Charles’ and Gay-Lussac’s laws state that at a constant pressure, the volume of a
gas is directly proportional to the change in the absolute temperature. If the pressure
is kept constant and the absolute temperature is doubled, the volume will
double. If temperature decreases, volume decreases. If volume instead of pressure
is kept constant (i.e., heating gas in a rigid container), then the absolute pressure
will change in proportion to the absolute temperature.
The formula for expressing Charles’/Gay-Lussac’s law when the pressure is
constant is:
The formula for expressing Charles’/Gay-Lussac’s law when the volume is
constant is:
Sample Problem 1. The on-board gas supply of a PTC is charged on deck to 3,000
psig at an ambient temperature of 32°C. The capsule is deployed to a depth of 850
fsw where the water temperature is 7°C. Determine the pressure in the gas supply
at the new temperature. Note that in this example the volume is constant; only
pressure and temperature change.
The pressure in the gas supply at the new temperature is 2749 psig.
Sample Problem 2. A habitat is deployed to a depth of 627 fsw at which the water
temperature is 40°F. It is pressurized from the surface to bottom pressure, and
because of the heat of compression, the internal temperature rises to 110°F. The
entrance hatch is opened at depth and the divers begin their work routine. During
the next few hours, the habitat atmosphere cools down to the surrounding sea
water temperature because of a malfunction in the internal heating system.
Determine the percentage of the internal volume that would be flooded by sea
water assuming no additional gas was added to the habitat. Note that in this
example pressure is constant; only volume and temperature change.
Sample Problem 3. A 6-cubic-foot flask is charged to 3000 psig and the
temperature in the flask room is 72°F. A fire in an adjoining space causes the
temperature in the flask room to reach 170°F. What will happen to the pressure in
the flask?
The pressure in the flask increased from 3,000 psig to 3,570.03 psia. Note that
the pressure increased even though the flask’s volume and the volume of the
gas remained the same.
