K). Degrees Rankine = °F + 460 (HyperPhysics puts the Rankine zero at −459.67 °F). Ordinary degrees give absurd results. Going from 10 °C to 20 °C looks like doubling, but in kelvin it’s 283 to 293 K, so the pressure rises by about 3.5%. From 50 °F to 100 °F (510 to 560 °R), it rises by about 10%. At tank pressures, using the gauge reading instead of absolute pressure barely changes the answer.
Try a question from the app
general gas law
Which equation combines Boyle’s law with the temperature laws?
Show the answer
Answer B. For a given amount of gas, pressure times volume divided by absolute temperature stays constant. A is Boyle’s law alone; C puts temperature on the wrong side; D would mean volume rises with pressure.
Worked example
A hot fill cools down. Filled to 220 bar at 50 °C. What will it read at 20 °C?
- Metric: P2 = 220 × (20 + 273) ÷ (50 + 273) = 220 × 293 ÷ 323 ≈ 200 bar.
- Imperial: filled to 3,300 psi at 120 °F (580 °R), cooled to 70 °F (530 °R): 3,300 × 530 ÷ 580 ≈ 3,020 psi.
The gauge shows about 20 bar (280 psi) less, though no gas escaped.
Worked example
A tank in a hot car. 200 bar at 25 °C, in a car that heats up to 55 °C.
- Metric: P2 = 200 × 328 ÷ 298 ≈ 220 bar.
- Imperial: 3,000 psi at 75 °F (535 °R), heated to 135 °F (595 °R): 3,000 × 595 ÷ 535 ≈ 3,340 psi.
About 10% more. Plugging in ordinary degrees would give 440 bar (5,400 psi): always convert first.
Worked example
From the deck into cold water. 200 bar at 30 °C on deck, then 10 °C water.
- Metric: P2 = 200 × 283 ÷ 303 ≈ 187 bar.
- Imperial: 3,000 psi at 86 °F (546 °R), into 50 °F (510 °R) water: 3,000 × 510 ÷ 546 ≈ 2,800 psi.
Plan with the lower number: that’s the air you have at the water’s temperature, as in air consumption and SAC rate.
Try a question from the app
pressure drop after cooling
On the boat, a diver says his cylinder read 200 bar (3000 psi) in the sun but reads less after a few minutes in the water. What’s the most likely cause?
Show the answer
Answer B. In a rigid cylinder, pressure follows absolute temperature: cooler water, lower pressure. A leak would show bubbles and keep the pressure dropping, so check if in doubt. Water pressure doesn’t measurably compress a metal cylinder.
What are the common Charles’s law mistakes?
- Using °C or °F directly. Add 273 or 460 first.
- Calling a cooling drop a leak. A cooled tank settles at a lower reading. A leak shows bubbles and keeps dropping, so check if in doubt.
- Turning the ratio upside down. Cooling must lower the pressure. If your answer rises, flip T2 ÷ T1.
- Mixing scales. Kelvin goes with °C, Rankine with °F. More unit traps in metric vs imperial dive math.
- Leaving tanks in the sun. A burst disc that lets go empties your tank on the spot.
Which dive course covers Charles’s law?
In Octo, Charles’s law is part of the Divemaster physics module, with the general gas law. The practical side, a tank that reads lower once it cools and tanks kept out of the heat, matters from your first dives. Every gas law is gathered in the dive theory formulas guide, and the Divemaster practice questions let you check yourself.
Frequently asked questions
Why does my tank pressure drop when I get in the water?
Because the gas cools to the water’s temperature, and in a rigid tank, pressure follows absolute temperature. A tank at 200 bar and 30 °C reads about 187 bar in 10 °C water; 3,000 psi at 86 °F reads about 2,800 psi at 50 °F. The drop stops when the temperature settles. A leak keeps going and shows bubbles.
Is it Charles’s law or Gay-Lussac’s law?
Both names are used. Strictly, Charles’s law links volume and temperature at constant pressure, and the pressure–temperature version is often credited to Gay-Lussac, sometimes to Amontons. Many dive courses use Charles’s name for both, so read each exam question carefully.
Can I leave a full tank in the car?
Avoid it, above all in a closed car in the sun. Warming from 25 °C to 55 °C (75 °F to 135 °F) raises a tank’s pressure by about 10%. The burst disc on the valve vents the gas before the pressure becomes dangerous, but when it goes, the tank empties at once. Keep tanks shaded and out of closed cars.
Does the cold affect my regulator too?
Yes, through a related effect: gas cools sharply as it expands quickly, so a free-flowing regulator in very cold water can freeze. Environmentally sealed first stages are designed to resist freezing. A free-flowing regulator can still be breathed: hold the mouthpiece loosely, sip the air you need and end the dive with your buddy.
Sources
- NASA Glenn Research Center, Charles and Gay-Lussac’s Law (Beginner’s Guide to Aeronautics, updated May 2024)
- Georgia State University, HyperPhysics, Ideal Gas Law (absolute temperature, Charles’s law)
- Georgia State University, HyperPhysics, Temperature (kelvin and Rankine scales)
- NIST, SI Units: Temperature
