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# Understanding Charles` Law in Physics IDC Dive Theory

Updated: Jul 1

Charles’ Law states that "the amount of change in either volume or pressure of a given gas volume is directly proportional to the change in the absolute temperature."

This means :

As the temperature increases, the volume of a flexible container will increase OR the pressure inside a non-flexible container will increase.

The opposite happens when the temperature decreases. As the temperature decreases, the volume of a flexible container will decrease OR the pressure inside a non-flexible container will decrease.

## Jacques Charles

Jacques Alexandre Cèsar Charles, Born November 12, 1746, Beaugency, Orléanais.

Died April 7, 1823 (aged 76) in Paris. He is known as a French inventor, scientist, mathematician and balloonist. He married a woman 37 years younger than him, Julie Françoise Bouchaud des Hérettes, who became the muse of French poet Alphonse de Lamartine who had fallen in love with her.

By studying Boyles Law, published 100 years earlier, Jacques Charles conceived the idea of using hydrogen as a suitable agent for lifting balloons. On August 27, 1783, he and the Roberts Brothers launched the worlds first hydrogen filled balloon on the site where the Eiffel Tower now stands, with Benjamin Franklin amongst the onlookers.

In 1787 he did the first experiments on pressure, volume and temperature. Even though this was later published by Joseph Louis Gay-Lussac in 1802, Gay-Lussac credited the work to the unpublished work of Charles.

## Charles` Law

Heat is the energy of molecular action. Therefore if you heat gases, the molecules move faster and impact the interior of a container with more force.

In a flexible container, this movement is absorbed by an increase in volume and the pressure is constant.

In a non-flexible container, this causes an increase in pressure and the volume is constant.

Cooling down means the molecules lose heat and slow down, reducing their impact and in turn reducing either pressure OR volume. ### Flexible Container For a flexible container, if you increase the temperature then the volume will increase but not the pressure (pressure is constant)

### Non-flexible Container For a nonflexible container, if you increase the temperature then the pressure will increase but not the volume (volume is constant). Also if you increase the pressure, the temperature will increase.

### Combined Law ## Applications BALLOON - If you leave a balloon outside in the sun, the volume will increase. SCUBA TANKS - If you leave a full tank outside in the sun, the pressure inside will increase showing more gas supply.

• If you take a full tank on a hot day but dive into very cold water, the pressure will decrease and, as a result, the gas supply.

• You can also increase temperature by filling tanks (adding gas to a fixed volume)

• You decrease temperature by releasing air from a tank (fixed volume). When you open a tank valve and let air out rapidly, the tank cools.

• This also explains why when ice diving, environmental seals are recommended in regulator first stages so that they do not freeze.

## Understanding Charles` Law

### Roughly

For every 1ºC change (up OR down) in temperature, there is a 0.6 bar change in pressure (0.6 bar per 1ºC or 5 psi per 1ºF), although this is a rule of thumb that is not precise but happens to work.

Example: A 12 litre tank is filled to 220 Bar at 28ºC. The tank is then used in 3ºC water, what is the pressure change inside the tank?

Volume does not change (inflexible)

28ºC - 3ºC = 25ºC change

25 × 0.6 bar = 15 Bar

220 Bar - 15 Bar = 205 Bar

### For precise calculations use the Combined Gas Law Combined Gas Law

P = Absolute Pressure

V = Volume

T = Absolute Temperature, such as Kelvin (+273ºC) or Rankin (+460ºF)

So lets use the same example as before (in metric again)

Example: A 12 litre tank is filled to 220 Bar at 28ºC. The tank is then used in 3ºC water, what is the pressure change inside the tank?

P1 = 220 bar + 1 bar (atmosphere) = 221 bar absolute

V1 = Cylinder volume does not change (V1=V2) so we can cancel them out from both sides of the equation

T1 = 28ºC + 273ºC= 301 kelvins (K)

T2 = 3ºC + 273ºC = 276 kelvins (K)

P2 = ??

so the formula now reads (Gay-Lussacs Law)

P1 = P2

T1 T2

P2 = P1T2

T1

P2 = 221 bar × 276K

301K

P2 = 202.6 bar absolute

202.6 bar absolute - 1 bar = 201.6 bar gauge

* So you can see that there is a difference between the "rule of thumb" and the Combined Gas Law with the Combined Gas Law being more precise.

Now lets take a more difficult example.

Example: Imagine that you are supplying air from the surface to a commercial diver at 65 meters. The compressor has a capacity of 1000 litres per minute. The temperature on the surface is 32ºC and the temperature of the water that the diver is in is 3ºC. How much air will the compressor be capable of supplying at that depth?

P1 1 bar absolute

V1 1000 litres

T1 305 K (32+273=305K)

P2 7.5 bar absolute (65÷10+1=7.5 ata)

T2 276 K (2+273=276K)

V2 unknown so the transposed equation would read as this

V2=P1V1T2

T1P2

Therefore

V2= 1 bar × 1000 litres × 276K

305K × 7.5 bar

= 276000

2287.5

=120.65 litres per min Test yourself with 12 questions based purely on Charles` Law

(1) The Encyclopedia of Recreational Diving (3rd ed.). (2008). PADI.

(2) Divemaster Course Instructor Guide (1999 edition). (2005). PADI

(3) Wikipedia contributors. (2021b, June 19). Jacques Charles. Wikipedia. https://en.wikipedia.org/wiki/Jacques_Charles

(4) Physics. (2019). NOAA Diving Manual - Physics of Diving. Published. https://www.ehs.ucsb.edu/files/docs/ds/physics.pdf

(5) An Explanation of Pressure and the Laws of Boyle, Charles, Dalton, and Henry. (1997). Scuba Diving Explained. http://www.lakesidepress.com/pulmonary/books/scuba/sectiond.htm